Gravitational attraction until relativistic equipartition of internal and translational kinetic energies

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. E.

2018-02-01

Translational ordering of the internal kinematic chaos provides the Special Relativity referents for the geodesic motion of warm thermodynamical bodies. Taking identical mathematics, relativistic physics of the low speed transport of time-varying heat-energies differs from Newton's physics of steady masses without internal degrees of freedom. General Relativity predicts geodesic changes of the internal heat-energy variable under the free gravitational fall and the geodesic turn in the radial field center. Internal heat variations enable cyclic dynamics of decelerated falls and accelerated takeoffs of inertial matter and its structural self-organization. The coordinate speed of the ordered spatial motion takes maximum under the equipartition of relativistic internal and translational kinetic energies. Observable predictions are discussed for verification/falsification of the principle of equipartition as a new basic for the ordered motion and self-organization in external fields, including gravitational, electromagnetic, and thermal ones.

Nonholonomic relativistic diffusion and exact solutions for stochastic Einstein spaces

NASA Astrophysics Data System (ADS)

Vacaru, S. I.

2012-03-01

We develop an approach to the theory of nonholonomic relativistic stochastic processes in curved spaces. The Itô and Stratonovich calculus are formulated for spaces with conventional horizontal (holonomic) and vertical (nonholonomic) splitting defined by nonlinear connection structures. Geometric models of the relativistic diffusion theory are elaborated for nonholonomic (pseudo) Riemannian manifolds and phase velocity spaces. Applying the anholonomic deformation method, the field equations in Einstein's gravity and various modifications are formally integrated in general forms, with generic off-diagonal metrics depending on some classes of generating and integration functions. Choosing random generating functions we can construct various classes of stochastic Einstein manifolds. We show how stochastic gravitational interactions with mixed holonomic/nonholonomic and random variables can be modelled in explicit form and study their main geometric and stochastic properties. Finally, the conditions when non-random classical gravitational processes transform into stochastic ones and inversely are analyzed.

Models for Accretion-Disk Fluctuations through Self-Organized Criticality Including Relativistic Effects

NASA Astrophysics Data System (ADS)

Xiong, Ying; Wiita, Paul J.; Bao, Gang

2000-12-01

The possibility that some of the observed X-ray and optical variability in active galactic nuclei and galactic black hole candidates are produced in accretion disks through the development of a self-organized critical state is reconsidered. New simulations, including more complete calculations of relativistic effects, do show that this model can produce light-curves and power-spectra for the variability which agree with the range observed in optical and X-ray studies of AGN and X-ray binaries. However, the universality of complete self-organized criticality has not quite been achieved. This is mainly because the character of the variations depend quite substantially on the extent of the unstable disk region. If it extends close to the innermost stable orbit, a physical scale is introduced and the scale-free character of self-organized criticality is vitiated. A significant dependence of the power spectrum density slope on the type of diffusion within the disk and a weaker dependence on the amount of differential rotation are noted. When general-relativistic effects are incorporated in the models, additional substantial differences are produced if the disk is viewed from directions far from the accretion disk axis.

Time-dependent inhomogeneous jet models for BL Lac objects

NASA Technical Reports Server (NTRS)

Marlowe, A. T.; Urry, C. M.; George, I. M.

1992-01-01

Relativistic beaming can explain many of the observed properties of BL Lac objects (e.g., rapid variability, high polarization, etc.). In particular, the broadband radio through X-ray spectra are well modeled by synchrotron-self Compton emission from an inhomogeneous relativistic jet. We have done a uniform analysis on several BL Lac objects using a simple but plausible inhomogeneous jet model. For all objects, we found that the assumed power-law distribution of the magnetic field and the electron density can be adjusted to match the observed BL Lac spectrum. While such models are typically unconstrained, consideration of spectral variability strongly restricts the allowed parameters, although to date the sampling has generally been too sparse to constrain the current models effectively. We investigate the time evolution of the inhomogeneous jet model for a simple perturbation propagating along the jet. The implications of this time evolution model and its relevance to observed data are discussed.

Time-dependent inhomogeneous jet models for BL Lac objects

NASA Astrophysics Data System (ADS)

Marlowe, A. T.; Urry, C. M.; George, I. M.

1992-05-01

Relativistic beaming can explain many of the observed properties of BL Lac objects (e.g., rapid variability, high polarization, etc.). In particular, the broadband radio through X-ray spectra are well modeled by synchrotron-self Compton emission from an inhomogeneous relativistic jet. We have done a uniform analysis on several BL Lac objects using a simple but plausible inhomogeneous jet model. For all objects, we found that the assumed power-law distribution of the magnetic field and the electron density can be adjusted to match the observed BL Lac spectrum. While such models are typically unconstrained, consideration of spectral variability strongly restricts the allowed parameters, although to date the sampling has generally been too sparse to constrain the current models effectively. We investigate the time evolution of the inhomogeneous jet model for a simple perturbation propagating along the jet. The implications of this time evolution model and its relevance to observed data are discussed.

PADÉ APPROXIMANTS FOR THE EQUATION OF STATE FOR RELATIVISTIC HYDRODYNAMICS BY KINETIC THEORY

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsai, Shang-Hsi; Yang, Jaw-Yen, E-mail: shanghsi@gmail.com

2015-07-20

A two-point Padé approximant (TPPA) algorithm is developed for the equation of state (EOS) for relativistic hydrodynamic systems, which are described by the classical Maxwell–Boltzmann statistics and the semiclassical Fermi–Dirac statistics with complete degeneracy. The underlying rational function is determined by the ratios of the macroscopic state variables with various orders of accuracy taken at the extreme relativistic limits. The nonunique TPPAs are validated by Taub's inequality for the consistency of the kinetic theory and the special theory of relativity. The proposed TPPA is utilized in deriving the EOS of the dilute gas and in calculating the specific heat capacity,more » the adiabatic index function, and the isentropic sound speed of the ideal gas. Some general guidelines are provided for the application of an arbitrary accuracy requirement. The superiority of the proposed TPPA is manifested in manipulating the constituent polynomials of the approximants, which avoids the arithmetic complexity of struggling with the modified Bessel functions and the hyperbolic trigonometric functions arising from the relativistic kinetic theory.« less

General Relativistic Radiative Transfer and General Relativistic MHD Simulations of Accretion and Outflows of Black Holes

NASA Technical Reports Server (NTRS)

Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Wu, Kinwah

2007-01-01

We have calculated the emission from relativistic flows in black hole systems using a fully general relativistic radiative transfer, with flow structures obtained by general relativistic magnetohydrodynamic simulations. We consider thermal free-free emission and thermal synchrotron emission. Bright filament-like features are found protruding (visually) from the accretion disk surface, which are enhancements of synchrotron emission when the magnetic field is roughly aligned with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We propose that variations and location drifts of the features are responsible for certain X-ray quasi-periodic oscillations (QPOs) observed in black-hole X-ray binaries.

General Relativistic Radiative Transfer and GeneralRelativistic MHD Simulations of Accretion and Outflows of Black Holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fuerst, Steven V.; /KIPAC, Menlo Park; Mizuno, Yosuke

2007-01-05

We calculate the emission from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by general relativistic magneto-hydrodynamic simulations. We consider thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We propose that variations and drifts of the features produce certain X-ray quasi-periodic oscillations (QPOs) observedmore » in black-hole X-ray binaries.« less

Relativistic corrections to a generalized sum rule

NASA Astrophysics Data System (ADS)

Sinky, H.; Leung, P. T.

2006-09-01

Relativistic corrections to a previously established generalized sum rule are obtained using the Foldy-Wouthysen transformation. This sum rule derived previously by Wang [Phys. Rev. A 60, 262 (1999)] for a nonrelativistic system contains both the well-known Thomas-Reiche-Kuhn and Bethe sum rules, for which relativistic corrections have been obtained in the literature. Our results for the generalized formula will be applied to recover several results obtained previously in the literature, as well as to another sum rule whose relativistic corrections will be obtained.

Turning Point Instabilities for Relativistic Stars and Black Holes

NASA Astrophysics Data System (ADS)

Schiffrin, Joshua; Wald, Robert

2014-03-01

In the light of recent results relating dynamic and thermodynamic stability of relativistic stars and black holes, we re-examine the relationship between ``turning points''--i.e., extrema of thermodynamic variables along a one-parameter family of solutions--and instabilities. We give a proof of Sorkin's general result--showing the existence of a thermodynamic instability on one side of a turning point--that does not rely on heuristic arguments involving infinite dimensional manifold structure. We use the turning point results to prove the existence of a dynamic instability of black rings in 5 spacetime dimensions in the region where cJ > 0 , in agreement with a result of Figueras, Murata, and Reall.

The relativistic equations of stellar structure and evolution

NASA Technical Reports Server (NTRS)

Thorne, K. S.

1975-01-01

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. A general relativistic version of the mixing-length formalism for convection is presented. It is argued that in work on spherical systems, general relativity theorists have identified the wrong quantity as total mass-energy inside radius r.

The absence of gravitational waves and the foundations of Relativistic Cosmology

NASA Astrophysics Data System (ADS)

Djidjian, Robert

2015-07-01

Modern relativistic cosmology is based on Albert Einstein's teaching of general relativity. Observational and experimental impressive verification of general relativity have created among the astrophysicists the conviction that general relativity and relativistic cosmology are absolutely true theories. Unfortunately, the most important conclusion of general relativity is that the necessary existence of gravitational waves has been rejected by all the experiments up to the present time. There is also a kind of direct objection to the conception of expanding Universe: with the expansion of space identically expands the measuring stick, which makes the distances between the galaxies unchanged. So it should be quite reasonable to open discussions regarding the status of both general relativity and relativistic cosmology.

EXACT RELATIVISTIC NEWTONIAN REPRESENTATION OF GRAVITATIONAL STATIC SPACETIME GEOMETRIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava, E-mail: sghosh@jcbose.ac.in, E-mail: ta.sa.nbu@hotmail.com, E-mail: aru_bhadra@yahoo.com

2016-09-01

We construct a self-consistent relativistic Newtonian analogue corresponding to gravitational static spherical symmetric spacetime geometries, starting directly from a generalized scalar relativistic gravitational action in a Newtonian framework, which gives geodesic equations of motion identical to those of the parent metric. Consequently, the derived velocity-dependent relativistic scalar potential, which is a relativistic generalization of the Newtonian gravitational potential, exactly reproduces the relativistic gravitational features corresponding to any static spherical symmetric spacetime geometry in its entirety, including all the experimentally tested gravitational effects in the weak field up to the present. This relativistic analogous potential is expected to be quite usefulmore » in studying a wide range of astrophysical phenomena, especially in strong field gravity.« less

Aspects of hot Galilean field theory

NASA Astrophysics Data System (ADS)

Jensen, Kristan

2015-04-01

We reconsider general aspects of Galilean-invariant thermal field theory. Using the proposal of our companion paper, we recast non-relativistic hydrodynamics in a manifestly covariant way and couple it to a background spacetime. We examine the concomitant consequences for the thermal partition functions of Galilean theories on a time-independent, but weakly curved background. We work out both the hydrodynamics and partition functions in detail for the example of parity-violating normal fluids in two dimensions to first order in the gradient expansion, finding results that differ from those previously reported in the literature. As for relativistic field theories, the equality-type constraints imposed by the existence of an entropy current appear to be in one-to-one correspondence with those arising from the existence of a hydrostatic partition function. Along the way, we obtain a number of useful results about non-relativistic hydrodynamics, including a manifestly boost-invariant presentation thereof, simplified Ward identities, the systematics of redefinitions of the fluid variables, and the positivity of entropy production.

The Riemann problem for the relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation

NASA Astrophysics Data System (ADS)

Shao, Zhiqiang

2018-04-01

The relativistic full Euler system with generalized Chaplygin proper energy density-pressure relation is studied. The Riemann problem is solved constructively. The delta shock wave arises in the Riemann solutions, provided that the initial data satisfy some certain conditions, although the system is strictly hyperbolic and the first and third characteristic fields are genuinely nonlinear, while the second one is linearly degenerate. There are five kinds of Riemann solutions, in which four only consist of a shock wave and a centered rarefaction wave or two shock waves or two centered rarefaction waves, and a contact discontinuity between the constant states (precisely speaking, the solutions consist in general of three waves), and the other involves delta shocks on which both the rest mass density and the proper energy density simultaneously contain the Dirac delta function. It is quite different from the previous ones on which only one state variable contains the Dirac delta function. The formation mechanism, generalized Rankine-Hugoniot relation and entropy condition are clarified for this type of delta shock wave. Under the generalized Rankine-Hugoniot relation and entropy condition, we establish the existence and uniqueness of solutions involving delta shocks for the Riemann problem.

Turning point instabilities for relativistic stars and black holes

NASA Astrophysics Data System (ADS)

Schiffrin, Joshua S.; Wald, Robert M.

2014-02-01

In the light of recent results relating dynamic and thermodynamic stability of relativistic stars and black holes, we re-examine the relationship between ‘turning points’—i.e., extrema of thermodynamic variables along a 1-parameter family of solutions—and instabilities. We give a proof of Sorkin’s general result—showing the existence of a thermodynamic instability on one side of a turning point—that does not rely on heuristic arguments involving infinite-dimensional manifold structure. We use the turning point results to prove the existence of a dynamic instability of black rings in five spacetime dimensions in the region where cJ > 0, in agreement with a result of Figueras, Murata and Reall. Communicated by H Reall

The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models

NASA Technical Reports Server (NTRS)

Thorne, K. S.; Zytkow, A. N.

1976-01-01

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."

BCS and generalized BCS superconductivity in relativistic quantum field theory. II. Numerical calculations

NASA Astrophysics Data System (ADS)

Ohsaku, Tadafumi

2002-08-01

We solve numerically various types of the gap equations developed in the relativistic BCS and generalized BCS framework, presented in part I of this paper. We apply the method for not only the usual solid metal but also other physical systems by using homogeneous fermion gas approximation. We examine the relativistic effects on the thermal properties and the Meissner effect of the BCS and generalized BCS superconductivity of various cases.

On the dispersion characteristics of extraordinary mode in a relativistic fully degenerate electron plasma

NASA Astrophysics Data System (ADS)

Noureen, S.; Abbas, G.; Sarfraz, M.

2018-01-01

The study of relativistic degenerate plasmas is important in many astrophysical and laboratory environments. Using linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. Employing Fermi-Dirac distribution at zero temperature, the dispersion relation of the extraordinary mode in a relativistic degenerate electron plasma is investigated. The propagation characteristics are examined in different relativistic density ranges. The shifting of cutoff points due to relativistic effects is observed analytically and graphically. Non-relativistic and ultra-relativistic limiting cases are also presented.

Relativistic stars in vector-tensor theories

NASA Astrophysics Data System (ADS)

Kase, Ryotaro; Minamitsuji, Masato; Tsujikawa, Shinji

2018-04-01

We study relativistic star solutions in second-order generalized Proca theories characterized by a U (1 )-breaking vector field with derivative couplings. In the models with cubic and quartic derivative coupling, the mass and radius of stars become larger than those in general relativity for negative derivative coupling constants. This phenomenon is mostly attributed to the increase of star radius induced by a slower decrease of the matter pressure compared to general relativity. There is a tendency that the relativistic star with a smaller mass is not gravitationally bound for a low central density and hence is dynamically unstable, but that with a larger mass is gravitationally bound. On the other hand, we show that the intrinsic vector-mode couplings give rise to general relativistic solutions with a trivial field profile, so the mass and radius are not modified from those in general relativity.

Radiatively driven relativistic jets in Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Vyas, Mukesh K.; Chattopadhyay, Indranil

2018-06-01

Context. Aims: We carry out a general relativistic study of radiatively driven conical fluid jets around non-rotating black holes and investigate the effects and significance of radiative acceleration, as well as radiation drag. Methods: We apply relativistic equations of motion in curved space-time around a Schwarzschild black hole for axis-symmetric one-dimensional jet in steady state, plying through the radiation field of the accretion disc. Radiative moments are computed using information of curved space-time. Slopes of physical variables at the sonic points are found using L'Hôpital's rule and employing Runge-Kutta's fourth order method to solve equations of motion. The analysis is carried out using the relativistic equation of state of the jet fluid. Results: The terminal speed of the jet depends on how much thermal energy is converted into jet momentum and how much radiation momentum is deposited onto the jet. Many classes of jet solutions with single sonic points, multiple sonic points, as well as those having radiation driven internal shocks are obtained. Variation of all flow variables along the jet-axis has been studied. Highly energetic electron-proton jets can be accelerated by intense radiation to terminal Lorentz factors γT 3. Moderate terminal speed vT 0.5 is obtained for moderately luminous discs. Lepton dominated jets may achieve γT 10. Conclusions: Thermal driving of the jet itself and radiation driving by accretion disc photons produce a wide-ranging jet solutions starting from moderately strong jets to the relativistic ones. Interplay of intensity, the nature of the radiation field, and the energetics of the jet result in a variety of jet solutions. We show that radiation field is able to induce steady shocks in jets, one of the criteria to explain high-energy power-law emission observed in spectra of some of the astrophysical objects.

Numerical 3+1 General Relativistic Magnetohydrodynamics: A Local Characteristic Approach

NASA Astrophysics Data System (ADS)

Antón, Luis; Zanotti, Olindo; Miralles, Juan A.; Martí, José M.; Ibáñez, José M.; Font, José A.; Pons, José A.

2006-01-01

We present a general procedure to solve numerically the general relativistic magnetohydrodynamics (GRMHD) equations within the framework of the 3+1 formalism. The work reported here extends our previous investigation in general relativistic hydrodynamics (Banyuls et al. 1997) where magnetic fields were not considered. The GRMHD equations are written in conservative form to exploit their hyperbolic character in the solution procedure. All theoretical ingredients necessary to build up high-resolution shock-capturing schemes based on the solution of local Riemann problems (i.e., Godunov-type schemes) are described. In particular, we use a renormalized set of regular eigenvectors of the flux Jacobians of the relativistic MHD equations. In addition, the paper describes a procedure based on the equivalence principle of general relativity that allows the use of Riemann solvers designed for special relativistic MHD in GRMHD. Our formulation and numerical methodology are assessed by performing various test simulations recently considered by different authors. These include magnetized shock tubes, spherical accretion onto a Schwarzschild black hole, equatorial accretion onto a Kerr black hole, and magnetized thick disks accreting onto a black hole and subject to the magnetorotational instability.

Time Domain Filtering of Resolved Images of Sgr A{sup ∗}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shiokawa, Hotaka; Doeleman, Sheperd S.; Gammie, Charles F.

The goal of the Event Horizon Telescope (EHT) is to provide spatially resolved images of Sgr A*, the source associated with the Galactic Center black hole. Because Sgr A* varies on timescales that are short compared to an EHT observing campaign, it is interesting to ask whether variability contains information about the structure and dynamics of the accretion flow. In this paper, we introduce “time-domain filtering,” a technique to filter time fluctuating images with specific temporal frequency ranges and to demonstrate the power and usage of the technique by applying it to mock millimeter wavelength images of Sgr A*. Themore » mock image data is generated from the General Relativistic Magnetohydrodynamic (GRMHD) simulation and the general relativistic ray-tracing method. We show that the variability on each line of sight is tightly correlated with a typical radius of emission. This is because disk emissivity fluctuates on a timescale of the order of the local orbital period. Time-domain filtered images therefore reflect the model dependent emission radius distribution, which is not accessible in time-averaged images. We show that, in principle, filtered data have the power to distinguish between models with different black-hole spins, different disk viewing angles, and different disk orientations in the sky.« less

Time Domain Filtering of Resolved Images of Sgr A∗

NASA Astrophysics Data System (ADS)

Shiokawa, Hotaka; Gammie, Charles F.; Doeleman, Sheperd S.

2017-09-01

The goal of the Event Horizon Telescope (EHT) is to provide spatially resolved images of Sgr A*, the source associated with the Galactic Center black hole. Because Sgr A* varies on timescales that are short compared to an EHT observing campaign, it is interesting to ask whether variability contains information about the structure and dynamics of the accretion flow. In this paper, we introduce “time-domain filtering,” a technique to filter time fluctuating images with specific temporal frequency ranges and to demonstrate the power and usage of the technique by applying it to mock millimeter wavelength images of Sgr A*. The mock image data is generated from the General Relativistic Magnetohydrodynamic (GRMHD) simulation and the general relativistic ray-tracing method. We show that the variability on each line of sight is tightly correlated with a typical radius of emission. This is because disk emissivity fluctuates on a timescale of the order of the local orbital period. Time-domain filtered images therefore reflect the model dependent emission radius distribution, which is not accessible in time-averaged images. We show that, in principle, filtered data have the power to distinguish between models with different black-hole spins, different disk viewing angles, and different disk orientations in the sky.

Lagrangian formulation of the general relativistic Poynting-Robertson effect

NASA Astrophysics Data System (ADS)

De Falco, Vittorio; Battista, Emmanuele; Falanga, Maurizio

2018-04-01

We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in general relativity through the help of an integrating factor, depending on the energy of the system. Generally, such kinds of inverse problems involving dissipative effects might not admit a Lagrangian formulation; especially, in general relativity, there are no examples of such attempts in the literature so far. We reduce this general relativistic Lagrangian formulation to the classic case in the weak-field limit. This approach facilitates further studies in improving the treatment of the radiation field, and it contains, for example, some implications for a deeper comprehension of the gravitational waves.

Relativistic quantum optics: The relativistic invariance of the light-matter interaction models

NASA Astrophysics Data System (ADS)

Martín-Martínez, Eduardo; Rodriguez-Lopez, Pablo

2018-05-01

In this article we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.

Covariant relativistic hydrodynamics of multispecies plasma and generalized Ohm's law

NASA Astrophysics Data System (ADS)

Gedalin, Michael

1996-04-01

Fully covariant hydrodynamical equations for a multispecies relativistic plasma in an external electromagnetic field are derived. The derived multifluid description takes into account binary Coulomb collisions, annihilation, and interaction with the photon background in terms of the invariant collision cross sections. A generalized Ohm's law is derived in a manifestly covariant form. Particular attention is devoted to the relativistic electron-positron plasma.

On relativistic generalization of Perelman's W-entropy and thermodynamic description of gravitational fields and cosmology

NASA Astrophysics Data System (ADS)

Ruchin, Vyacheslav; Vacaru, Olivia; Vacaru, Sergiu I.

2017-03-01

Using double 2+2 and 3+1 nonholonomic fibrations on Lorentz manifolds, we extend the concept of W-entropy for gravitational fields in general relativity (GR). Such F- and W-functionals were introduced in the Ricci flow theory of three dimensional (3-d) Riemannian metrics by Perelman (the entropy formula for the Ricci flow and its geometric applications. arXiv:math.DG/0211159). Non-relativistic 3-d Ricci flows are characterized by associated statistical thermodynamical values determined by W-entropy. Generalizations for geometric flows of 4-d pseudo-Riemannian metrics are considered for models with local thermodynamical equilibrium and separation of dissipative and non-dissipative processes in relativistic hydrodynamics. The approach is elaborated in the framework of classical field theories (relativistic continuum and hydrodynamic models) without an underlying kinetic description, which will be elaborated in other work. The 3+1 splitting allows us to provide a general relativistic definition of gravitational entropy in the Lyapunov-Perelman sense. It increases monotonically as structure forms in the Universe. We can formulate a thermodynamic description of exact solutions in GR depending, in general, on all spacetime coordinates. A corresponding 2+2 splitting with nonholonomic deformation of linear connection and frame structures is necessary for generating in very general form various classes of exact solutions of the Einstein and general relativistic geometric flow equations. Finally, we speculate on physical macrostates and microstate interpretations of the W-entropy in GR, geometric flow theories and possible connections to string theory (a second unsolved problem also contained in Perelman's work) in Polyakov's approach.

Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory

NASA Astrophysics Data System (ADS)

Sciarappa, Antonio

2017-10-01

We provide a proposal, motivated by Separation of Variables and gauge theory arguments, for constructing exact solutions to the quantum Baxter equation associated to the N-particle relativistic Toda chain and test our proposal against numerical results. Quantum Mechanical non-perturbative corrections, essential in order to obtain a sensible solution, are taken into account in our gauge theory approach by considering codimension two defects on curved backgrounds (squashed S 5 and degenerate limits) rather than flat space; this setting also naturally incorporates exact quantization conditions and energy spectrum of the relativistic Toda chain as well as its modular dual structure.

Riemann Solvers in Relativistic Hydrodynamics: Basics and Astrophysical Applications

NASA Astrophysics Data System (ADS)

Ibanez, Jose M.

2001-12-01

My contribution to these proceedings summarizes a general overview on t High Resolution Shock Capturing methods (HRSC) in the field of relativistic hydrodynamics with special emphasis on Riemann solvers. HRSC techniques achieve highly accurate numerical approximations (formally second order or better) in smooth regions of the flow, and capture the motion of unresolved steep gradients without creating spurious oscillations. In the first part I will show how these techniques have been extended to relativistic hydrodynamics, making it possible to explore some challenging astrophysical scenarios. I will review recent literature concerning the main properties of different special relativistic Riemann solvers, and discuss several 1D and 2D test problems which are commonly used to evaluate the performance of numerical methods in relativistic hydrodynamics. In the second part I will illustrate the use of HRSC methods in several astrophysical applications where special and general relativistic hydrodynamical processes play a crucial role.

Cosmological tachyon condensation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bilic, Neven; Tupper, Gary B.; Viollier, Raoul D.

2009-07-15

We consider the prospects for dark matter/energy unification in k-essence type cosmologies. General mappings are established between the k-essence scalar field, the hydrodynamic and braneworld descriptions. We develop an extension of the general relativistic dust model that incorporates the effects of both pressure and the associated acoustic horizon. Applying this to a tachyon model, we show that this inhomogeneous 'variable Chaplygin gas' does evolve into a mixed system containing cold dark matter like gravitational condensate in significant quantities. Our methods can be applied to any dark energy model, as well as to mixtures of dark energy and traditional dark matter.

Beyond the plane-parallel and Newtonian approach: wide-angle redshift distortions and convergence in general relativity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bertacca, Daniele; Maartens, Roy; Raccanelli, Alvise

We extend previous analyses of wide-angle correlations in the galaxy power spectrum in redshift space to include all general relativistic effects. These general relativistic corrections to the standard approach become important on large scales and at high redshifts, and they lead to new terms in the wide-angle correlations. We show that in principle the new terms can produce corrections of nearly 10% on Gpc scales over the usual Newtonian approximation. General relativistic corrections will be important for future large-volume surveys such as SKA and Euclid, although the problem of cosmic variance will present a challenge in observing this.

Making Sense of Black Holes: Modeling the Galactic Center and Other Low-power AGN

NASA Astrophysics Data System (ADS)

Falcke, Heino; Moscibrodzka, Monika

2018-06-01

The Galactic center host a well-known flat-spectrum radio source, Sgr A*, that is akin to the radio nuclei of quasars and radio galaxies. It is the main target of the Event Horizon Telescope to image the shadow of the black hole. There is, however, still considerable discussion on where the near-horizon emission originates from. Does it come from an accretion flow or is it produced in a relativistic jet-like outflow? Using advanced three-dimensional general relativistic magnetohydrodynamics simulations coupled to general relativistic ray tracing simulations, we now model the dynamics and emission of the plasma around starving black holes in great detail out to several thousand Schwarzschild radii. Jets appear almost naturally in theses simulations. A crucial parameter is the heating of radiating electrons and we argue that electron-proton coupling is low in the accretion flow and high in the magnetized region of the jets, making the jet an important ingredient for the overall appearance of the source. This comprehensive model is able to predict the radio size and appearance, the spectral energy distribution from radio to X-rays, the variability, and the time lags of Sgr A* surprisingly well. Interestingly, the same model can be easily generalized to other low-power AGN like M87, suggesting that GRMHD models for AGN are finally becoming predictive. With upcoming submm-VLBI experiment on the ground and in space, we will be able to further test these models in great detail and see black holes in action.

A relativistic gravity train

NASA Astrophysics Data System (ADS)

Parker, Edward

2017-08-01

A nonrelativistic particle released from rest at the edge of a ball of uniform charge density or mass density oscillates with simple harmonic motion. We consider the relativistic generalizations of these situations where the particle can attain speeds arbitrarily close to the speed of light; generalizing the electrostatic and gravitational cases requires special and general relativity, respectively. We find exact closed-form relations between the position, proper time, and coordinate time in both cases, and find that they are no longer harmonic, with oscillation periods that depend on the amplitude. In the highly relativistic limit of both cases, the particle spends almost all of its proper time near the turning points, but almost all of the coordinate time moving through the bulk of the ball. Buchdahl's theorem imposes nontrivial constraints on the general-relativistic case, as a ball of given density can only attain a finite maximum radius before collapsing into a black hole. This article is intended to be pedagogical, and should be accessible to those who have taken an undergraduate course in general relativity.

New General Relativistic Contribution to Mercury's Perihelion Advance

NASA Astrophysics Data System (ADS)

Will, Clifford M.

2018-05-01

We point out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the second-post-Newtonian contribution. It arises in part from relativistic "crossterms" in the post-Newtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 1 06 of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018.

New General Relativistic Contribution to Mercury's Perihelion Advance.

PubMed

Will, Clifford M

2018-05-11

We point out the existence of a new general relativistic contribution to the perihelion advance of Mercury that, while smaller than the contributions arising from the solar quadrupole moment and angular momentum, is 100 times larger than the second-post-Newtonian contribution. It arises in part from relativistic "crossterms" in the post-Newtonian equations of motion between Mercury's interaction with the Sun and with the other planets, and in part from an interaction between Mercury's motion and the gravitomagnetic field of the moving planets. At a few parts in 10^{6} of the leading general relativistic precession of 42.98 arcseconds per century, these effects are likely to be detectable by the BepiColombo mission to place and track two orbiters around Mercury, scheduled for launch around 2018.

Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

NASA Astrophysics Data System (ADS)

Luo, Shao-Kai; He, Jin-Man; Xu, Yan-Li; Zhang, Xiao-Tian

2016-07-01

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

Different Paths to Some Fundamental Physical Laws: Relativistic Polarization of a Moving Magnetic Dipole

ERIC Educational Resources Information Center

Kholmetskii, Alexander L.; Yarman, T.

2010-01-01

In this paper we consider the relativistic polarization of a moving magnetic dipole and show that this effect can be understood via the relativistic generalization of Kirchhoff's first law to a moving closed circuit with a steady current. This approach allows us to better understand the law of relativistic transformation of four-current density…

RELATIVISTIC MAGNETOHYDRODYNAMICS: RENORMALIZED EIGENVECTORS AND FULL WAVE DECOMPOSITION RIEMANN SOLVER

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anton, Luis; MartI, Jose M; Ibanez, Jose M

2010-05-01

We obtain renormalized sets of right and left eigenvectors of the flux vector Jacobians of the relativistic MHD equations, which are regular and span a complete basis in any physical state including degenerate ones. The renormalization procedure relies on the characterization of the degeneracy types in terms of the normal and tangential components of the magnetic field to the wave front in the fluid rest frame. Proper expressions of the renormalized eigenvectors in conserved variables are obtained through the corresponding matrix transformations. Our work completes previous analysis that present different sets of right eigenvectors for non-degenerate and degenerate states, andmore » can be seen as a relativistic generalization of earlier work performed in classical MHD. Based on the full wave decomposition (FWD) provided by the renormalized set of eigenvectors in conserved variables, we have also developed a linearized (Roe-type) Riemann solver. Extensive testing against one- and two-dimensional standard numerical problems allows us to conclude that our solver is very robust. When compared with a family of simpler solvers that avoid the knowledge of the full characteristic structure of the equations in the computation of the numerical fluxes, our solver turns out to be less diffusive than HLL and HLLC, and comparable in accuracy to the HLLD solver. The amount of operations needed by the FWD solver makes it less efficient computationally than those of the HLL family in one-dimensional problems. However, its relative efficiency increases in multidimensional simulations.« less

Texas Symposium on Relativistic Astrophysics, 11th, Austin, TX, December 12-17, 1982, Proceedings

NASA Technical Reports Server (NTRS)

Evans, D. S. (Editor)

1984-01-01

Various papers on relativistic astrophysics are presented. The general subjects addressed include: particle physics and astrophysics, general relativity, large-scale structure, big bang cosmology, new-generation telescopes, pulsars, supernovae, high-energy astrophysics, and active galaxies.

General relativistic description of the observed galaxy power spectrum: Do we understand what we measure?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoo, Jaiyul

2010-10-15

We extend the general relativistic description of galaxy clustering developed in Yoo, Fitzpatrick, and Zaldarriaga (2009). For the first time we provide a fully general relativistic description of the observed matter power spectrum and the observed galaxy power spectrum with the linear bias ansatz. It is significantly different from the standard Newtonian description on large scales and especially its measurements on large scales can be misinterpreted as the detection of the primordial non-Gaussianity even in the absence thereof. The key difference in the observed galaxy power spectrum arises from the real-space matter fluctuation defined as the matter fluctuation at themore » hypersurface of the observed redshift. As opposed to the standard description, the shape of the observed galaxy power spectrum evolves in redshift, providing additional cosmological information. While the systematic errors in the standard Newtonian description are negligible in the current galaxy surveys at low redshift, correct general relativistic description is essential for understanding the galaxy power spectrum measurements on large scales in future surveys with redshift depth z{>=}3. We discuss ways to improve the detection significance in the current galaxy surveys and comment on applications of our general relativistic formalism in future surveys.« less

Relativistic GLONASS and geodesy

NASA Astrophysics Data System (ADS)

Mazurova, E. M.; Kopeikin, S. M.; Karpik, A. P.

2016-12-01

GNSS technology is playing a major role in applications to civil, industrial and scientific areas. Nowadays, there are two fully functional GNSS: American GPS and Russian GLONASS. Their data processing algorithms have been historically based on the Newtonian theory of space and time with only a few relativistic effects taken into account as small corrections preventing the system from degradation on a fairly long time. Continuously growing accuracy of geodetic measurements and atomic clocks suggests reconsidering the overall approach to the GNSS theoretical model based on the Einstein theory of general relativity. This is essentially more challenging but fundamentally consistent theoretical approach to relativistic space geodesy. In this paper, we overview the basic principles of the relativistic GNSS model and explain the advantages of such a system for GLONASS and other positioning systems. Keywords: relativistic GLONASS, Einstein theory of general relativity.

Search for general relativistic effects in table-top displacement metrology

NASA Technical Reports Server (NTRS)

Halverson, Peter G.; Macdonald, Daniel R.; Diaz, Rosemary T.

2004-01-01

As displacement metrology accuracy improves, general relativistic effects will become noticeable. Metrology gauges developed for the Space Interferometry Mission were used to search for locally anisotropic space-time, with a null result at the 10 to the negative tenth power level.

General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

NASA Astrophysics Data System (ADS)

Donmez, Orhan

We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

Chaos in pseudo-Newtonian black holes with halos

NASA Astrophysics Data System (ADS)

Guéron, E.; Letelier, P. S.

2001-03-01

Newtonian as well as special relativistic dynamics are used to study the stability of orbits of a test particle moving around a black hole with a dipolar halo. The black hole is modeled by either the usual monopole potential or the Paczyńki-Wiita pseudo-Newtonian potential. The full general relativistic similar case is also considered. The Poincaré section method and the Lyapunov characteristic exponents show that the orbits for the pseudo-Newtonian potential models are more unstable than the corresponding general relativistic geodesics.

RELATIVISTIC MEASUREMENTS FROM TIMING THE BINARY PULSAR PSR B1913+16

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weisberg, J. M.; Huang, Y., E-mail: jweisber@carleton.edu

2016-09-20

We present relativistic analyses of 9257 measurements of times-of-arrival from the first binary pulsar, PSR B1913+16, acquired over the last 35 years. The determination of the “Keplerian” orbital elements plus two relativistic terms completely characterizes the binary system, aside from an unknown rotation about the line of sight, leading to a determination of the masses of the pulsar and its companion: 1.438 ± 0.001 M {sub ☉} and 1.390 ± 0.001 M {sub ☉}, respectively. In addition, the complete system characterization allows for the creation of relativistic gravitation test by comparing measured and predicted sizes of various relativistic phenomena. Wemore » find that the ratio of the observed orbital period decrease caused by gravitational wave damping (corrected by a kinematic term) to the general relativistic prediction is 0.9983 ± 0.0016, thereby confirms the existence and strength of gravitational radiation as predicted by general relativity. For the first time in this system, we have also successfully measured the two parameters characterizing the Shapiro gravitational propagation delay, and found that their values are consistent with general relativistic predictions. For the first time in any system, we have also measured the relativistic shape correction to the elliptical orbit, δ {sub θ} , although its intrinsic value is obscured by currently unquantified pulsar emission beam aberration. We have also marginally measured the time derivative of the projected semimajor axis, which, when improved in combination with beam aberration modeling from geodetic precession observations, should ultimately constrain the pulsar’s moment of inertia.« less

Relativistic optical model on the basis of the Moscow potential and lower phase shifts for nucleon-nucleon scattering at laboratory energies of up to 3 GeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Knyr, V. A.; Neudatchin, V. G.; Khokhlov, N. A.

Data of a partial-wave analysis of nucleon-nucleon scattering at energies of up to E{sub lab} = 3 GeV (lower partial waves) and the properties of the deuteron are described within the relativistic optical model based on deep attractive quasipotentials involving forbidden states (as exemplified by the Moscow potential). Partial-wave potentials are derived by the inverse-scattering-problem method based on the Marchenko equation by using present-day data from the partial-wave analysis of nucleon-nucleon scattering at energies of up to 3 GeV. Channel coupling is taken into account. The imaginary parts of the potentials are deduced from the phase equation of the variable-phasemore » approach. The general situation around the manifestation of quark effects in nucleon-nucleon interaction is discussed.« less

Search for general relativistic effects in table-top displacement metrology

NASA Technical Reports Server (NTRS)

Halverson, Peter G.; Diaz, Rosemary T.; Macdonald, Daniel R.

2004-01-01

As displacement metrology accuracy improves, general relativistic effects will become noticeable. Metrology gauges developed for the Space Interferometry Mission, were used to search for locally anisotropic space-time, with a null result at the 10 to the negative 10th power level.

Classical dynamics on curved Snyder space

NASA Astrophysics Data System (ADS)

Ivetić, B.; Meljanac, S.; Mignemi, S.

2014-05-01

We study the classical dynamics of a particle in nonrelativistic Snyder-de Sitter space. We show that for spherically symmetric systems, parameterizing the solutions in terms of an auxiliary time variable, which is a function only of the physical time and of the energy and angular momentum of the particles, one can reduce the problem to the equivalent one in classical mechanics. We also discuss a relativistic extension of these results, and a generalization to the case in which the algebra is realized in flat space.

Towards Observational Astronomy of Jets in Active Galaxies from General Relativistic Magnetohydrodynamic Simulations

NASA Astrophysics Data System (ADS)

Anantua, Richard; Roger Blandford, Jonathan McKinney and Alexander Tchekhovskoy

2016-01-01

We carry out the process of "observing" simulations of active galactic nuclei (AGN) with relativistic jets (hereafter called jet/accretion disk/black hole (JAB) systems) from ray tracing between image plane and source to convolving the resulting images with a point spread function. Images are generated at arbitrary observer angle relative to the black hole spin axis by implementing spatial and temporal interpolation of conserved magnetohydrodynamic flow quantities from a time series of output datablocks from fully general relativistic 3D simulations. We also describe the evolution of simulations of JAB systems' dynamical and kinematic variables, e.g., velocity shear and momentum density, respectively, and the variation of these variables with respect to observer polar and azimuthal angles. We produce, at frequencies from radio to optical, fixed observer time intensity and polarization maps using various plasma physics motivated prescriptions for the emissivity function of physical quantities from the simulation output, and analyze the corresponding light curves. Our hypothesis is that this approach reproduces observed features of JAB systems such as superluminal bulk flow projections and quasi-periodic oscillations in the light curves more closely than extant stylized analytical models, e.g., cannonball bulk flows. Moreover, our development of user-friendly, versatile C++ routines for processing images of state-of-the-art simulations of JAB systems may afford greater flexibility for observing a wide range of sources from high power BL-Lacs to low power quasars (possibly with the same simulation) without requiring years of observation using multiple telescopes. Advantages of observing simulations instead of observing astrophysical sources directly include: the absence of a diffraction limit, panoramic views of the same object and the ability to freely track features. Light travel time effects become significant for high Lorentz factor and small angles between observer direction and incident light rays; this regime is relevant for the study of AGN blazars in JAB simulations.

Generalized Galilean algebras and Newtonian gravity

NASA Astrophysics Data System (ADS)

González, N.; Rubio, G.; Salgado, P.; Salgado, S.

2016-04-01

The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

General-relativistic celestial mechanics. 4: Theory of satellite motion

NASA Astrophysics Data System (ADS)

Damour, T.; Soffel, M.; Xu, C.

1993-09-01

The basic equations needed for developing a complete relativistic theory of artificial Earth satellites are explicitly written down. These equations are given both in a local, geocentric frame and in the global, barycentric one. They are derived within our recently introduced general-relativistic celestial mechanics framework. Our approach is more satisfactory than previous ones, especially with regard to its consistency, completeness, and flexibility. In particular, the problem of representing the relativistic gravitational effects associated with the quadrupole and higher multipole moments of the moving Earth, which caused difficulties in several other approaches, is easily dealth with in our approach, thanks to the use of previously developed tools: definition of relativistic multipole moments and transformation theory between reference frames. With this last paper in a series, we hope to indicate the way of using our formalism in specific problems in applied celestial mechanics and astrometry.

Study of the O-mode in a relativistic degenerate electron plasma

NASA Astrophysics Data System (ADS)

Azra, Kalsoom; Ali, Muddasir; Hussain, Azhar

2017-03-01

Using the linearized relativistic Vlasov-Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. The dispersion relation for the O-mode in a relativistic degenerate electron plasma is investigated by employing the Fermi-Dirac distribution function. The propagation characteristics of the O-mode (cut offs, resonances, propagation regimes, harmonic structure) are examined by using specific values of the density and the magnetic field that correspond to different relativistic dense environments. Further, it is observed that due to the relativistic effects the cut off and the resonance points are shifted to low frequency values, as a result the propagation regime is reduced. The dispersion relations for the non-relativistic and the ultra-relativistic limits are also presented.

Dark matter: a problem in relativistic metrology?

NASA Astrophysics Data System (ADS)

Lusanna, Luca

2017-05-01

Besides the tidal degrees of freedom of Einstein general relativity (GR) (namely the two polarizations of gravitational waves after linearization of the theory) there are the inertial gauge ones connected with the freedom in the choice of the 4-coordinates of the space-time, i.e. in the choice of the notions of time and 3-space (the 3+1 splitting of space-time) and in their use to define a non-inertial frame (the inertial ones being forbidden by the equivalence principle) by means of a set of conventions for the relativistic metrology of the space-time (like the GPS ones near the Earth). The canonical York basis of canonical ADM gravity allows us to identify the Hamiltonian inertial gauge variables in globally hyperbolic asymptotically Minkowskian space-times without super-translations and to define the family of non-harmonic Schwinger time gauges. In these 3+1 splittings of space-time the freedom in the choice of time (the problem of clock synchronization) is described by the inertial gauge variable York time (the trace of the extrinsic curvature of the instantaneous 3-spaces). This inertial gauge freedom and the non-Euclidean nature of the instantaneous 3-spaces required by the equivalence principle need to be incorporated as metrical conventions in a relativistic suitable extension of the existing (essentially Galilean) ICRS celestial reference system. In this paper I make a short review of the existing possibilities to explain the presence of dark matter (or at least of part of it) as a relativistic inertial effect induced by the non- Euclidean nature of the 3-spaces. After a Hamiltonian Post-Minkowskian (HPM) linearization of canonical ADM tetrad gravity with particles, having equal inertial and gravitational masses, as matter, followed by a Post-Newtonian (PN) expansion, we find that the Newtonian equality of inertial and gravitational masses breaks down and that the inertial gauge York time produces an increment of the inertial masses explaining at least part of what is called dark matter in all its astrophysical signatures.

Radio-loud AGN Variability from Propagating Relativistic Jets

NASA Astrophysics Data System (ADS)

Li, Yutong; Schuh, Terance; Wiita, Paul J.

2018-06-01

The great majority of variable emission in radio-loud AGNs is understood to arise from the relativistic flows of plasma along two oppositely directed jets. We study this process using the Athena hydrodynamics code to simulate propagating three-dimensional relativistic jets for a wide range of input jet velocities and jet-to-ambient matter density ratios. We then focus on those simulations that remain essentially stable for extended distances (60-120 times the jet radius). Adopting results for the densities, pressures and velocities from these propagating simulations we estimate emissivities from each cell. The observed emissivity from each cell is strongly dependent upon its variable Doppler boosting factor, which depends upon the changing bulk velocities in those zones with respect to our viewing angle to the jet. We then sum the approximations to the fluxes from a large number of zones upstream of the primary reconfinement shock. The light curves so produced are similar to those of blazars, although turbulence on sub-grid scales is likely to be important for the variability on the shortest timescales.

A general relativistic signature in the galaxy bispectrum: the local effects of observing on the lightcone

DOE Office of Scientific and Technical Information (OSTI.GOV)

Umeh, Obinna; Jolicoeur, Sheean; Maartens, Roy

Next-generation galaxy surveys will increasingly rely on the galaxy bispectrum to improve cosmological constraints, especially on primordial non-Gaussianity. A key theoretical requirement that remains to be developed is the analysis of general relativistic effects on the bispectrum, which arise from observing galaxies on the past lightcone, as well as from relativistic corrections to the dynamics. As an initial step towards a fully relativistic analysis of the galaxy bispectrum, we compute for the first time the local relativistic lightcone effects on the bispectrum, which come from Doppler and gravitational potential contributions. For the galaxy bispectrum, the problem is much more complexmore » than for the power spectrum, since we need the lightcone corrections at second order. Mode-coupling contributions at second order mean that relativistic corrections can be non-negligible at smaller scales than in the case of the power spectrum. In a primordial Gaussian universe, we show that the local lightcone projection effects for squeezed shapes at z ∼ 1 mean that the bispectrum can differ from the Newtonian prediction by ∼> 10% when the short modes are k ∼< (50 Mpc){sup −1}. These relativistic projection effects, if ignored in the analysis of observations, could be mistaken for primordial non-Gaussianity. For upcoming surveys which probe equality scales and beyond, all relativistic lightcone effects and relativistic dynamical corrections should be included for an accurate measurement of primordial non-Gaussianity.« less

Expanding space-time and variable vacuum energy

NASA Astrophysics Data System (ADS)

Parmeggiani, Claudio

2017-08-01

The paper describes a cosmological model which contemplates the presence of a vacuum energy varying, very slightly (now), with time. The constant part of the vacuum energy generated, some 6 Gyr ago, a deceleration/acceleration transition of the metric expansion; so now, in an aged Universe, the expansion is inexorably accelerating. The vacuum energy varying part is instead assumed to be eventually responsible of an acceleration/deceleration transition, which occurred about 14 Gyr ago; this transition has a dynamic origin: it is a consequence of the general relativistic Einstein-Friedmann equations. Moreover, the vacuum energy (constant and variable) is here related to the zero-point energy of some quantum fields (scalar, vector, or spinor); these fields are necessarily described in a general relativistic way: their structure depends on the space-time metric, typically non-flat. More precisely, the commutators of the (quantum field) creation/annihilation operators are here assumed to depend on the local value of the space-time metric tensor (and eventually of its curvature); furthermore, these commutators rapidly decrease for high momentum values and they reduce to the standard ones for a flat metric. In this way, the theory is ”gravitationally” regularized; in particular, the zero-point (vacuum) energy density has a well defined value and, for a non static metric, depends on the (cosmic) time. Note that this varying vacuum energy can be negative (Fermi fields) and that a change of its sign typically leads to a minimum for the metric expansion factor (a ”bounce”).

The Gravitational Analogue to the Hydrogen Atom

ERIC Educational Resources Information Center

Kober, Martin; Koch, Ben; Bleicher, Marcus

2007-01-01

This paper reports on a student summer project performed in 2006 at the University of Frankfurt. It is addressed to undergraduate students familiar with the basic principles of relativistic quantum mechanics and general relativity. The aim of the project was to study the Dirac equation in curved spacetime. To obtain the general relativistic Dirac…

Relativistic covariance of Ohm's law

NASA Astrophysics Data System (ADS)

Starke, R.; Schober, G. A. H.

2016-04-01

The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an alternative route to this problem, which is motivated by the tremendous progress in first-principles materials physics in general and ab initio electronic structure theory in particular. We start from the most general, Lorentz-covariant first-order response law, which is written in terms of the fundamental response tensor χμ ν relating induced four-currents to external four-potentials. By showing the equivalence of this description to Ohm's law, we prove the validity of Ohm's law in every inertial frame. We further use the universal relation between χμ ν and the microscopic conductivity tensor σkℓ to derive a fully relativistic transformation law for the latter, which includes all effects of anisotropy and relativistic retardation. In the special case of a constant, scalar conductivity, this transformation law can be used to rederive a standard textbook generalization of Ohm's law.

General relativistic treatment of the thermal, magnetic and rotational evolution of isolated neutron stars with crustal magnetic fields

NASA Astrophysics Data System (ADS)

Page, D.; Geppert, U.; Zannias, T.

2000-08-01

We investigate the thermal, magnetic and rotational evolution of isolated neutron stars assuming that the dipolar magnetic field is confined to the crust. Our treatment, for the first time, uses a fully general relativistic formalism not only for the thermal but also for the magnetic part, and includes partial general relativistic effects in the rotational part. Due to the fact that the combined evolution depends crucially upon the compactness of the star, three different equations of state have been employed in the calculations. In the absence of general relativistic effects, while upon increasing compactness a decrease of the crust thickness takes place leading into an accelerating field decay, the inclusion of general relativistic effects intend to "decelerate this acceleration". As a consequence we find that, within the crustal field hypothesis, a given equation of state is compatible with the observed distribution of pulsar periods P and period derivative &mathaccent "705Frelax dot; provided the initial field strength and current location as well as the magnitude of the impurity content are appropriately constrained. Finally, we access the flexibility of the soft, medium and stiff classes of equations of state as candidates in describing the state of the matter in the neutron star interiors. The comparison of our model calculations with observations, together with the consideration of independent information about neutron star evolution, suggests that a not too soft equation of state describes neutron star interiors and its cooling proceeds along the `standard' scenario.

Newton's absolute time and space in general relativity

NASA Astrophysics Data System (ADS)

Gautreau, Ronald

2000-04-01

I describe a reference system in a spherically symmetric gravitational field that is built around times recorded by radially moving geodesic clocks. The geodesic time coordinate t and the curvature spatial radial coordinate R result in spacetime descriptions of the motion of the geodesic clocks that are exactly identical with equations following from Newton's absolute time and space used with his inverse square law. I show how to use the resulting Newtonian/general-relativistic equations for geodesic clocks to generate exact relativistic metric forms in terms of the coordinates (R,t). Newtonian theory does not describe light. However, the motion of light can be determined from the (R,t) general-relativistic metric forms obtained from Newtonian theory by setting ds2(R,t)=0. In this sense, a theory of light can be related to absolute time and space of Newtonian gravitational theory. I illustrate the (R,t) methodology by first solving the equations that result from a Newtonian picture and then examining the exact metric forms for the general-relativistic problems of the Schwarzschild field, gravitational collapse and expansion of a zero-pressure perfect fluid, and zero-pressure big-bang cosmology. I also briefly describe other applications of the Newtonian/general-relativistic formulation to: embedding a Schwarzschild mass into cosmology; continuously following an expanding universe from radiation to matter domination; Dirac's Large Numbers hypothesis; the incompleteness of Kruskal-Szekeres spacetime; double valuedness in cosmology; and the de Sitter universe.

Relativistic spin precession in the double pulsar.

PubMed

Breton, Rene P; Kaspi, Victoria M; Kramer, Michael; McLaughlin, Maura A; Lyutikov, Maxim; Ransom, Scott M; Stairs, Ingrid H; Ferdman, Robert D; Camilo, Fernando; Possenti, Andrea

2008-07-04

The double pulsar PSR J0737-3039A/B consists of two neutron stars in a highly relativistic orbit that displays a roughly 30-second eclipse when pulsar A passes behind pulsar B. Describing this eclipse of pulsar A as due to absorption occurring in the magnetosphere of pulsar B, we successfully used a simple geometric model to characterize the observed changing eclipse morphology and to measure the relativistic precession of pulsar B's spin axis around the total orbital angular momentum. This provides a test of general relativity and alternative theories of gravity in the strong-field regime. Our measured relativistic spin precession rate of 4.77 degrees (-0 degrees .65)(+0 degrees .66) per year (68% confidence level) is consistent with that predicted by general relativity within an uncertainty of 13%.

Radiatively-driven general relativistic jets

NASA Astrophysics Data System (ADS)

Vyas, Mukesh K.; Chattopadhyay, Indranil

2018-02-01

We use moment formalism of relativistic radiation hydrodynamics to obtain equations of motion of radial jets and solve them using polytropic equation of state of the relativistic gas. We consider curved space-time around black holes and obtain jets with moderately relativistic terminal speeds. In addition, the radiation field from the accretion disc, is able to induce internal shocks in the jet close to the horizon. Under combined effect of thermal as well as radiative driving, terminal speeds up to 0.75 (units of light speed) are obtained.

The Nustar Spectrum of Mrk 335: Extreme Relativistic Effects Within Two Gravitational Radii of the Event Horizon?

NASA Technical Reports Server (NTRS)

Parker, M. L.; Wilkins, D. R.; Fabian, A. C.; Grupe, D.; Dauser, T.; Matt, G.; Harrison, F. A.; Brenneman, L.; Boggs, S. E.; Christensen, F. E.;

Sound speed and viscosity of semi-relativistic relic neutrinos

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krauss, Lawrence; Long, Andrew J., E-mail: krauss@asu.edu, E-mail: andrewjlong@kicp.uchicago.edu

2016-07-01

Generalized fluid equations, using sound speed c {sub eff}{sup 2} and viscosity c {sub vis}{sup 2} as effective parameters, provide a convenient phenomenological formalism for testing the relic neutrino 'null hypothesis,' i.e. that that neutrinos are relativistic and free-streaming prior to recombination. In this work, we relax the relativistic assumption and ask 'to what extent can the generalized fluid equations accommodate finite neutrino mass?' We consider both the mass of active neutrinos, which are largely still relativistic at recombination m {sup 2} / T {sup 2} ∼ 0.2, and the effect of a semi-relativistic sterile component. While there is nomore » one-to-one mapping between mass/mixing parameters and c {sub eff}{sup 2} and c {sub vis}{sup 2}, we demonstrate that the existence of a neutrino mass could induce a bias to measurements of c {sub eff}{sup 2} and c {sub vis}{sup 2} at the level of 0.01 m {sup 2} / T {sup 2} ∼ 10{sup -3}.« less

Simple solutions for relativistic generalizations of the Child-Langmuir law and the Langmuir-Blodgett law

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang Yongpeng; Northwest Institute of Nuclear Technology, P.O. Box 69-13, Xi'an 710024; Liu Guozhi

In this paper, the Child-Langmuir law and Langmuir-Blodgett law are generalized to the relativistic regime by a simple method. Two classical laws suitable for the nonrelativistic regime are modified to simple approximate expressions applicable for calculating the space-charge-limited currents of one-dimensional steady-state planar diodes and coaxial diodes under the relativistic regime. The simple approximate expressions, extending the Child-Langmuir law and Langmuir-Blodgett law to fit the full range of voltage, have small relative errors less than 1% for one-dimensional planar diodes and less than 5% for coaxial diodes.

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

Aldaya, Victor; Guerrero, J.

1995-01-01

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

Solution of D dimensional Dirac equation for coulombic potential using NU method and its thermodynamics properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cari, C., E-mail: cari@staff.uns.ac.id; Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Yunianto, M., E-mail: muhtaryunianto@staff.uns.ac.id

2016-02-08

The analytical solution of Ddimensional Dirac equation for Coulombic potential is investigated using Nikiforov-Uvarov method. The D dimensional relativistic energy spectra are obtained from relativistic energy eigenvalue equation by using Mat Lab software.The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi and Laguerre Polynomials. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy which will be applied to determine some thermodynamical properties of the system. The thermodynamical properties of the system are expressed in terms of error function and imaginary error function.

The statistical mechanics of relativistic orbits around a massive black hole

NASA Astrophysics Data System (ADS)

Bar-Or, Ben; Alexander, Tal

2014-12-01

Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the evolution of orbital angular momentum by resonant relaxation. This drives many phenomena near MBHs, such as extreme mass-ratio gravitational wave inspirals, the warping of accretion disks, and the formation of exotic stellar populations. We present here a formal statistical mechanics framework to analyze such systems, where the background potential is described as a correlated Gaussian noise. We derive the leading order, phase-averaged 3D stochastic Hamiltonian equations of motion, for evolving the orbital elements of a test star, and obtain the effective Fokker-Planck equation for a general correlated Gaussian noise, for evolving the stellar distribution function. We show that the evolution of angular momentum depends critically on the temporal smoothness of the background potential fluctuations. Smooth noise has a maximal variability frequency {{ν }max }. We show that in the presence of such noise, the evolution of the normalized angular momentum j=\\sqrt{1-{{e}2}} of a relativistic test star, undergoing Schwarzschild (in-plane) general relativistic precession with frequency {{ν }GR}/{{j}2}, is exponentially suppressed for j\\lt {{j}b}, where {{ν }GR}/jb2˜ {{ν }max }, due to the adiabatic invariance of the precession against the slowly varying random background torques. This results in an effective Schwarzschild precession-induced barrier in angular momentum. When jb is large enough, this barrier can have significant dynamical implications for processes near the MBH.

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carrie, Michael; Shadwick, B. A.

2016-01-04

Here, we present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Juttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviors that do not exist in the non relativistic case.more » The numerical study of the relativistic two-stream instability completes the set of benchmarking tests.« less

Effects of general relativity on glitch amplitudes and pulsar mass upper bounds

NASA Astrophysics Data System (ADS)

Antonelli, M.; Montoli, A.; Pizzochero, P. M.

2018-04-01

Pinning of vortex lines in the inner crust of a spinning neutron star may be the mechanism that enhances the differential rotation of the internal neutron superfluid, making it possible to freeze some amount of angular momentum which eventually can be released, thus causing a pulsar glitch. We investigate the general relativistic corrections to pulsar glitch amplitudes in the slow-rotation approximation, consistently with the stratified structure of the star. We thus provide a relativistic generalization of a previous Newtonian model that was recently used to estimate upper bounds on the masses of glitching pulsars. We find that the effect of general relativity on the glitch amplitudes obtained by emptying the whole angular momentum reservoir is less than 30 per cent. Moreover, we show that the Newtonian upper bounds on the masses of large glitchers obtained from observations of their maximum recorded event differ by less than a few percent from those calculated within the relativistic framework. This work can also serve as a basis to construct more sophisticated models of angular momentum reservoir in a relativistic context: in particular, we present two alternative scenarios for macroscopically rigid and slack pinned vortex lines, and we generalize the Feynman-Onsager relation to the case when both entrainment coupling between the fluids and a strong axisymmetric gravitational field are present.

Relativistic viscoelastic fluid mechanics.

PubMed

Fukuma, Masafumi; Sakatani, Yuho

2011-08-01

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for the propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.

Relativistic viscoelastic fluid mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fukuma, Masafumi; Sakatani, Yuho

2011-08-15

A detailed study is carried out for the relativistic theory of viscoelasticity which was recently constructed on the basis of Onsager's linear nonequilibrium thermodynamics. After rederiving the theory using a local argument with the entropy current, we show that this theory universally reduces to the standard relativistic Navier-Stokes fluid mechanics in the long time limit. Since effects of elasticity are taken into account, the dynamics at short time scales is modified from that given by the Navier-Stokes equations, so that acausal problems intrinsic to relativistic Navier-Stokes fluids are significantly remedied. We in particular show that the wave equations for themore » propagation of disturbance around a hydrostatic equilibrium in Minkowski space-time become symmetric hyperbolic for some range of parameters, so that the model is free of acausality problems. This observation suggests that the relativistic viscoelastic model with such parameters can be regarded as a causal completion of relativistic Navier-Stokes fluid mechanics. By adjusting parameters to various values, this theory can treat a wide variety of materials including elastic materials, Maxwell materials, Kelvin-Voigt materials, and (a nonlinearly generalized version of) simplified Israel-Stewart fluids, and thus we expect the theory to be the most universal description of single-component relativistic continuum materials. We also show that the presence of strains and the corresponding change in temperature are naturally unified through the Tolman law in a generally covariant description of continuum mechanics.« less

Multiple scattering calculations of relativistic electron energy loss spectra

NASA Astrophysics Data System (ADS)

Jorissen, K.; Rehr, J. J.; Verbeeck, J.

2010-04-01

A generalization of the real-space Green’s-function approach is presented for ab initio calculations of relativistic electron energy loss spectra (EELS) which are particularly important in anisotropic materials. The approach incorporates relativistic effects in terms of the transition tensor within the dipole-selection rule. In particular, the method accounts for relativistic corrections to the magic angle in orientation resolved EELS experiments. The approach is validated by a study of the graphite CK edge, for which we present an accurate magic angle measurement consistent with the predicted value.

Decoherence and discrete symmetries in deformed relativistic kinematics

NASA Astrophysics Data System (ADS)

Arzano, Michele

2018-01-01

Models of deformed Poincaré symmetries based on group valued momenta have long been studied as effective modifications of relativistic kinematics possibly capturing quantum gravity effects. In this contribution we show how they naturally lead to a generalized quantum time evolution of the type proposed to model fundamental decoherence for quantum systems in the presence of an evaporating black hole. The same structures which determine such generalized evolution also lead to a modification of the action of discrete symmetries and of the CPT operator. These features can in principle be used to put phenomenological constraints on models of deformed relativistic symmetries using precision measurements of neutral kaons.

A Non-Perturbative, Finite Particle Number Approach to Relativistic Scattering Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lindesay, James V

2001-05-11

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a non-perturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the non-relativistic limit to the non-relativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require ''renormalization'' ormore » ''dressing'' of these parameters to connect them to the boundary states.« less

Multiphoton ionization of many-electron atoms and highly-charged ions in intense laser fields: a relativistic time-dependent density functional theory approach

NASA Astrophysics Data System (ADS)

Tumakov, Dmitry A.; Telnov, Dmitry A.; Maltsev, Ilia A.; Plunien, Günter; Shabaev, Vladimir M.

2017-10-01

We develop an efficient numerical implementation of the relativistic time-dependent density functional theory (RTDDFT) to study multielectron highly-charged ions subject to intense linearly-polarized laser fields. The interaction with the electromagnetic field is described within the electric dipole approximation. The resulting time-dependent relativistic Kohn-Sham (RKS) equations possess an axial symmetry and are solved accurately and efficiently with the help of the time-dependent generalized pseudospectral method. As a case study, we calculate multiphoton ionization probabilities of the neutral argon atom and argon-like xenon ion. Relativistic effects are assessed by comparison of our present results with existing non-relativistic data.

Optical Variability Signatures from Massive Black Hole Binaries

NASA Astrophysics Data System (ADS)

Kasliwal, Vishal P.; Frank, Koby Alexander; Lidz, Adam

2017-01-01

The hierarchical merging of dark matter halos and their associated galaxies should lead to a population of supermassive black hole binaries (MBHBs). We consider plausible optical variability signatures from MBHBs at sub-parsec separations and search for these using data from the Catalina Real-Time Transient Survey (CRTS). Specifically, we model the impact of relativistic Doppler beaming on the accretion disk emission from the less massive, secondary black hole. We explore whether this Doppler modulation may be separated from other sources of stochastic variability in the accretion flow around the MBHBs, which we describe as a damped random walk (DRW). In the simple case of a circular orbit, relativistic beaming leads to a series of broad peaks — located at multiples of the orbital frequency — in the fluctuation power spectrum. We extend our analysis to the case of elliptical orbits and discuss the effect of beaming on the flux power spectrum and auto-correlation function using simulations. We present a code to model an observed light curve as a stochastic DRW-type time series modulated by relativistic beaming and apply the code to CRTS data.

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miserev, D. S., E-mail: d.miserev@student.unsw.edu.au, E-mail: erazorheader@gmail.com

2016-06-15

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reducedmore » to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.« less

Gaussian and Airy wave packets of massive particles with orbital angular momentum

NASA Astrophysics Data System (ADS)

Karlovets, Dmitry V.

2015-01-01

While wave-packet solutions for relativistic wave equations are oftentimes thought to be approximate (paraxial), we demonstrate, by employing a null-plane- (light-cone-) variable formalism, that there is a family of such solutions that are exact. A scalar Gaussian wave packet in the transverse plane is generalized so that it acquires a well-defined z component of the orbital angular momentum (OAM), while it may not acquire a typical "doughnut" spatial profile. Such quantum states and beams, in contrast to the Bessel states, may have an azimuthal-angle-dependent probability density and finite uncertainty of the OAM, which is determined by the packet's width. We construct a well-normalized Airy wave packet, which can be interpreted as a one-particle state for a relativistic massive boson, show that its center moves along the same quasiclassical straight path, and, which is more important, spreads with time and distance exactly as a Gaussian wave packet does, in accordance with the uncertainty principle. It is explained that this fact does not contradict the well-known "nonspreading" feature of the Airy beams. While the effective OAM for such states is zero, its uncertainty (or the beam's OAM bandwidth) is found to be finite, and it depends on the packet's parameters. A link between exact solutions for the Klein-Gordon equation in the null-plane-variable formalism and the approximate ones in the usual approach is indicated; generalizations of these states for a boson in the external field of a plane electromagnetic wave are also presented.

Recovery Schemes for Primitive Variables in General-relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Siegel, Daniel M.; Mösta, Philipp; Desai, Dhruv; Wu, Samantha

2018-05-01

General-relativistic magnetohydrodynamic (GRMHD) simulations are an important tool to study a variety of astrophysical systems such as neutron star mergers, core-collapse supernovae, and accretion onto compact objects. A conservative GRMHD scheme numerically evolves a set of conservation equations for “conserved” quantities and requires the computation of certain primitive variables at every time step. This recovery procedure constitutes a core part of any conservative GRMHD scheme and it is closely tied to the equation of state (EOS) of the fluid. In the quest to include nuclear physics, weak interactions, and neutrino physics, state-of-the-art GRMHD simulations employ finite-temperature, composition-dependent EOSs. While different schemes have individually been proposed, the recovery problem still remains a major source of error, failure, and inefficiency in GRMHD simulations with advanced microphysics. The strengths and weaknesses of the different schemes when compared to each other remain unclear. Here we present the first systematic comparison of various recovery schemes used in different dynamical spacetime GRMHD codes for both analytic and tabulated microphysical EOSs. We assess the schemes in terms of (i) speed, (ii) accuracy, and (iii) robustness. We find large variations among the different schemes and that there is not a single ideal scheme. While the computationally most efficient schemes are less robust, the most robust schemes are computationally less efficient. More robust schemes may require an order of magnitude more calls to the EOS, which are computationally expensive. We propose an optimal strategy of an efficient three-dimensional Newton–Raphson scheme and a slower but more robust one-dimensional scheme as a fall-back.

Polarimetric Imaging of the Relativistic Accretion Flow in Sagittarius A*

NASA Astrophysics Data System (ADS)

Liu, Siming; Huang, L.; Shen, Z.; Cai, M. J.; Li, H.; Fryer, C. L.

2007-12-01

We perform general relativistic ray-tracing calculations of the transfer of polarized synchrotron radiation through the relativistic accretion flow in Sagittarius A*. The birefringence effects are treated self-consistently. By fitting the spectrum and polarization of Sgr A* from the millimeter to the NIR band with the model, we are able to not only constrain the basic parameters related to the magneto-rotational instability and the electron heating rate, but also limit the orientation of the accretion torus. These constraints lead to unique images of the four Stokes parameters, which may be compared with future mm and sub-mm VLBI observations. In combination with general relativistic MHD simulations, the model can be used to test the theory of the magneto-rotational instability with observations of Sgr A*. This work was funded in part under the auspices of the US Department of Energy, and supported by its contract W-7405-ENG-36 to Los Alamos National Laboratory.

Statistical thermodynamics of a two-dimensional relativistic gas.

PubMed

Montakhab, Afshin; Ghodrat, Malihe; Barati, Mahmood

2009-03-01

In this paper we study a fully relativistic model of a two-dimensional hard-disk gas. This model avoids the general problems associated with relativistic particle collisions and is therefore an ideal system to study relativistic effects in statistical thermodynamics. We study this model using molecular-dynamics simulation, concentrating on the velocity distribution functions. We obtain results for x and y components of velocity in the rest frame (Gamma) as well as the moving frame (Gamma;{'}) . Our results confirm that Jüttner distribution is the correct generalization of Maxwell-Boltzmann distribution. We obtain the same "temperature" parameter beta for both frames consistent with a recent study of a limited one-dimensional model. We also address the controversial topic of temperature transformation. We show that while local thermal equilibrium holds in the moving frame, relying on statistical methods such as distribution functions or equipartition theorem are ultimately inconclusive in deciding on a correct temperature transformation law (if any).

CoCoNuT: General relativistic hydrodynamics code with dynamical space-time evolution

NASA Astrophysics Data System (ADS)

Dimmelmeier, Harald; Novak, Jérôme; Cerdá-Durán, Pablo

2012-02-01

CoCoNuT is a general relativistic hydrodynamics code with dynamical space-time evolution. The main aim of this numerical code is the study of several astrophysical scenarios in which general relativity can play an important role, namely the collapse of rapidly rotating stellar cores and the evolution of isolated neutron stars. The code has two flavors: CoCoA, the axisymmetric (2D) magnetized version, and CoCoNuT, the 3D non-magnetized version.

Rescattering effects on intensity interferometry and initial conditions in relativistic heavy ion collisions

NASA Astrophysics Data System (ADS)

Li, Yang

The properties of the quark-gluon plasma are being thoroughly studied by utilizing relativistic heavy ion collisions. After its invention in astronomy in the 1950s, intensity interferometry was found to be a robust method to probe the spatial and temporal information of the nuclear collisions also. Although rescattering effects are negligible in elementary particle collisions, it may be very important for heavy ion collisions at RHIC and in the future LHC. Rescattering after production will modify the measured correlation function and make it harder to extract the dynamical information from data. To better understand the data which are dimmed by this final state process, we derive a general formula for intensity interferometry which can calculate rescattering effects easily. The formula can be used both non-relativistically and relativistically. Numerically, we found that rescattering effects on kaon interferometry for RHIC experiments can modify the measured ratio of the outward radius to the sideward radius, which is a sensitive probe to the equation of state, by as large as 15%. It is a nontrivial contribution which should be included to understand the data more accurately. The second part of this thesis is on the initial conditions in relativistic heavy ion collisions. Although relativistic hydrodynamics is successful in explaining many aspects of the data, it is only valid after some finite time after nuclear contact. The results depend on the choice of initial conditions which, so far, have been very uncertain. I describe a formula based on the McLerran-Venugopalan model to compute the initial energy density. The soft gluon fields produced immediately after the overlap of the nuclei can be expanded as a power series of the proper time t. Solving Yang-Mills equations with color current conservation can give us the analytical formulas for the fields. The local color charges on the transverse plane are stochastic variables and have to be taken care of by random walks. It is found that the fields are mainly longitudinal at early time. The initial energy densities are computed both for RHIC and LHC.

A fully relativistic twisted disc around a slowly rotating Kerr black hole: derivation of dynamical equations and the shape of stationary configurations

NASA Astrophysics Data System (ADS)

Zhuravlev, V. V.; Ivanov, P. B.

2011-08-01

In this paper we derive equations describing the dynamics and stationary configurations of a twisted fully relativistic thin accretion disc around a slowly rotating black hole. We assume that the inclination angle of the disc is small and that the standard relativistic generalization of the α model of accretion discs is valid when the disc is flat. We find that similar to the case of non-relativistic twisted discs the disc dynamics and stationary shapes can be determined by a pair of equations formulated for two complex variables describing the orientation of the disc rings and velocity perturbations induced by the twist. We analyse analytically and numerically the shapes of stationary twisted configurations of accretion discs having non-zero inclinations with respect to the black hole equatorial plane at large distances r from the black hole. It is shown that the stationary configurations depend on two parameters - the viscosity parameter α and the parameter ?, where δ* is the opening angle (δ*˜h/r, where h is the disc half-thickness and r is large) of a flat disc and a is the black hole rotational parameter. When a > 0 and ? the shapes depend drastically on the value of α. When α is small the disc inclination angle oscillates with radius with amplitude and radial frequency of the oscillations dramatically increasing towards the last stable orbit, Rms. When α has a moderately small value the oscillations do not take place but the disc does not align with the equatorial plane at small radii. The disc inclination angle either is increasing towards Rms or exhibits a non-monotonic dependence on the radial coordinate. Finally, when α is sufficiently large the disc aligns with the equatorial plane at small radii. When a < 0 the disc aligns with the equatorial plane for all values of α. The results reported here may have implications for determining the structure and variability of accretion discs close to Rms as well as for modelling of emission spectra coming from different sources, which are supposed to contain black holes.

A unified construction for the algebro-geometric quasiperiodic solutions of the Lotka-Volterra and relativistic Lotka-Volterra hierarchy

NASA Astrophysics Data System (ADS)

Zhao, Peng; Fan, Engui

2015-04-01

In this paper, a new type of integrable differential-difference hierarchy, namely, the generalized relativistic Lotka-Volterra (GRLV) hierarchy, is introduced. This hierarchy is closely related to Lotka-Volterra lattice and relativistic Lotka-Volterra lattice, which allows us to provide a unified and effective way to obtain some exact solutions for both the Lotka-Volterra hierarchy and the relativistic Lotka-Volterra hierarchy. In particular, we shall construct algebro-geometric quasiperiodic solutions for the LV hierarchy and the RLV hierarchy in a unified manner on the basis of the finite gap integration theory.

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

NASA Technical Reports Server (NTRS)

Zylka, Christian; Vojta, Guenter

1993-01-01

The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms

NASA Astrophysics Data System (ADS)

Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M.

2018-07-01

The phenomenological Landau–Lifshitz–Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy–Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

Generalisation of Gilbert damping and magnetic inertia parameter as a series of higher-order relativistic terms.

PubMed

Mondal, Ritwik; Berritta, Marco; Oppeneer, Peter M

2018-05-17

The phenomenological Landau-Lifshitz-Gilbert (LLG) equation of motion remains as the cornerstone of contemporary magnetisation dynamics studies, wherein the Gilbert damping parameter has been attributed to first-order relativistic effects. To include magnetic inertial effects the LLG equation has previously been extended with a supplemental inertia term; the arising inertial dynamics has been related to second-order relativistic effects. Here we start from the relativistic Dirac equation and, performing a Foldy-Wouthuysen transformation, derive a generalised Pauli spin Hamiltonian that contains relativistic correction terms to any higher order. Using the Heisenberg equation of spin motion we derive general relativistic expressions for the tensorial Gilbert damping and magnetic inertia parameters, and show that these tensors can be expressed as series of higher-order relativistic correction terms. We further show that, in the case of a harmonic external driving field, these series can be summed and we provide closed analytical expressions for the Gilbert and inertial parameters that are functions of the frequency of the driving field.

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Gammie, Charles, F.; McKinney, Jonathan C.; Tóth, Gábor

2012-09-01

HARM uses a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. On smooth flows HARM converges at second order.

Code Development of Three-Dimensional General Relativistic Hydrodynamics with AMR (Adaptive-Mesh Refinement) and Results from Special and General Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Dönmez, Orhan

2004-09-01

In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.

Numerical Hydrodynamics in Special Relativity.

PubMed

Martí, José Maria; Müller, Ewald

2003-01-01

This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods in SRHD. Results of a set of demanding test bench simulations obtained with different numerical SRHD methods are compared. Three applications (astrophysical jets, gamma-ray bursts and heavy ion collisions) of relativistic flows are discussed. An evaluation of various SRHD methods is presented, and future developments in SRHD are analyzed involving extension to general relativistic hydrodynamics and relativistic magneto-hydrodynamics. The review further provides FORTRAN programs to compute the exact solution of a 1D relativistic Riemann problem with zero and nonzero tangential velocities, and to simulate 1D relativistic flows in Cartesian Eulerian coordinates using the exact SRHD Riemann solver and PPM reconstruction. Supplementary material is available for this article at 10.12942/lrr-2003-7 and is accessible for authorized users.

Solution of D dimensional Dirac equation for hyperbolic tangent potential using NU method and its application in material properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suparmi, A., E-mail: soeparmi@staff.uns.ac.id; Cari, C., E-mail: cari@staff.uns.ac.id; Pratiwi, B. N., E-mail: namakubetanurpratiwi@gmail.com

2016-02-08

The analytical solution of D-dimensional Dirac equation for hyperbolic tangent potential is investigated using Nikiforov-Uvarov method. In the case of spin symmetry the D dimensional Dirac equation reduces to the D dimensional Schrodinger equation. The D dimensional relativistic energy spectra are obtained from D dimensional relativistic energy eigen value equation by using Mat Lab software. The corresponding D dimensional radial wave functions are formulated in the form of generalized Jacobi polynomials. The thermodynamically properties of materials are generated from the non-relativistic energy eigen-values in the classical limit. In the non-relativistic limit, the relativistic energy equation reduces to the non-relativistic energy.more » The thermal quantities of the system, partition function and specific heat, are expressed in terms of error function and imaginary error function which are numerically calculated using Mat Lab software.« less

Relativity time-delay experiments utilizing 'Mariner' spacecraft

NASA Technical Reports Server (NTRS)

Esposito, P. B.; Anderson, J. D.

1974-01-01

Relativity predicts that the transit time of a signal propagated from the earth to a spacecraft and retransmitted back to earth ought to exhibit an additional, variable time delay. The present work describes some of the analytical techniques employed in experiments using Mariner spacecraft designed to test the accuracy of this prediction. Two types of data are analyzed in these relativity experiments; these include phase-coherent, two-way Doppler shift and round-trip, transit-time measurements. Results of Mariner 6 and 7 relativistic time-delay experiments are in agreement with Einstein's theory of general relativity with an uncertainty of 3%.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

NASA Astrophysics Data System (ADS)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; Stocks, G. Malcolm

2018-03-01

The Green function plays an essential role in the Korringa-Kohn-Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn-Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). The pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. By using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Xianglin; Wang, Yang; Eisenbach, Markus

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). Themore » pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.« less

Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

DOE PAGES

Liu, Xianglin; Wang, Yang; Eisenbach, Markus; ...

2017-10-28

The Green function plays an essential role in the Korringa–Kohn–Rostoker(KKR) multiple scattering method. In practice, it is constructed from the regular and irregular solutions of the local Kohn–Sham equation and robust methods exist for spherical potentials. However, when applied to a non-spherical potential, numerical errors from the irregular solutions give rise to pathological behaviors of the charge density at small radius. Here we present a full-potential implementation of the fully-relativistic KKR method to perform ab initio self-consistent calculation by directly solving the Dirac differential equations using the generalized variable phase (sine and cosine matrices) formalism Liu et al. (2016). Themore » pathology around the origin is completely eliminated by carrying out the energy integration of the single-site Green function along the real axis. Here, by using an efficient pole-searching technique to identify the zeros of the well-behaved Jost matrices, we demonstrated that this scheme is numerically stable and computationally efficient, with speed comparable to the conventional contour energy integration method, while free of the pathology problem of the charge density. As an application, this method is utilized to investigate the crystal structures of polonium and their bulk properties, which is challenging for a conventional real-energy scheme. The noble metals are also calculated, both as a test of our method and to study the relativistic effects.« less

Bayesian Techniques for Comparing Time-dependent GRMHD Simulations to Variable Event Horizon Telescope Observations

NASA Astrophysics Data System (ADS)

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan; Medeiros, Lia; Özel, Feryal; Psaltis, Dimitrios

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.

BAYESIAN TECHNIQUES FOR COMPARING TIME-DEPENDENT GRMHD SIMULATIONS TO VARIABLE EVENT HORIZON TELESCOPE OBSERVATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kim, Junhan; Marrone, Daniel P.; Chan, Chi-Kwan

2016-12-01

The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long-baseline interferometry (VLBI) experiment that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore themore » robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. Moreover, neglecting the variability in the data and the models often leads to erroneous model selections. We finally apply our method to the early EHT data on Sgr A*.« less

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

NASA Astrophysics Data System (ADS)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation provides a minimum first order accuracy to Schwarzschild's solution to Einstein's field equations.

Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit

NASA Astrophysics Data System (ADS)

Rohrlich, Daniel

Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.

Time Operator in Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

Khorasani, Sina

2017-07-01

It is first shown that the Dirac’s equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli’s objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found.

A time-implicit numerical method and benchmarks for the relativistic Vlasov–Ampere equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carrié, Michael, E-mail: mcarrie2@unl.edu; Shadwick, B. A., E-mail: shadwick@mailaps.org

2016-01-15

We present a time-implicit numerical method to solve the relativistic Vlasov–Ampere system of equations on a two dimensional phase space grid. The time-splitting algorithm we use allows the generalization of the work presented here to higher dimensions keeping the linear aspect of the resulting discrete set of equations. The implicit method is benchmarked against linear theory results for the relativistic Landau damping for which analytical expressions using the Maxwell-Jüttner distribution function are derived. We note that, independently from the shape of the distribution function, the relativistic treatment features collective behaviours that do not exist in the nonrelativistic case. The numericalmore » study of the relativistic two-stream instability completes the set of benchmarking tests.« less

Relativistic corrections for screening effects on the energies of hydrogen-like atoms embedded in plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Poszwa, A., E-mail: poszwa@matman.uwm.edu.p; Bahar, M. K., E-mail: mussiv58@gmail.com

2015-01-15

The influence of relativistic and plasma screening effects on energies of hydrogen-like atoms embedded in plasmas has been studied. The Dirac equation with a more general exponential cosine screened potential has been solved numerically and perturbatively, by employing the direct perturbation theory. Properties of spectra corresponding to bound states and to different sets of the potential parameters have been studied both in nonrelativistic and relativistic approximations. Binding energies, fine-structure splittings, and relativistic energy shifts have been determined as functions of parameters of the potential. The results have been compared with the ones known from the literature.

Relativistic baryonic jets from an ultraluminous supersoft X-ray source.

PubMed

Liu, Ji-Feng; Bai, Yu; Wang, Song; Justham, Stephen; Lu, You-Jun; Gu, Wei-Min; Liu, Qing-Zhong; Di Stefano, Rosanne; Guo, Jin-Cheng; Cabrera-Lavers, Antonio; Álvarez, Pedro; Cao, Yi; Kulkarni, Shri

2015-12-03

The formation of relativistic jets by an accreting compact object is one of the fundamental mysteries of astrophysics. Although the theory is poorly understood, observations of relativistic jets from systems known as microquasars (compact binary stars) have led to a well established phenomenology. Relativistic jets are not expected to be produced by sources with soft or supersoft X-ray spectra, although two such systems are known to produce relatively low-velocity bipolar outflows. Here we report the optical spectra of an ultraluminous supersoft X-ray source (ULS) in the nearby galaxy M81 (M81 ULS-1; refs 9, 10). Unexpectedly, the spectra show blueshifted, broad Hα emission lines, characteristic of baryonic jets with relativistic speeds. These time-variable emission lines have projected velocities of about 17 per cent of the speed of light, and seem to be similar to those from the prototype microquasar SS 433 (refs 11, 12). Such relativistic jets are not expected to be launched from white dwarfs, and an origin from a black hole or a neutron star is hard to reconcile with the persistence of M81 ULS-1's soft X-rays. Thus the unexpected presence of relativistic jets in a ULS challenges canonical theories of jet formation, but might be explained by a long-speculated, supercritically accreting black hole with optically thick outflows.

A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ojeda-Guillén, D., E-mail: dojedag@ipn.mx; Mota, R. D.; Granados, V. D.

2016-06-15

We introduce a generalization of the Jaynes-Cummings model and study some of its properties. We obtain the energy spectrum and eigenfunctions of this model by using the tilting transformation and the squeezed number states of the one-dimensional harmonic oscillator. As physical applications, we connect this new model to two important and novelty problems: the relativistic parametric amplifier and the quantum simulation of a single trapped ion.

Republication of: Relativistic cosmology

NASA Astrophysics Data System (ADS)

Ellis, George F. R.

2009-03-01

This is a republication of a paper by G.F.R. Ellis first published in Proceedings of the International School of Physics: General Relativity and Cosmology, 1971, in which he formulated the framework for relativistic cosmology with an arbitrary background geometry. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. The paper is accompanied by a Golden Oldie Editorial comprising an editorial note written by Bill Stoeger and Ellis’ brief autobiography.

General Relativistic Simulations of Magnetized Plasmas Around Merging Supermassive Black Holes

NASA Technical Reports Server (NTRS)

Giacomazzo, Bruno; Baker, John G.; Miller, M. Coleman; Reynolds, Christopher S.; van Meter, James R.

2012-01-01

Coalescing supermassive black hole binaries are produced by the mergers of galaxies and are the most powerful sources of gravitational waves accessible to space-based gravitational observatories. Some such mergers may occur in the presence of matter and magnetic fields and hence generate an electromagnetic counterpart. In this paper we present the first general relativistic simulations of magnetized plasma around merging supermassive black holes using the general relativistic magnetohydrodynamic code Whisky. By considering different magnetic field strengths, going from non-magnetically dominated to magnetically dominated regimes, we explore how magnetic fields affect the dynamics of the plasma and the possible emission of electromagnetic signals. In particular we observe, total amplification of the magnetic field of approx 2 orders of magnitude which is driven by the accretion onto the binary and that leads to stronger electromagnetic signals than in the force-free regime where such amplifications are not possible.

Curved non-relativistic spacetimes, Newtonian gravitation and massive matter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu

2015-10-15

There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge fieldmore » which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.« less

Exact solution of the relativistic quantum Toda chain

NASA Astrophysics Data System (ADS)

Zhang, Xin; Cao, Junpeng; Yang, Wen-Li; Shi, Kangjie; Wang, Yupeng

2017-03-01

The relativistic quantum Toda chain model is studied with the generalized algebraic Bethe Ansatz method. By employing a set of local gauge transformations, proper local vacuum states can be obtained for this model. The exact spectrum and eigenstates of the model are thus constructed simultaneously.

General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies

NASA Technical Reports Server (NTRS)

Kopeikin, Sergei

2003-01-01

The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.

Relativistic g-modes in rapidly rotating neutron stars

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaertig, Erich; Kokkotas, Kostas D.; Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124

2009-09-15

We study the g-modes of fast rotating stratified neutron stars in the general relativistic Cowling approximation, where we neglect metric perturbations and where the background models take into account the buoyant force due to composition gradients. This is the first paper studying this problem in a general relativistic framework. In a recent paper [A. Passamonti, B. Haskell, N. Andersson, D. I. Jones, and I. Hawke, Mon. Not. R. Astron. Soc. 394, 730 (2009)], a similar study was performed within the Newtonian framework, where the authors presented results about the onset of CFS-unstable g-modes and the close connection between inertial andmore » gravity modes for sufficiently high rotation rates and small composition gradients. This correlation arises from the interplay between the buoyant force which is the restoring force for g-modes and the Coriolis force which is responsible for the existence of inertial modes. In our relativistic treatment of the problem, we find an excellent qualitative agreement with respect to the Newtonian results.« less

Non-Relativistic Twistor Theory and Newton-Cartan Geometry

NASA Astrophysics Data System (ADS)

Dunajski, Maciej; Gundry, James

2016-03-01

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O oplus O(2)}. We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.

General Relativistic MHD Simulations of Jet Formation

NASA Technical Reports Server (NTRS)

Mizuno, Y.; Nishikawa, K.-I.; Hardee, P.; Koide, S.; Fishman, G. J.

2005-01-01

We have performed 3-dimensional general relativistic magnetohydrodynamic (GRMHD) simulations of jet formation from an accretion disk with/without initial perturbation around a rotating black hole. We input a sinusoidal perturbation (m = 5 mode) in the rotation velocity of the accretion disk. The simulation results show the formation of a relativistic jet from the accretion disk. Although the initial perturbation becomes weakened by the coupling among different modes, it survives and triggers lower modes. As a result, complex non-axisymmetric density structure develops in the disk and the jet. Newtonian MHD simulations of jet formation with a non-axisymmetric mode show the growth of the m = 2 mode but GRMHD simulations cannot see the clear growth of the m = 2 mode.

A Missing-link in the Supernova-GRB Connection: The Case of SN 2012ap

NASA Astrophysics Data System (ADS)

Chakraborti, Sayan; Soderberg, Alicia; Chomiuk, Laura; Kamble, Atish; Yadav, Naveen; Ray, Alak; Hurley, Kevin; Margutti, Raffaella; Milisavljevic, Dan; Bietenholz, Michael; Brunthaler, Andreas; Pignata, Giuliano; Pian, Elena; Mazzali, Paolo; Fransson, Claes; Bartel, Norbert; Hamuy, Mario; Levesque, Emily; MacFadyen, Andrew; Dittmann, Jason; Krauss, Miriam; Briggs, M. S.; Connaughton, V.; Yamaoka, K.; Takahashi, T.; Ohno, M.; Fukazawa, Y.; Tashiro, M.; Terada, Y.; Murakami, T.; Goldsten, J.; Barthelmy, S.; Gehrels, N.; Cummings, J.; Krimm, H.; Palmer, D.; Golenetskii, S.; Aptekar, R.; Frederiks, D.; Svinkin, D.; Cline, T.; Mitrofanov, I. G.; Golovin, D.; Litvak, M. L.; Sanin, A. B.; Boynton, W.; Fellows, C.; Harshman, K.; Enos, H.; von Kienlin, A.; Rau, A.; Zhang, X.; Savchenko, V.

2015-06-01

Gamma-ray bursts (GRBs) are characterized by ultra-relativistic outflows, while supernovae are generally characterized by non-relativistic ejecta. GRB afterglows decelerate rapidly, usually within days, because their low-mass ejecta rapidly sweep up a comparatively larger mass of circumstellar material. However, supernovae with heavy ejecta can be in nearly free expansion for centuries. Supernovae were thought to have non-relativistic outflows except for a few relativistic ones accompanied by GRBs. This clear division was blurred by SN 2009bb, the first supernova with a relativistic outflow without an observed GRB. However, the ejecta from SN 2009bb was baryon loaded and in nearly free expansion for a year, unlike GRBs. We report the first supernova discovered without a GRB but with rapidly decelerating mildly relativistic ejecta, SN 2012ap. We discovered a bright and rapidly evolving radio counterpart driven by the circumstellar interaction of the relativistic ejecta. However, we did not find any coincident GRB with an isotropic fluence of more than one-sixth of the fluence from GRB 980425. This shows for the first time that central engines in SNe Ic, even without an observed GRB, can produce both relativistic and rapidly decelerating outflows like GRBs.

Relativistic Navigation: A Theoretical Foundation

NASA Technical Reports Server (NTRS)

Turyshev, Slava G.

1996-01-01

We present a theoretical foundation for relativistic astronomical measurements in curved space-time. In particular, we discuss a new iterative approach for describing the dynamics of an isolated astronomical N-body system in metric theories of gravity. To do this, we generalize the Fock-Chandrasekhar method of the weak-field and slow-motion approximation (WFSMA) and develop a theory of relativistic reference frames (RF's) for a gravitationally bounded many-extended-body problem. In any proper RF constructed in the immediate vicinity of an arbitrary body, the N-body solutions of the gravitational field equations are formally presented as a sum of the Riemann-flat inertial space-time, the gravitational field generated by the body itself, the unperturbed solutions for each body in the system transformed to the coordinates of this proper RF, and the gravitational interaction term. We develop the basic concept of a general WFSMA theory of the celestial RF's applicable to a wide class of metric theories of gravity and an arbitrary model of matter distribution. We apply the proposed method to general relativity. Celestial bodies are described using a perfect fluid model; as such, they possess any number of internal mass and current multipole moments that explicitly characterize their internal structures. The obtained relativistic corrections to the geodetic equations of motion arise because of a coupling of the bodies' multiple moments to the surrounding gravitational field. The resulting relativistic transformations between the different RF's extend the Poincare group to the motion of deformable self-gravitating bodies. Within the present accuracy of astronomical measurements we discuss the properties of the Fermi-normal-like proper RF that is defined in the immediate vicinity of the extended compact bodies. We further generalize the proposed approximation method and include two Eddington parameters (gamma, Beta). This generalized approach was used to derive the relativistic equations of satellite motion in the vicinity of the extended bodies. Anticipating improvements in radio and laser tracking technologies over the next few decades, we apply this method to spacecraft orbit determination. We emphasize the number of feasible relativistic gravity tests that may be performed within the context of the parameterized WFSMA. Based on the planeto-centric equations of motion of a spacecraft around the planet, we suggested a new null test of the Strong Equivalence Principle (SEP). The experiment to measure the corresponding SEP violation effect could be performed with the future Mercury Orbiter mission. We discuss other relativistic effects, including the perihelion advance and the redshift and geodetic precession of the orbiter's orbital plane about Mercury, as well as the possible future implementation of the proposed formalism in software codes developed for solar-system orbit determination. All the important calculations are completely documented, and the references contain an extensive list of cited literature.

Nada: A new code for studying self-gravitating tori around black holes

NASA Astrophysics Data System (ADS)

Montero, Pedro J.; Font, José A.; Shibata, Masaru

2008-09-01

We present a new two-dimensional numerical code called Nada designed to solve the full Einstein equations coupled to the general relativistic hydrodynamics equations. The code is mainly intended for studies of self-gravitating accretion disks (or tori) around black holes, although it is also suitable for regular spacetimes. Concerning technical aspects the Einstein equations are formulated and solved in the code using a formulation of the standard 3+1 Arnowitt-Deser-Misner canonical formalism system, the so-called Baumgarte-Shapiro Shibata-Nakamura approach. A key feature of the code is that derivative terms in the spacetime evolution equations are computed using a fourth-order centered finite difference approximation in conjunction with the Cartoon method to impose the axisymmetry condition under Cartesian coordinates (the choice in Nada), and the puncture/moving puncture approach to carry out black hole evolutions. Correspondingly, the general relativistic hydrodynamics equations are written in flux-conservative form and solved with high-resolution, shock-capturing schemes. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code, namely, (single) black hole evolutions, shock tubes, and evolutions of both spherical and rotating relativistic stars in equilibrium, the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. In addition, paving the way for specific applications of the code, we also present results from fully general relativistic numerical simulations of a system formed by a black hole surrounded by a self-gravitating torus in equilibrium.

Covariant and 3 + 1 Equations for Dynamo-Chiral General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Del Zanna, L.; Bucciantini, N.

2018-06-01

The exponential amplification of initial seed magnetic fields in relativistic plasmas is a very important topic in astrophysics, from the conditions in the early Universe to the interior of neutron stars. While dynamo action in a turbulent plasma is often invoked, in the last years a novel mechanism of quantum origin has gained increasingly more attention, namely the Chiral Magnetic Effect (CME). This has been recognized in semi-metals and it is most likely at work in the quark-gluon plasma formed in heavy-ion collision experiments, where the highest magnetic fields in nature, up to B ˜ 1018 G, are produced. This effect is expected to survive even at large hydrodynamical/MHD scales and it is based on the chiral anomaly due to an imbalance between left- and right-handed relativistic fermions in the constituent plasma. Such imbalance leads to an electric current parallel to an external magnetic field, which is precisely the same mechanism of an α-dynamo action in classical MHD. Here we extend the close parallelism between the chiral and the dynamo effects to relativistic plasmas and we propose a unified, fully covariant formulation of the generalized Ohm's law. Moreover, we derive for the first time the 3 + 1 general relativistic MHD equations for a chiral plasma both in flat and curved spacetimes, in view of numerical investigation of the CME in compact objects, especially magnetars, or of the interplay among the non-ideal magnetic effects of dynamo, the CME and reconnection.

Polarization signatures of relativistic magnetohydrodynamic shocks in the blazar emission region. I. Force-free helical magnetic fields

DOE PAGES

Zhang, Haocheng; Deng, Wei; Li, Hui; ...

2016-01-20

The optical radiation and polarization signatures in blazars are known to be highly variable during flaring activities. It is frequently argued that shocks are the main driver of the flaring events. However, the spectral variability modelings generally lack detailed considerations of the self-consistent magnetic field evolution modeling; thus, so far the associated optical polarization signatures are poorly understood. We present the first simultaneous modeling of the optical radiation and polarization signatures based on 3D magnetohydrodynamic simulations of relativistic shocks in the blazar emission environment, with the simplest physical assumptions. By comparing the results with observations, we find that shocks inmore » a weakly magnetized environment will largely lead to significant changes in the optical polarization signatures, which are seldom seen in observations. Hence an emission region with relatively strong magnetization is preferred. In such an environment, slow shocks may produce minor flares with either erratic polarization fluctuations or considerable polarization variations, depending on the parameters; fast shocks can produce major flares with smooth polarization angle rotations. In addition, the magnetic fields in both cases are observed to actively revert to the original topology after the shocks. In addition, all these features are consistent with observations. Future observations of the radiation and polarization signatures will further constrain the flaring mechanism and the blazar emission environment.« less

Relativistic and the first sectorial harmonics corrections in the critical inclination

NASA Astrophysics Data System (ADS)

Rahoma, W. A.; Khattab, E. H.; Abd El-Salam, F. A.

2014-05-01

The problem of the critical inclination is treated in the Hamiltonian framework taking into consideration post-Newtonian corrections as well as the main correction term of sectorial harmonics for an earth-like planet. The Hamiltonian is expressed in terms of Delaunay canonical variables. A canonical transformation is applied to eliminate short period terms. A modified critical inclination is obtained due to relativistic and the first sectorial harmonics corrections.

Development and application of numerical techniques for general-relativistic magnetohydrodynamics simulations of black hole accretion

NASA Astrophysics Data System (ADS)

White, Christopher Joseph

We describe the implementation of sophisticated numerical techniques for general-relativistic magnetohydrodynamics simulations in the Athena++ code framework. Improvements over many existing codes include the use of advanced Riemann solvers and of staggered-mesh constrained transport. Combined with considerations for computational performance and parallel scalability, these allow us to investigate black hole accretion flows with unprecedented accuracy. The capability of the code is demonstrated by exploring magnetically arrested disks.

GENERAL RELATIVITY DERIVATION OF BEAM REST-FRAME HAMILTONIAN.

DOE Office of Scientific and Technical Information (OSTI.GOV)

WEI,J.

2001-06-18

Analysis of particle interaction in the laboratory frame of storage rings is often complicated by the fact that particle motion is relativistic, and that reference particle trajectory is curved. Rest frame of the reference particle is a convenient coordinate system to work with, within which particle motion is non-relativistic. We have derived the equations of motion in the beam rest frame from the general relativity formalism, and have successfully applied them to the analysis of crystalline beams [1].

Relativistic theory of radiofrequency current drive

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balescu, R.; Metens, T.

1991-05-01

A fully relativistic kinetic theory of rf current drive in a tokamak is developed for both the lower hybrid and the electron cyclotron mechanisms. The problem is treated as a generalization of the classical transport equations, in which the thermodynamic forces are modified by the addition of a rf-source term. In the limit of weak rf amplitude and neglecting toroidal effects (such as particle trapping), explicit analytical expressions are obtained for the rf-generated current, the dissipated power, and the current drive efficiency. These expressions are fully relativistic and are valid over the whole admissible range of frequencies and for allmore » electron temperatures. The relation between efficiency and parallel relativistic transport coefficients is exhibited. The most important relativistic effect is a dramatic broadening of the frequency range over which the rf-generated current is significantly different from zero.« less

Relativistic effects on magnetic circular dichroism studied by GUHF/SECI method

NASA Astrophysics Data System (ADS)

Honda, Y.; Hada, M.; Ehara, M.; Nakatsuji, H.; Downing, J.; Michl, J.

2002-04-01

Quasi-relativistic formulation of the Magnetic circular dichroism (MCD) Faraday terms are presented using the generalized unrestricted Hartree-Fock (GUHF)/single excitation configuration interaction (SECI) method combined with the finite perturbation method and applied to the MCD of the three n-σ ∗ states ( 3Q1, 3Q0, 1Q1) of CH 3I. The Faraday B term for the 1Q1 state was 0.1976( Debye) 2( Bohr magneton )/(10 3 cm-1) in the non-relativistic theory, but was dramatically improved by the relativistic effect and became 0.0184 in agreement with the experimental values, 0.014 and 0.0257. This change was mainly due to the one-electron spin-orbit (SO1) term rather than the spin-free relativistic (SFR) and the two-electron spin-orbit (SO2) terms.

Two-spinor description of massive particles and relativistic spin projection operators

NASA Astrophysics Data System (ADS)

Isaev, A. P.; Podoinitsyn, M. A.

2018-04-01

On the basis of the Wigner unitary representations of the covering group ISL (2 , C) of the Poincaré group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the Dirac-Pauli-Fierz equations. In the framework of the two-spinor formalism we construct spin-vectors of polarizations and obtain conditions that fix the corresponding relativistic spin projection operators (Behrends-Fronsdal projection operators). With the help of these conditions we find explicit expressions for relativistic spin projection operators for integer spins (Behrends-Fronsdal projection operators) and then find relativistic spin projection operators for half integer spins. These projection operators determine the numerators in the propagators of fields of relativistic particles. We deduce generalizations of the Behrends-Fronsdal projection operators for arbitrary space-time dimensions D > 2.

Relativistic differential-difference momentum operators and noncommutative differential calculus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mir-Kasimov, R. M., E-mail: mirkr@theor.jinr.ru

2013-09-15

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irrepsmore » of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.« less

The Lifshitz-Kosevich-Shoenberg theory of relativistic electronic gas in neutron stars

NASA Astrophysics Data System (ADS)

Wang, Zhaojun; Lü, Guoliang; Zhu, Chunhua

2014-10-01

Similar to the de Haas-van Alphen magnetic oscillatory in some normal metals when the Landau quantization is predominant, the magnetic oscillation can also occur in highly degenerate and relativistic electron gas in neutron stars. At large Landau quantum number (Landau quantum number r≥2), we generalize the Lifshitz-Kosevich-Shoenberg theory in non-relativistic electron gas to relativistic gas. At small Landau quantum number ( r<2), we expand the grand potential into Fourier series and get similar harmonic oscillatory formula of magnetization. These results indicate that magnetic phase transition similar as Condon transition observed in metals can appear in neutron stars when the differential susceptibility exceeds 1/4 π.

Simplified Relativistic Force Transformation Equation.

ERIC Educational Resources Information Center

Stewart, Benjamin U.

1979-01-01

A simplified relativistic force transformation equation is derived and then used to obtain the equation for the electromagnetic forces on a charged particle, calculate the electromagnetic fields due to a point charge with constant velocity, transform electromagnetic fields in general, derive the Biot-Savart law, and relate it to Coulomb's law.…

Highly accurate calculation of rotating neutron stars

NASA Astrophysics Data System (ADS)

Ansorg, M.; Kleinwächter, A.; Meinel, R.

2002-01-01

A new spectral code for constructing general-relativistic models of rapidly rotating stars with an unprecedented accuracy is presented. As a first application, we reexamine uniformly rotating homogeneous stars and compare our results with those obtained by several previous codes. Moreover, representative relativistic examples corresponding to highly flattened rotating bodies are given.

Relativistic Electron Precipitation in the Auroral Zone. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Simons, D. J.

1975-01-01

The energy spectra and pitch angle distributions of electrons in the energy range from 50 keV to 2 MeV were determined by a solid state electron energy spectrometer during the Relativistic Electron Precipitation (REP) event of 31 May 1972. The pitch angle distributions were determined from a knowledge of the rocket aspect and the direction in space of the earth's magnetic field. The rocket aspect determination was therefore treated in depth and a method was developed to compensate for the malfunctioning of the aspect magnetometer. The electron fluxes during the REP event were highly variable demonstrating correlated energy, flux, and pitch angle pulsations with time periods of less than one second. A theoretical model for the production of relativistic electrons was proposed. It follows from this model that, at comparatively low background electron densities, the anomalous Doppler resonance leads to the acceleration of near relativistic particles.

Universal formulation of second-order generalized Møller-Plesset perturbation theory for a spin-dependent two-component relativistic many-electron Hamiltonian

NASA Astrophysics Data System (ADS)

Nakano, Masahiko; Seino, Junji; Nakai, Hiromi

2017-05-01

We have derived and implemented a universal formulation of the second-order generalized Møller-Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas-Kroll-Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac-Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.

Radio and X-ray variability of the nucleus of Centaurus A (NGC 5128)

NASA Technical Reports Server (NTRS)

Beall, J. H.; Rose, W. K.; Graf, W.; Price, K. M.; Dent, W. A.; Hobbs, R. W.; Conklin, E. K.; Ulich, B. L.; Dennis, B. R.; Crannell, C. J.

1977-01-01

Centaurus A was observed at radio frequencies of 10.7, 31.4, 85.2, and 89 GHz and at X-ray energies greater than 20 keV. The source exhibits significant variability in all the observed radio frequencies. The observed radio and X-ray intensities show some concurrent variations but do not track one another throughout the observations. A model of the source in which X-rays are produced by inverse Compton scattering of blackbody photons by relativistic electrons is proposed to explain these observations. The observed variations in the electromagnetic spectrum are consistent with adiabatic expansion of a trapped plasma in conjunction with turbulent accelerations of the relativistic electrons.

General Relativistic Radiative Transfer: Applications to Black-Hole Systems

NASA Technical Reports Server (NTRS)

Wu, Kinwah; Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Branduardi-Raymont, Graziella; Lee, Khee-Gan

2007-01-01

We present general relativistic radiation transfer formulations which include opacity effects due to absorption, emission and scattering explicitly. We consider a moment expansions for the transfer in the presence of scattering. The formulation is applied to calculation emissions from accretion and outflows in black-hole systems. Cases with thin accretion disks and accretion tori are considered. Effects, such as emission anisotropy, non-stationary flows and geometrical self-occultation are investigated. Polarisation transfer in curved space-time is discussed qualitatively.

General relativistic corrections to the weak lensing convergence power spectrum

NASA Astrophysics Data System (ADS)

Giblin, John T.; Mertens, James B.; Starkman, Glenn D.; Zentner, Andrew R.

2017-11-01

We compute the weak lensing convergence power spectrum, Cℓκκ, in a dust-filled universe using fully nonlinear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and partially utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, ℓ˜2 - 3 , and percent-level corrections at intermediate angular scales of ℓ˜20 - 30 .

Brst-Bfv Quantization and the Schwinger Action Principle

NASA Astrophysics Data System (ADS)

Garcia, J. Antonio; Vergara, J. David; Urrutia, Luis F.

We introduce an operator version of the BRST-BFV effective action for arbitrary systems with first class constraints. Using the Schwinger action principle we calculate the propagators corresponding to: (i) the parametrized nonrelativistic free particle, (ii) the relativistic free particle and (iii) the spinning relativistic free particle. Our calculation correctly imposes the BRST invariance at the end points. The precise use of the additional boundary terms required in the description of fermionic variables is incorporated.

Empirical Foundations of the Relativistic Gravity

NASA Astrophysics Data System (ADS)

Ni, Wei-Tou

In 1859, Le Verrier discovered the mercury perihelion advance anomaly. This anomaly turned out to be the first relativistic-gravity effect observed. During the 141 years to 2000, the precisions of laboratory and space experiments, and astrophysical and cosmological observations on relativistic gravity have been improved by 3 orders of magnitude. In 1999, we envisaged a 3-6 order improvement in the next 30 years in all directions of tests of relativistic gravity. In 2000, the interferometric gravitational wave detectors began their runs to accumulate data. In 2003, the measurement of relativistic Shapiro time-delay of the Cassini spacecraft determined the relativistic-gravity parameter γ to be 1.000021 ± 0.000023 of general relativity — a 1.5-order improvement. In October 2004, Ciufolini and Pavlis reported a measurement of the Lense-Thirring effect on the LAGEOS and LAGEOS2 satellites to be 0.99 ± 0.10 of the value predicted by general relativity. In April 2004, Gravity Probe B (Stanford relativity gyroscope experiment to measure the Lense-Thirring effect to 1%) was launched and has been accumulating science data for more than 170 days now. μSCOPE (MICROSCOPE: MICRO-Satellite à trainée Compensée pour l'Observation du Principle d'Équivalence) is on its way for a 2008 launch to test Galileo equivalence principle to 10-15. LISA Pathfinder (SMART2), the technological demonstrator for the LISA (Laser Interferometer Space Antenna) mission is well on its way for a 2009 launch. STEP (Satellite Test of Equivalence Principle), and ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) are in good planning stage. Various astrophysical tests and cosmological tests of relativistic gravity will reach precision and ultra-precision stages. Clock tests and atomic interferometry tests of relativistic gravity will reach an ever-increasing precision. These will give revived interest and development both in experimental and theoretical aspects of gravity, and may lead to answers to some profound questions of gravity and the cosmos.

A MISSING-LINK IN THE SUPERNOVA–GRB CONNECTION: THE CASE OF SN 2012ap

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chakraborti, Sayan; Soderberg, Alicia; Kamble, Atish

2015-06-01

Gamma-ray bursts (GRBs) are characterized by ultra-relativistic outflows, while supernovae are generally characterized by non-relativistic ejecta. GRB afterglows decelerate rapidly, usually within days, because their low-mass ejecta rapidly sweep up a comparatively larger mass of circumstellar material. However, supernovae with heavy ejecta can be in nearly free expansion for centuries. Supernovae were thought to have non-relativistic outflows except for a few relativistic ones accompanied by GRBs. This clear division was blurred by SN 2009bb, the first supernova with a relativistic outflow without an observed GRB. However, the ejecta from SN 2009bb was baryon loaded and in nearly free expansion formore » a year, unlike GRBs. We report the first supernova discovered without a GRB but with rapidly decelerating mildly relativistic ejecta, SN 2012ap. We discovered a bright and rapidly evolving radio counterpart driven by the circumstellar interaction of the relativistic ejecta. However, we did not find any coincident GRB with an isotropic fluence of more than one-sixth of the fluence from GRB 980425. This shows for the first time that central engines in SNe Ic, even without an observed GRB, can produce both relativistic and rapidly decelerating outflows like GRBs.« less

Minimal position-velocity uncertainty wave packets in relativistic and non-relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Al-Hashimi, M. H.; Wiese, U.-J.

2009-12-01

We consider wave packets of free particles with a general energy-momentum dispersion relation E(p). The spreading of the wave packet is determined by the velocity v=∂pE. The position-velocity uncertainty relation ΔxΔv⩾12|<∂p2E>| is saturated by minimal uncertainty wave packets Φ(p)=Aexp(-αE(p)+βp). In addition to the standard minimal Gaussian wave packets corresponding to the non-relativistic dispersion relation E(p)=p2/2m, analytic calculations are presented for the spreading of wave packets with minimal position-velocity uncertainty product for the lattice dispersion relation E(p)=-cos(pa)/ma2 as well as for the relativistic dispersion relation E(p)=p2+m2. The boost properties of moving relativistic wave packets as well as the propagation of wave packets in an expanding Universe are also discussed.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics.

PubMed

Aguayo-Ortiz, A; Mendoza, S; Olvera, D

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and "Rankine-Hugoniot" jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges.

Ideal engine durations for gamma-ray-burst-jet launch

NASA Astrophysics Data System (ADS)

Hamidani, Hamid; Takahashi, Koh; Umeda, Hideyuki; Okita, Shinpei

2017-08-01

Aiming to study gamma-ray-burst (GRB) engine duration, we present numerical simulations to investigate collapsar jets. We consider typical explosion energy (1052 erg) but different engine durations, in the widest domain to date from 0.1 to 100 s. We employ an adaptive mesh refinement 2D hydrodynamical code. Our results show that engine duration strongly influences jet nature. We show that the efficiency of launching and collimating relativistic outflow increases with engine duration, until the intermediate engine range where it is the highest, past this point to long engine range, the trend is slightly reversed; we call this point where acceleration and collimation are the highest 'sweet spot' (˜10-30 s). Moreover, jet energy flux shows that variability is also high in this duration domain. We argue that not all engine durations can produce the collimated, relativistic and variable long GRB jets. Considering a typical progenitor and engine energy, we conclude that the ideal engine duration to reproduce a long GRB is ˜10-30 s, where the launch of relativistic, collimated and variable jets is favoured. We note that this duration domain makes a good link with a previous study suggesting that the bulk of Burst and Transient Source Experiment's long GRBs is powered by ˜10-20 s collapsar engines.

A direct Primitive Variable Recovery Scheme for hyperbolic conservative equations: The case of relativistic hydrodynamics

PubMed Central

Mendoza, S.; Olvera, D.

2018-01-01

In this article we develop a Primitive Variable Recovery Scheme (PVRS) to solve any system of coupled differential conservative equations. This method obtains directly the primitive variables applying the chain rule to the time term of the conservative equations. With this, a traditional finite volume method for the flux is applied in order avoid violation of both, the entropy and “Rankine-Hugoniot” jump conditions. The time evolution is then computed using a forward finite difference scheme. This numerical technique evades the recovery of the primitive vector by solving an algebraic system of equations as it is often used and so, it generalises standard techniques to solve these kind of coupled systems. The article is presented bearing in mind special relativistic hydrodynamic numerical schemes with an added pedagogical view in the appendix section in order to easily comprehend the PVRS. We present the convergence of the method for standard shock-tube problems of special relativistic hydrodynamics and a graphical visualisation of the errors using the fluctuations of the numerical values with respect to exact analytic solutions. The PVRS circumvents the sometimes arduous computation that arises from standard numerical methods techniques, which obtain the desired primitive vector solution through an algebraic polynomial of the charges. PMID:29659602

Diffeomorphism Group Representations in Relativistic Quantum Field Theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldin, Gerald A.; Sharp, David H.

We explore the role played by the di eomorphism group and its unitary representations in relativistic quantum eld theory. From the quantum kinematics of particles described by representations of the di eomorphism group of a space-like surface in an inertial reference frame, we reconstruct the local relativistic neutral scalar eld in the Fock representation. An explicit expression for the free Hamiltonian is obtained in terms of the Lie algebra generators (mass and momentum densities). We suggest that this approach can be generalized to elds whose quanta are spatially extended objects.

Towards an exact relativistic theory of Earth's geoid undulation

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei M.; Mazurova, Elena M.; Karpik, Alexander P.

2015-08-01

The present paper extends the Newtonian concept of the geoid in classic geodesy towards the realm of general relativity by utilizing the covariant geometric methods of the perturbation theory of curved manifolds. It yields a covariant definition of the anomalous (disturbing) gravity potential and formulates differential equation for it in the form of a covariant Laplace equation. The paper also derives the Bruns equation for calculation of geoid's height with full account for relativistic effects beyond the Newtonian approximation. A brief discussion of the relativistic Bruns formula is provided.

On a viable first-order formulation of relativistic viscous fluids and its applications to cosmology

NASA Astrophysics Data System (ADS)

Disconzi, Marcelo M.; Kephart, Thomas W.; Scherrer, Robert J.

We consider a first-order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation-of-state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first-order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged nonlinear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach explored here and other theories of relativistic viscosity, including the Mueller-Israel-Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. As the topic of (relativistic) viscous fluids is also of interest outside the general relativity and cosmology communities, such as, for instance, in applications involving heavy-ion collisions, we make our presentation largely self-contained.

A study on the steady-state solutions of a relativistic Bursian diode in the presence of a transverse magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pramanik, Sourav; Chakrabarti, Nikhil; Kuznetsov, V. I.

2016-08-15

A comprehensive study on the steady states of a planar vacuum diode driven by a cold relativistic electron beam in the presence of an external transverse magnetic field is presented. The regimes, where no electrons are turned around by the external magnetic field and where they are reflected back to the emitter by the magnetic field, are both considered in a generalized way. The problem is solved by two methods: with the Euler and the Lagrange formulation. Taking non-relativistic limit, the solutions are compared with the similar ones which were obtained for the Bursian diode with a non-relativistic electron beammore » in previous work [Pramanik et al., Phys. Plasmas 22, 112108 (2015)]. It is shown that, at a moderate value of the relativistic factor of the injected beam, the region of the ambiguous solutions located to the right of the SCL bifurcation point (space charge limit) in the non-relativistic regime disappears. In addition, the dependencies of the characteristic bifurcation points and the transmitted current on the Larmor frequency as well as on the relativistic factor are explored.« less

A high-density relativistic reflection origin for the soft and hard X-ray excess emission from Mrk 1044

NASA Astrophysics Data System (ADS)

Mallick, L.; Alston, W. N.; Parker, M. L.; Fabian, A. C.; Pinto, C.; Dewangan, G. C.; Markowitz, A.; Gandhi, P.; Kembhavi, A. K.; Misra, R.

2018-06-01

We present the first results from a detailed spectral-timing analysis of a long (˜130 ks) XMM-Newton observation and quasi-simultaneous NuSTAR and Swift observations of the highly-accreting narrow-line Seyfert 1 galaxy Mrk 1044. The broadband (0.3-50 keV) spectrum reveals the presence of a strong soft X-ray excess emission below ˜1.5 keV, iron Kα emission complex at ˜6 -7 keV and a `Compton hump' at ˜15 -30 keV. We find that the relativistic reflection from a high-density accretion disc with a broken power-law emissivity profile can simultaneously explain the soft X-ray excess, highly ionized broad iron line and the Compton hump. At low frequencies ([2 - 6] × 10-5 Hz), the power-law continuum dominated 1.5-5 keV band lags behind the reflection dominated 0.3-1 keV band, which is explained with a combination of propagation fluctuation and Comptonization processes, while at higher frequencies ([1 - 2] × 10-4 Hz), we detect a soft lag which is interpreted as a signature of X-ray reverberation from the accretion disc. The fractional root-mean-squared (rms) variability of the source decreases with energy and is well described by two variable components: a less variable relativistic disc reflection and a more variable direct coronal emission. Our combined spectral-timing analyses suggest that the observed broadband X-ray variability of Mrk 1044 is mainly driven by variations in the location or geometry of the optically thin, hot corona.

Collisionless distribution function for the relativistic force-free Harris sheet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stark, C. R.; Neukirch, T.

A self-consistent collisionless distribution function for the relativistic analogue of the force-free Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the non-relativistic collisionless force-free Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters ofmore » the distribution function and the macroscopic parameters such as the current sheet thickness is discussed.« less

General relativistic radiative transfer code in rotating black hole space-time: ARTIST

NASA Astrophysics Data System (ADS)

Takahashi, Rohta; Umemura, Masayuki

2017-02-01

We present a general relativistic radiative transfer code, ARTIST (Authentic Radiative Transfer In Space-Time), that is a perfectly causal scheme to pursue the propagation of radiation with absorption and scattering around a Kerr black hole. The code explicitly solves the invariant radiation intensity along null geodesics in the Kerr-Schild coordinates, and therefore properly includes light bending, Doppler boosting, frame dragging, and gravitational redshifts. The notable aspect of ARTIST is that it conserves the radiative energy with high accuracy, and is not subject to the numerical diffusion, since the transfer is solved on long characteristics along null geodesics. We first solve the wavefront propagation around a Kerr black hole that was originally explored by Hanni. This demonstrates repeated wavefront collisions, light bending, and causal propagation of radiation with the speed of light. We show that the decay rate of the total energy of wavefronts near a black hole is determined solely by the black hole spin in late phases, in agreement with analytic expectations. As a result, the ARTIST turns out to correctly solve the general relativistic radiation fields until late phases as t ˜ 90 M. We also explore the effects of absorption and scattering, and apply this code for a photon wall problem and an orbiting hotspot problem. All the simulations in this study are performed in the equatorial plane around a Kerr black hole. The ARTIST is the first step to realize the general relativistic radiation hydrodynamics.

Explanatory and illustrative visualization of special and general relativity.

PubMed

Weiskopf, Daniel; Borchers, Marc; Ertl, Thomas; Falk, Martin; Fechtig, Oliver; Frank, Regine; Grave, Frank; King, Andreas; Kraus, Ute; Müller, Thomas; Nollert, Hans-Peter; Rica Mendez, Isabel; Ruder, Hanns; Schafhitzel, Tobias; Schär, Sonja; Zahn, Corvin; Zatloukal, Michael

2006-01-01

This paper describes methods for explanatory and illustrative visualizations used to communicate aspects of Einstein's theories of special and general relativity, their geometric structure, and of the related fields of cosmology and astrophysics. Our illustrations target a general audience of laypersons interested in relativity. We discuss visualization strategies, motivated by physics education and the didactics of mathematics, and describe what kind of visualization methods have proven to be useful for different types of media, such as still images in popular science magazines, film contributions to TV shows, oral presentations, or interactive museum installations. Our primary approach is to adopt an egocentric point of view: The recipients of a visualization participate in a visually enriched thought experiment that allows them to experience or explore a relativistic scenario. In addition, we often combine egocentric visualizations with more abstract illustrations based on an outside view in order to provide several presentations of the same phenomenon. Although our visualization tools often build upon existing methods and implementations, the underlying techniques have been improved by several novel technical contributions like image-based special relativistic rendering on GPUs, special relativistic 4D ray tracing for accelerating scene objects, an extension of general relativistic ray tracing to manifolds described by multiple charts, GPU-based interactive visualization of gravitational light deflection, as well as planetary terrain rendering. The usefulness and effectiveness of our visualizations are demonstrated by reporting on experiences with, and feedback from, recipients of visualizations and collaborators.

Zeroth order regular approximation approach to electric dipole moment interactions of the electron.

PubMed

Gaul, Konstantin; Berger, Robert

2017-07-07

A quasi-relativistic two-component approach for an efficient calculation of P,T-odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.

Zeroth order regular approximation approach to electric dipole moment interactions of the electron

NASA Astrophysics Data System (ADS)

Gaul, Konstantin; Berger, Robert

2017-07-01

A quasi-relativistic two-component approach for an efficient calculation of P ,T -odd interactions caused by a permanent electric dipole moment of the electron (eEDM) is presented. The approach uses a (two-component) complex generalized Hartree-Fock and a complex generalized Kohn-Sham scheme within the zeroth order regular approximation. In applications to select heavy-elemental polar diatomic molecular radicals, which are promising candidates for an eEDM experiment, the method is compared to relativistic four-component electron-correlation calculations and confirms values for the effective electric field acting on the unpaired electron for RaF, BaF, YbF, and HgF. The calculations show that purely relativistic effects, involving only the lower component of the Dirac bi-spinor, are well described by treating only the upper component explicitly.

Regulative feedback in pattern formation: towards a general relativistic theory of positional information.

PubMed

Jaeger, Johannes; Irons, David; Monk, Nick

2008-10-01

Positional specification by morphogen gradients is traditionally viewed as a two-step process. A gradient is formed and then interpreted, providing a spatial metric independent of the target tissue, similar to the concept of space in classical mechanics. However, the formation and interpretation of gradients are coupled, dynamic processes. We introduce a conceptual framework for positional specification in which cellular activity feeds back on positional information encoded by gradients, analogous to the feedback between mass-energy distribution and the geometry of space-time in Einstein's general theory of relativity. We discuss how such general relativistic positional information (GRPI) can guide systems-level approaches to pattern formation.

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Gammie, Charles F.; McKinney, Jonathan C.; Tóth, Gábor

2003-05-01

We describe a conservative, shock-capturing scheme for evolving the equations of general relativistic magnetohydrodynamics. The fluxes are calculated using the Harten, Lax, & van Leer scheme. A variant of constrained transport, proposed earlier by Tóth, is used to maintain a divergence-free magnetic field. Only the covariant form of the metric in a coordinate basis is required to specify the geometry. We describe code performance on a full suite of test problems in both special and general relativity. On smooth flows we show that it converges at second order. We conclude by showing some results from the evolution of a magnetized torus near a rotating black hole.

Fourier analysis of blazar variability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Finke, Justin D.; Becker, Peter A., E-mail: justin.finke@nrl.navy.mil

Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and timemore » lag behaviors associated with variability in the synchrotron, synchrotron self-Compton, and external Compton emission components, from submillimeter to γ-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We also find that FSRQs should have steeper γ-ray PSD power-law indices than BL Lac objects at Fourier frequencies ≲ 10{sup –4} Hz, in qualitative agreement with previously reported observations by the Fermi Large Area Telescope.« less

A propulsion-mass tensor coupling in relativistic rocket motion

NASA Astrophysics Data System (ADS)

Brito, Hector Hugo

1998-01-01

Following earlier speculations about antigravity machines and works on the relativistic dynamics of constant and variable rest mass point particles, a mass tensor is found in connection with the closed system consisting of the rocket driven spaceship and its propellant mass, provided a ``solidification'' point other than the system center of mass is considered. Therefore, the mass tensor form depends on whether the system is open or closed, and upon where the ``solidification'' point is located. An alternative propulsion principle is subsequently derived from the tensor mass approach. The new principle, the covariant equivalent of Newton's Third Law for the physical interpretation of the relativistic rocket motion, reads: A spaceship undergoes a propulsion effect when the whole system mass 4-ellipsoid warps.

On the theory of the relativistic motion of a charged particle in the field of intense electromagnetic radiation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Milant'ev, V. P., E-mail: vmilantiev@sci.pfu.edu.ru; Castillo, A. J., E-mail: vmilant@mail.ru

2013-04-15

Averaged relativistic equations of motion of a charged particle in the field of intense electromagnetic radiation have been obtained in the geometrical optics approximation using the Bogoliubov method. Constraints are determined under which these equations are valid. Oscillating additions to the smoothed dynamical variables of the particle have been found; they are reduced to known expressions in the case of the circularly and linearly polarized plane waves. It has been shown that the expressions for the averaged relativistic force in both cases contain new additional small terms weakening its action. The known difference between the expressions for the ponderomotive forcemore » in the cases of circularly and linearly polarized waves has been confirmed.« less

Relativistic (2,3)-threshold quantum secret sharing

NASA Astrophysics Data System (ADS)

Ahmadi, Mehdi; Wu, Ya-Dong; Sanders, Barry C.

2017-09-01

In quantum secret sharing protocols, the usual presumption is that the distribution of quantum shares and players' collaboration are both performed inertially. Here we develop a quantum secret sharing protocol that relaxes these assumptions wherein we consider the effects due to the accelerating motion of the shares. Specifically, we solve the (2,3)-threshold continuous-variable quantum secret sharing in noninertial frames. To this aim, we formulate the effect of relativistic motion on the quantum field inside a cavity as a bosonic quantum Gaussian channel. We investigate how the fidelity of quantum secret sharing is affected by nonuniform motion of the quantum shares. Furthermore, we fully characterize the canonical form of the Gaussian channel, which can be utilized in quantum-information-processing protocols to include relativistic effects.

Modulated high-energy gamma-ray emission from the microquasar Cygnus X-3.

PubMed

Abdo, A A; Ackermann, M; Ajello, M; Axelsson, M; Baldini, L; Ballet, J; Barbiellini, G; Bastieri, D; Baughman, B M; Bechtol, K; Bellazzini, R; Berenji, B; Blandford, R D; Bloom, E D; Bonamente, E; Borgland, A W; Brez, A; Brigida, M; Bruel, P; Burnett, T H; Buson, S; Caliandro, G A; Cameron, R A; Caraveo, P A; Casandjian, J M; Cecchi, C; Celik, O; Chaty, S; Cheung, C C; Chiang, J; Ciprini, S; Claus, R; Cohen-Tanugi, J; Cominsky, L R; Conrad, J; Corbel, S; Corbet, R; Dermer, C D; de Palma, F; Digel, S W; do Couto e Silva, E; Drell, P S; Dubois, R; Dubus, G; Dumora, D; Farnier, C; Favuzzi, C; Fegan, S J; Focke, W B; Fortin, P; Frailis, M; Fusco, P; Gargano, F; Gehrels, N; Germani, S; Giavitto, G; Giebels, B; Giglietto, N; Giordano, F; Glanzman, T; Godfrey, G; Grenier, I A; Grondin, M-H; Grove, J E; Guillemot, L; Guiriec, S; Hanabata, Y; Harding, A K; Hayashida, M; Hays, E; Hill, A B; Hjalmarsdotter, L; Horan, D; Hughes, R E; Jackson, M S; Jóhannesson, G; Johnson, A S; Johnson, T J; Johnson, W N; Kamae, T; Katagiri, H; Kawai, N; Kerr, M; Knödlseder, J; Kocian, M L; Koerding, E; Kuss, M; Lande, J; Latronico, L; Lemoine-Goumard, M; Longo, F; Loparco, F; Lott, B; Lovellette, M N; Lubrano, P; Madejski, G M; Makeev, A; Marchand, L; Marelli, M; Max-Moerbeck, W; Mazziotta, M N; McColl, N; McEnery, J E; Meurer, C; Michelson, P F; Migliari, S; Mitthumsiri, W; Mizuno, T; Monte, C; Monzani, M E; Morselli, A; Moskalenko, I V; Murgia, S; Nolan, P L; Norris, J P; Nuss, E; Ohsugi, T; Omodei, N; Ong, R A; Ormes, J F; Paneque, D; Parent, D; Pelassa, V; Pepe, M; Pesce-Rollins, M; Piron, F; Pooley, G; Porter, T A; Pottschmidt, K; Rainò, S; Rando, R; Ray, P S; Razzano, M; Rea, N; Readhead, A; Reimer, A; Reimer, O; Richards, J L; Rochester, L S; Rodriguez, J; Rodriguez, A Y; Romani, R W; Ryde, F; Sadrozinski, H F-W; Sander, A; Saz Parkinson, P M; Sgrò, C; Siskind, E J; Smith, D A; Smith, P D; Spinelli, P; Starck, J-L; Stevenson, M; Strickman, M S; Suson, D J; Takahashi, H; Tanaka, T; Thayer, J B; Thompson, D J; Tibaldo, L; Tomsick, J A; Torres, D F; Tosti, G; Tramacere, A; Uchiyama, Y; Usher, T L; Vasileiou, V; Vilchez, N; Vitale, V; Waite, A P; Wang, P; Wilms, J; Winer, B L; Wood, K S; Ylinen, T; Ziegler, M

2009-12-11

Microquasars are accreting black holes or neutron stars in binary systems with associated relativistic jets. Despite their frequent outburst activity, they have never been unambiguously detected emitting high-energy gamma rays. The Fermi Large Area Telescope (LAT) has detected a variable high-energy source coinciding with the position of the x-ray binary and microquasar Cygnus X-3. Its identification with Cygnus X-3 is secured by the detection of its orbital period in gamma rays, as well as the correlation of the LAT flux with radio emission from the relativistic jets of Cygnus X-3. The gamma-ray emission probably originates from within the binary system, opening new areas in which to study the formation of relativistic jets.

Local U(2,2) symmetry in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Finster, Felix

1998-12-01

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

Relativistic H-theorem and nonextensive kinetic theory

NASA Astrophysics Data System (ADS)

Silva, R.; Lima, J. A. S.

2003-08-01

In 1988 Tsallis proposed a striking generalization of the Boltzmann-Gibbs entropy functional form given by [1] (1) where kB is Boltzmann's constant, pi is the probability of the i-th microstate, and the parameter q is any real number. Nowadays, the q-thermostatistics associated with Sq is being hailed as the possible basis of a theoretical framework appropriate to deal with nonextensive settings. There is a growing body of evidence suggesting that Sq provides a convenient frame for the thermostatistical analysis of many physical systems and processes ranging from the laboratory scale to the astrophysical domain [2]. However, all the basic results, including the proof of the H-theorem has been worked in the classical non-relativistic domain [3]. In this context we discuss the relativistic kinetic foundations of the Tsallis' nonextensive approach through the full Boltzmann's transport equation. Our analysis follows from a nonextensive generalization of the "molecular chaos hypothesis". For q > 0, the q-transport equation satisfies a relativistic H-theorem based on Tsallis entropy. It is also proved that the collisional equilibrium is given by the relativistic Tsallis' q-nonextensive velocity distribution. References [1] C. Tsallis, J. Stat. Phys. 52, 479 (1988). [2] J. A. S. Lima, R. Silva, and J. Santos, Astron. and Astrophys. 396, 309 (2002). [3] J. A. S. Lima, R. Silva, and A. R. Plastino, Phys. Rev. Lett. 86, 2938 (2001).

A quantum relativistic battle of the sexes cellular automaton

NASA Astrophysics Data System (ADS)

Alonso-Sanz, Ramón; Situ, Haozhen

2017-02-01

The effect of variable entangling on the dynamics of a spatial quantum relativistic formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests. Despite the full range of quantum parameters initially accessible, they promptly converge into fairly stable configurations, that often show rich spatial structures in simulations with no negligible entanglement.

Space–time and spatial geodesic orbits in Schwarzschild geometry

NASA Astrophysics Data System (ADS)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

Variational principles for relativistic smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Monaghan, J. J.; Price, D. J.

2001-12-01

In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non-relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation.

Going beyond the Kaiser redshift-space distortion formula: A full general relativistic account of the effects and their detectability in galaxy clustering

NASA Astrophysics Data System (ADS)

Yoo, Jaiyul; Hamaus, Nico; Seljak, Uroš; Zaldarriaga, Matias

2012-09-01

Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M≥1012h-1M⊙ (this can increase to 10-σ or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.

Increasing the perceptual salience of relationships in parallel coordinate plots.

PubMed

Harter, Jonathan M; Wu, Xunlei; Alabi, Oluwafemi S; Phadke, Madhura; Pinto, Lifford; Dougherty, Daniel; Petersen, Hannah; Bass, Steffen; Taylor, Russell M

2012-01-01

We present three extensions to parallel coordinates that increase the perceptual salience of relationships between axes in multivariate data sets: (1) luminance modulation maintains the ability to preattentively detect patterns in the presence of overplotting, (2) adding a one-vs.-all variable display highlights relationships between one variable and all others, and (3) adding a scatter plot within the parallel-coordinates display preattentively highlights clusters and spatial layouts without strongly interfering with the parallel-coordinates display. These techniques can be combined with one another and with existing extensions to parallel coordinates, and two of them generalize beyond cases with known-important axes. We applied these techniques to two real-world data sets (relativistic heavy-ion collision hydrodynamics and weather observations with statistical principal component analysis) as well as the popular car data set. We present relationships discovered in the data sets using these methods.

ELECTRONIC STRUCTURE FOR THE GROUND STATE OF T1H FROM RELATIVISTIC MULTICONFIGURATION SCF CALCULATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christiansen, P.A.; Pitzer, K.S.

The dissociation curve for the ground state of TlH was computed using a relativistic {omega}-{omega} coupling formalism. The relativistic effects represented by the Dirac equation were introduced using effective potentials generated from atomic Dirac-Fock wave functions using a generalization of the improved effective potential formulation of Christiansen, Lee, and Pitzer. The multiconfiguration SCF treatment used is a generalization of the two-component molecular spinor formalism of Lee, Ermler, and Pitzer. Using a five configuration wave function we were able to obtain approximately 85% of the experimental dissociation energy. Our computations indicate that the bond is principally sigma in form, despite themore » large spin-orbit splitting in atomic thallium. Furthermore the bond appears to be slightly ionic (Tl{sup +}H{sup -}) with about 0.3 extra electron charge on the hydrogen.« less

Electronic structure for the ground state of TlH from relativistic multiconfiguration SCF calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christiansen, P.A.; Pitzer, K.S.

The dissociation curve for the ground state of TlH was computed using a relativistic ..omega..--..omega.. coupling formalism. The relativistic effects represented by the Dirac equation were introduced using effective potentials generated from atomic Dirac--Fock wave functions using a generalization of the improved effective potential formulation of Christiansen, Lee, and Pitzer. The multiconfiguration SCF treatment used is a generalization of the two-component molecular spinor formalism of Lee, Ermler, and Pitzer. Using a five configuration wave function we were able to obtain approximately 85% of the experimental dissociation energy. Our computations indicate that the bond is principally sigma in form, despite themore » large spin--orbit splitting in atomic thallium. Furthermore the bond appears to be slightly ionic (Tl/sup +/H/sup -/) with about 0.3 extra electron charge on the hydrogen.« less

Relativistic Spin-Orbit Heavy Atom on the Light Atom NMR Chemical Shifts: General Trends Across the Periodic Table Explained.

PubMed

Vícha, Jan; Komorovsky, Stanislav; Repisky, Michal; Marek, Radek; Straka, Michal

2018-06-12

The importance of relativistic effects on the NMR parameters in heavy-atom (HA) compounds, particularly the SO-HALA (Spin-Orbit Heavy Atom on the Light Atom) effect on NMR chemical shifts, has been known for about 40 years. Yet, a general correlation between the electronic structure and SO-HALA effect has been missing. By analyzing 1 H NMR chemical shifts of the sixth-period hydrides (Cs-At), we discovered general electronic-structure principles and mechanisms that dictate the size and sign of the SO-HALA NMR chemical shifts. In brief, partially occupied HA valence shells induce relativistic shielding at the light atom (LA) nuclei, while empty HA valence shells induce relativistic deshielding. In particular, the LA nucleus is relativistically shielded in 5d 2 -5d 8 and 6p 4 HA hydrides and deshielded in 4f 0 , 5d 0 , 6s 0 , and 6p 0 HA hydrides. This general and intuitive concept explains periodic trends in the 1 H NMR chemical shifts along the sixth-period hydrides (Cs-At) studied in this work. We present substantial evidence that the introduced principles have a general validity across the periodic table and can be extended to nonhydride LAs. The decades-old question of why compounds with occupied frontier π molecular orbitals (MOs) cause SO-HALA shielding at the LA nuclei, while the frontier σ MOs cause deshielding is answered. We further derive connection between the SO-HALA NMR chemical shifts and Spin-Orbit-induced Electron Deformation Density (SO-EDD), a property that can be obtained easily from differential electron densities and can be represented graphically. SO-EDD provides an intuitive understanding of the SO-HALA effect in terms of the depletion/concentration of the electron density at LA nuclei caused by spin-orbit coupling due to HA in the presence of a magnetic field. Using an analogy between the SO-EDD concept and arguments from classic NMR theory, the complex question of the SO-HALA NMR chemical shifts becomes easily understandable for a wide chemical audience.

On the Relativistic Correction of Particles Trajectory in Tandem Type Electrostatic Accelerator

NASA Astrophysics Data System (ADS)

Minárik, Stanislav

2015-08-01

A constant potential is applied to the acceleration of the ion-beam in the tandem type electrostatic accelerator. However, not just one voltage is applied, but instead a number of applications can be made in succession by means of the tandem arrangement of high voltage tubes. This number of voltage applications, which is the number of so-called "stages" of a tandem accelerator, may be two, three, or four, depending on the chosen design. Electrostatic field with approximately constant intensity acts on ions in any stage. In general, non-relativistic dynamics is used for the description of the ion transport in tandem accelerator. Energies of accelerated ions are too low and relativistic effects cannot be commonly observed by standard experimental technique. Estimation of possible relativistic correction of ion trajectories is therefore only a matter of calculation. In this note, we briefly present such calculation. Our aim is to show how using the relativistic dynamics modifies the particles trajectory in tandem type accelerator and what parameters determine this modification.

Dynamics of oscillating relativistic tori around Kerr black holes

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Font, José A.; Rezzolla, Luciano; Montero, Pedro J.

2005-02-01

We present a comprehensive numerical study of the dynamics of relativistic axisymmetric accretion tori with a power-law distribution of specific angular momentum orbiting in the background space-time of a Kerr black hole. By combining general relativistic hydrodynamics simulations with a linear perturbative approach we investigate the main dynamical properties of these objects over a large parameter space. The astrophysical implications of our results extend and improve two interesting results that have been recently reported in the literature. First, the induced quasi-periodic variation of the mass quadrupole moment makes relativistic tori of nuclear matter densities, as those formed during the last stages of binary neutron star mergers, promising sources of gravitational radiation, potentially detectable by interferometric instruments. Secondly, p-mode oscillations in relativistic tori of low rest-mass densities could be used to explain high-frequency quasi-periodic oscillations observed in X-ray binaries containing a black hole candidate under conditions more generic than those considered so far.

Planar and non-planar nucleus-acoustic shock structures in self-gravitating degenerate quantum plasma systems

NASA Astrophysics Data System (ADS)

Zaman, D. M. S.; Amina, M.; Dip, P. R.; Mamun, A. A.

2017-11-01

The basic properties of planar and non-planar (spherical and cylindrical) nucleus-acoustic (NA) shock structures (SSs) in a strongly coupled self-gravitating degenerate quantum plasma system (containing strongly coupled non-relativistically degenerate heavy nuclear species, weakly coupled non-relativistically degenerate light nuclear species, and inertialess non-/ultra-relativistically degenerate electrons) have been investigated. The generalized quantum hydrodynamic model and the reductive perturbation method have been used to derive the modified Burgers equation. It is shown that the strong correlation among heavy nuclear species acts as the source of dissipation and is responsible for the formation of the NA SSs with positive (negative) electrostatic (self-gravitational) potential. It is also observed that the effects of non-/ultra-relativistically degenerate electron pressure, dynamics of non-relativistically degenerate light nuclear species, spherical geometry, etc., significantly modify the basic features of the NA SSs. The applications of our results in astrophysical compact objects like white dwarfs and neutron stars are briefly discussed.

GRMHD/RMHD Simulations and Stability of Magnetized Spine-Sheath Relativistic Jets

NASA Technical Reports Server (NTRS)

Hardee, Philip; Mizuno, Yosuke; Nishikawa, Ken-Ichi

2007-01-01

A new general relativistic magnetohydrodynamics (GRMHD ) code "RAISHIN" used to simulate jet generation by rotating and non-rotating black holes with a geometrically thin Keplarian accretion disk finds that the jet develops a spine-sheath structure in the rotating black hole case. Spine-sheath structure and strong magnetic fields significantly modify the Kelvin-Helmholtz (KH) velocity shear driven instability. The RAISHIN code has been used in its relativistic magnetohydrodynamic (RMHD) configuration to study the effects of strong magnetic fields and weakly relativistic sheath motion, cl2, on the KH instability associated with a relativistic, Y = 2.5, jet spine-sheath interaction. In the simulations sound speeds up to ? c/3 and Alfven wave speeds up to ? 0.56 c are considered. Numerical simulation results are compared to theoretical predictions from a new normal mode analysis of the RMHD equations. Increased stability of a weakly magnetized system resulting from c/2 sheath speeds and stabilization of a strongly magnetized system resulting from d 2 sheath speeds is found.

Relativistic low angular momentum accretion: long time evolution of hydrodynamical inviscid flows

NASA Astrophysics Data System (ADS)

Mach, Patryk; Piróg, Michał; Font, José A.

2018-05-01

We investigate relativistic low angular momentum accretion of inviscid perfect fluid onto a Schwarzschild black hole. The simulations are performed with a general-relativistic, high-resolution (second-order), shock-capturing, hydrodynamical numerical code. We use horizon-penetrating Eddington–Finkelstein coordinates to remove inaccuracies in regions of strong gravity near the black hole horizon and show the expected convergence of the code with the Michel solution and stationary Fishbone–Moncrief toroids. We recover, in the framework of relativistic hydrodynamics, the qualitative behavior known from previous Newtonian studies that used a Bondi background flow in a pseudo-relativistic gravitational potential with a latitude-dependent angular momentum at the outer boundary. Our models exhibit characteristic ‘turbulent’ behavior and the attained accretion rates are lower than those of the Bondi–Michel radial flow. For sufficiently low values of the asymptotic sound speed, geometrically thick tori form in the equatorial plane surrounding the black hole horizon while accretion takes place mainly through the poles.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mueller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald, E-mail: bjmuellr@mpa-garching.mpg.d, E-mail: thj@mpa-garching.mpg.d, E-mail: harrydee@mpa-garching.mpg.d

We present a new general relativistic code for hydrodynamical supernova simulations with neutrino transport in spherical and azimuthal symmetry (one dimension and two dimensions, respectively). The code is a combination of the COCONUT hydro module, which is a Riemann-solver-based, high-resolution shock-capturing method, and the three-flavor, fully energy-dependent VERTEX scheme for the transport of massless neutrinos. VERTEX integrates the coupled neutrino energy and momentum equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the 'ray-by-ray plus' approximation in two dimensions, assuming the neutrino distribution to be axially symmetric around the radial direction at every pointmore » in space, and thus the neutrino flux to be radial. Our spacetime treatment employs the Arnowitt-Deser-Misner 3+1 formalism with the conformal flatness condition for the spatial three metric. This approach is exact for the one-dimensional case and has previously been shown to yield very accurate results for spherical and rotational stellar core collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with grid-based Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number in the neutrino transport with better accuracy and higher numerical stability in the high-energy tail of the spectrum. To verify our code, we conduct a series of tests in spherical symmetry, including a detailed comparison with published results of the collapse, shock formation, shock breakout, and accretion phases. Long-time simulations of proto-neutron star cooling until several seconds after core bounce both demonstrate the robustness of the new COCONUT-VERTEX code and show the approximate treatment of relativistic effects by means of an effective relativistic gravitational potential as in PROMETHEUS-VERTEX to be remarkably accurate in spherical symmetry.« less

Time-Integral Correlations of Multiple Variables With the Relativistic-Electron Flux at Geosynchronous Orbit: The Strong Roles of Substorm-Injected Electrons and the Ion Plasma Sheet

NASA Astrophysics Data System (ADS)

Borovsky, Joseph E.

2017-12-01

Time-integral correlations are examined between the geosynchronous relativistic electron flux index Fe1.2 and 31 variables of the solar wind and magnetosphere. An "evolutionary algorithm" is used to maximize correlations. Time integrations (into the past) of the variables are found to be superior to time-lagged variables for maximizing correlations with the radiation belt. Physical arguments are given as to why. Dominant correlations are found for the substorm-injected electron flux at geosynchronous orbit and for the pressure of the ion plasma sheet. Different sets of variables are constructed and correlated with Fe1.2: some sets maximize the correlations, and some sets are based on purely solar wind variables. Examining known physical mechanisms that act on the radiation belt, sets of correlations are constructed (1) using magnetospheric variables that control those physical mechanisms and (2) using the solar wind variables that control those magnetospheric variables. Fe1.2-increasing intervals are correlated separately from Fe1.2-decreasing intervals, and the introduction of autoregression into the time-integral correlations is explored. A great impediment to discerning physical cause and effect from the correlations is the fact that all solar wind variables are intercorrelated and carry much of the same information about the time sequence of the solar wind that drives the time sequence of the magnetosphere.

Relativistic Thomas-Fermi treatment of compressed atoms and compressed nuclear matter cores of stellar dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rotondo, M.; Rueda, Jorge A.; Xue, S.-S.

The Feynman-Metropolis-Teller treatment of compressed atoms is extended to the relativistic regimes. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy. The nonrelativistic treatment assumes a pointlike nucleus and infinite values of the electron Fermi energy can be attained. In the relativistic treatment there exists a limiting configuration, reached when the Wigner-Seitz cell radius equals the radius of the nucleus, with a maximum value of the electron Fermi energy (E{sub e}{sup F}){sub max}, here expressed analytically in the ultrarelativistic approximation. The corrections given by the relativistic Thomas-Fermi-Dirac exchange term are alsomore » evaluated and shown to be generally small and negligible in the relativistic high-density regime. The dependence of the relativistic electron Fermi energies by compression for selected nuclei are compared and contrasted to the nonrelativistic ones and to the ones obtained in the uniform approximation. The relativistic Feynman-Metropolis-Teller approach here presented overcomes some difficulties in the Salpeter approximation generally adopted for compressed matter in physics and astrophysics. The treatment is then extrapolated to compressed nuclear matter cores of stellar dimensions with A{approx_equal}(m{sub Planck}/m{sub n}){sup 3}{approx}10{sup 57} or M{sub core}{approx}M{sub {circle_dot}}. A new family of equilibrium configurations exists for selected values of the electron Fermi energy varying in the range 0

Generalized Causal Quantum Theories

NASA Astrophysics Data System (ADS)

Parmeggiani, Claudio

2007-12-01

We shall show that is always possible to construct causal Quantum Theories fully equivalent (as predictive tools) to acausal, standard Quantum Theory, relativistic or not relativistic; we re-obtain, as a particular case, the usual Quantum Bohmian Theory. Then we consider the measurement process, in causal theories, and we conclude that the state of affairs is not really improved, with respect to standard theories.

Ohm's law in the fast lane: general relatiivistic charge dynamics

NASA Technical Reports Server (NTRS)

Meier, D.

2004-01-01

Fully relativistic and causal equations for the flow of charge in curved spacetime are derived. It is believed that this is the first set of equations to be published that correctly describes the flow of charge, as well as the evolution of the electromagnetic field, in highly dynamical relativistic environments on timescales much shorter than the collapse time (GM/c3).

Testing the relativistic Doppler boost hypothesis for supermassive black hole binary candidates

NASA Astrophysics Data System (ADS)

Charisi, Maria; Haiman, Zoltán; Schiminovich, David; D'Orazio, Daniel J.

2018-06-01

Supermassive black hole binaries (SMBHBs) should be common in galactic nuclei as a result of frequent galaxy mergers. Recently, a large sample of sub-parsec SMBHB candidates was identified as bright periodically variable quasars in optical surveys. If the observed periodicity corresponds to the redshifted binary orbital period, the inferred orbital velocities are relativistic (v/c ≈ 0.1). The optical and ultraviolet (UV) luminosities are expected to arise from gas bound to the individual BHs, and would be modulated by the relativistic Doppler effect. The optical and UV light curves should vary in tandem with relative amplitudes which depend on the respective spectral slopes. We constructed a control sample of 42 quasars with aperiodic variability, to test whether this Doppler colour signature can be distinguished from intrinsic chromatic variability. We found that the Doppler signature can arise by chance in ˜20 per cent (˜37 per cent) of quasars in the nUV (fUV) band. These probabilities reflect the limited quality of the control sample and represent upper limits on how frequently quasars mimic the Doppler brightness+colour variations. We performed separate tests on the periodic quasar candidates, and found that for the majority, the Doppler boost hypothesis requires an unusually steep UV spectrum or an unexpectedly large BH mass and orbital velocity. We conclude that at most approximately one-third of these periodic candidates can harbor Doppler-modulated SMBHBs.

Kinetic Modeling of Radiative Turbulence in Relativistic Astrophysical Plasmas: Particle Acceleration and High-Energy Flares

NASA Astrophysics Data System (ADS)

Uzdensky, Dmitri

Relativistic astrophysical plasma environments routinely produce intense high-energy emission, which is often observed to be nonthermal and rapidly flaring. The recently discovered gamma-ray (> 100 MeV) flares in Crab Pulsar Wind Nebula (PWN) provide a quintessential illustration of this, but other notable examples include relativistic active galactic nuclei (AGN) jets, including blazars, and Gamma-ray Bursts (GRBs). Understanding the processes responsible for the very efficient and rapid relativistic particle acceleration and subsequent emission that occurs in these sources poses a strong challenge to modern high-energy astrophysics, especially in light of the necessity to overcome radiation reaction during the acceleration process. Magnetic reconnection and collisionless shocks have been invoked as possible mechanisms. However, the inferred extreme particle acceleration requires the presence of coherent electric-field structures. How such large-scale accelerating structures (such as reconnecting current sheets) can spontaneously arise in turbulent astrophysical environments still remains a mystery. The proposed project will conduct a first-principles computational and theoretical study of kinetic turbulence in relativistic collisionless plasmas with a special focus on nonthermal particle acceleration and radiation emission. The main computational tool employed in this study will be the relativistic radiative particle-in-cell (PIC) code Zeltron, developed by the team members at the Univ. of Colorado. This code has a unique capability to self-consistently include the synchrotron and inverse-Compton radiation reaction force on the relativistic particles, while simultaneously computing the resulting observable radiative signatures. This proposal envisions performing massively parallel, large-scale three-dimensional simulations of driven and decaying kinetic turbulence in physical regimes relevant to real astrophysical systems (such as the Crab PWN), including the radiation reaction effects. In addition to measuring the general fluid-level statistical properties of kinetic turbulence (e.g., the turbulent spectrum in the inertial and sub-inertial range), as well as the overall energy dissipation and particle acceleration, the proposed study will also investigate their intermittency and time variability, resulting in direction- and time-resolved emitted photon spectra and direction- and energy-resolved light curves, which can then be compared with observations. To gain deeper physical insight into the intermittent particle acceleration processes in turbulent astrophysical environments, the project will also identify and analyze statistically the current sheets, shocks, and other relevant localized particle-acceleration structures found in the simulations. In particular, it will assess whether relativistic kinetic turbulence in PWN can self-consistently generate such structures that are long and strong enough to accelerate large numbers of particles to the PeV energies required to explain the Crab gamma-ray flares, and where and under what conditions such acceleration can occur. The results of this research will also advance our understanding the origin of ultra-rapid TeV flares in blazar jets and will have important implications for GRB prompt emission, as well as AGN radio-lobes and radiatively-inefficient accretion flows, such as the flow onto the supermassive black hole at our Galactic Center.

General Relativistic Effects on Neutrino-driven Winds from Young, Hot Neutron Stars and r-Process Nucleosynthesis

NASA Astrophysics Data System (ADS)

Otsuki, Kaori; Tagoshi, Hideyuki; Kajino, Toshitaka; Wanajo, Shin-ya

2000-04-01

Neutrino-driven winds from young hot neutron stars, which are formed by supernova explosions, are the most promising candidate site for r-process nucleosynthesis. We study general relativistic effects on this wind in Schwarzschild geometry in order to look for suitable conditions for successful r-process nucleosynthesis. It is quantitatively demonstrated that general relativistic effects play a significant role in increasing the entropy and decreasing the dynamic timescale of the neutrino-driven wind. Exploring the wide parameter region that determines the expansion dynamics of the wind, we find interesting physical conditions that lead to successful r-process nucleosynthesis. The conditions that we found are realized in a neutrino-driven wind with a very short dynamic timescale, τdyn~6 ms, and a relatively low entropy, S~140. We carry out α-process and r-process nucleosynthesis calculations on these conditions with our single network code, which includes over 3000 isotopes, and confirm quantitatively that the second and third r-process abundance peaks are produced in neutrino-driven winds.

A semiquantitative general-relativistic model of quasar Markarian 205 interpreted as a massive black hole ejected from NGC 4319

NASA Astrophysics Data System (ADS)

Horak, Z.

1982-09-01

In 1979 I developed a special-relativistic analysis explaining the discrepancy of observed redshifts of spiral NGC 4319 and its companion quasar Markarian 205 by considering besides the Lorentz time dilatation also the gravitational redshift due to the gravitational field of Markarian 205 interpreted in terms of accretion of mass onto a black hole ejected from NGC 4319. In the present paper, a general-relativistic analysis is given. Numerical results of the special and general theories do not differ from each other significantly and admit the conclusion that the radius, r, of the radiating region of Markarian 205 is of the order of the tidal radius of black hole. Several models for various values of the ratio of r to the Schwarzschild radius, r~, are constructed. Models with 8.5 ~ r/r~ ~ 8.7 seem to be most realistic. It becomes clear that the interpretation of quasars in terms of huge black holes accreting stars can explain, in principle, the observed redshifts of quasars ejected from parent galaxies

Relativistic magnetic reconnection driven by a moderately intense laser interacting with a micro-plasma-slab

NASA Astrophysics Data System (ADS)

Yi, Longqing; Shen, Baifei; Pukhov, Alexander; Fülöp, Tünde

2017-10-01

Magnetic reconnection (MR) in the relativistic regime is generally thought to be responsible for powering rapid bursts of non-thermal radiation in astrophysical events. It is therefore of significant importance to study how the field energy is transferred to the plasma to power the observed emission. However, due to the difficulty in making direct measurements in astrophysical systems or achieving relativistic MR in laboratory environments, the particle acceleration is usually studied using fully kinetic PIC simulations. Here we present a numerical study of a readily available (TW-mJ-class) laser interacting with a micro-scale plasma slab. The simulations show when the electron beams excited on both sides of the slab approach the end of the plasma structure, ultrafast relativistic MR occurs. As the field topology changes, the explosive release of magnetic energy results in emission of relativistic electron jets with cut-off energy 12 MeV. The proposed novel scenario can be straightforwardly implemented in experiments, and might significantly improve the understanding of fundamental questions such as field dissipation and particle acceleration in relativistic MR. This work is supported by the Knut and Alice Wallenberg Foundation and the European Research Council (ERC-2014-CoG Grant 64712).

Bivelocity Picture in the Nonrelativistic Limit of Relativistic Hydrodynamics

NASA Astrophysics Data System (ADS)

Koide, Tomoi; Ramos, Rudnei O.; Vicente, Gustavo S.

2015-02-01

We discuss the nonrelativistic limit of the relativistic Navier-Fourier-Stokes (NFS) theory. The next-to-leading order relativistic corrections to the NFS theory for the Landau-Lifshitz fluid are obtained. While the lowest order truncation of the velocity expansion leads to the usual NFS equations of nonrelativistic fluids, we show that when the next-to-leading order relativistic corrections are included, the equations can be expressed concurrently with two different fluid velocities. One of the fluid velocities is parallel to the conserved charge current (which follows the Eckart definition) and the other one is parallel to the energy current (which follows the Landau-Lifshitz definition). We compare this next-to-leading order relativistic hydrodynamics with bivelocity hydrodynamics, which is one of the generalizations of the NFS theory and is formulated in such a way to include the usual mass velocity and also a new velocity, called the volume velocity. We find that the volume velocity can be identified with the velocity obtained in the Landau-Lifshitz definition. Then, the structure of bivelocity hydrodynamics, which is derived using various nontrivial assumptions, is reproduced in the NFS theory including the next-to-leading order relativistic corrections.

A fully implicit numerical integration of the relativistic particle equation of motion

NASA Astrophysics Data System (ADS)

Pétri, J.

2017-04-01

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithms can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to 9$ , we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three-dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well, as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hwang, Jai-chan; Noh, Hyerim

Special relativistic hydrodynamics with weak gravity has hitherto been unknown in the literature. Whether such an asymmetric combination is possible has been unclear. Here, the hydrodynamic equations with Poisson-type gravity, considering fully relativistic velocity and pressure under the weak gravity and the action-at-a-distance limit, are consistently derived from Einstein’s theory of general relativity. An analysis is made in the maximal slicing, where the Poisson’s equation becomes much simpler than our previous study in the zero-shear gauge. Also presented is the hydrodynamic equations in the first post-Newtonian approximation, now under the general hypersurface condition. Our formulation includes the anisotropic stress.

General-relativistic rotation: Self-gravitating fluid tori in motion around black holes

NASA Astrophysics Data System (ADS)

Karkowski, Janusz; Kulczycki, Wojciech; Mach, Patryk; Malec, Edward; Odrzywołek, Andrzej; Piróg, Michał

2018-05-01

We obtain from the first principles a general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. This is an extension of a former rotation law that was designed mainly for toroids around spinless black holes. We integrate numerically axial stationary Einstein equations with self-gravitating disks around spinless or spinning black holes; that includes the first ever integration of the Keplerian selfgravitating tori. This construction can be used for the description of tight black hole-torus systems produced during coalescences of two neutron stars or modelling of compact active galactic nuclei.

Nonextensive kinetic theory and H-theorem in general relativity

NASA Astrophysics Data System (ADS)

Santos, A. P.; Silva, R.; Alcaniz, J. S.; Lima, J. A. S.

2017-11-01

The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [ 0 , 2 ] . As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.

Narrow-Line Seyfert 1 Galaxies and their place in the Universe

NASA Astrophysics Data System (ADS)

Foschini, L.; Colpi, M.; Gallo, L.; Grupe, D.; Komossa, S.; Leighly, K.; Mathur, S.

In 1978, Davidson and Kinman wrote about Markarian 359: "This unusual object merits further observations...". In 1985, Osterbrock and Pogge defined a new class of active galactic nuclei (AGN), named Narrow-Line Seyfert 1 (NLS1). Twenty-five years later, NLS1s still continue to intrigue and bewilder. NLS1s manifest extreme behaviour at all wavelengths. They exhibit the most extreme X-ray variability seen in radio-quiet AGN, the most intense optical FeII emission, and high rates of star formation. In general, their characteristics are consistent of AGNs with relatively low mass black holes accreting close to the Eddington rate. The 2009 Fermi Gamma-ray Space Telescope discovery of high-energy (E>100 MeV) gamma rays in a handful of NLS1s has established the existence of relativistic jets in these systems -- a fact previously hinted at by the flat radio spectrum and high brightness temperature seen in some objects. Since NLS1 are generally hosted by spirals, this poses some intriguing questions on the galaxy evolution and on how relativistic jets are generated. It is therefore time for the broad community to come together and discuss what we have discovered in the last quarter century and lay the foundation for future work. Workshop Topics: * Central engine: BH mass, accretion disk, BLR/NLR, jet * Host galaxy: morphology, star formation, merging history * NLS1 in the Universe: comparison with other types of AGN, surveys/statistics, formation/merging, cosmological evolution

The Duffin-Kemmer-Petiau oscillator

NASA Technical Reports Server (NTRS)

Nedjadi, Youcef; Barrett, Roger

1995-01-01

In view of current interest in relativistic spin-one systems and the recent work on the Dirac Oscillator, we introduce the Duffin-Kemmer-Petiau (DKP) equation obtained by using an external potential linear in r. Since, in the non-relativistic limit, the spin 1 representation leads to a harmonic oscillator with a spin-orbit coupling of the Thomas form, we call the equation the DKP oscillator. This oscillator is a relativistic generalization of the quantum harmonic oscillator for scalar and vector bosons. We show that it conserves total angular momentum and that it is exactly solvable. We calculate and discuss the eigenspectrum of the DKP oscillator in the spin 1 representation.

A relativistic toy model for Unruh black holes

NASA Astrophysics Data System (ADS)

Carbonaro, P.

2014-08-01

We consider the wave propagation in terms of acoustic geometry in a quantum relativistic system. This reduces, in the hydrodynamic limit, to the equations which govern the motion of a relativistic Fermi-degenerate gas in one space dimension. The derivation of an acoustic metric for one-dimensional (1D) systems is in general plagued with the impossibility of defining a conformal factor. Here we show that, although the system is intrinsically one-dimensional, the Unruh procedure continues to work because of the particular structure symmetry of the model. By analyzing the dispersion relation, attention is also paid to the quantum effects on the wave propagation.

On the multistream approach of relativistic Weibel instability. II. Bernstein-Greene-Kruskal-type waves in magnetic trapping

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghizzo, A.

2013-08-15

The stationary state with magnetically trapped particles is investigated at the saturation of the relativistic Weibel instability, within the “multiring” model in a Hamiltonian framework. The multistream model and its multiring extension have been developed in Paper I, under the assumption that the generalized canonical momentum is conserved in the perpendicular direction. One dimensional relativistic Bernstein-Greene-Kruskal waves with deeply trapped particles are addressed using similar mathematical formalism developed by Lontano et al.[Phys. Plasmas 9, 2562 (2002); Phys. Plasmas 10, 639 (2003)] using several streams and in the presence of both electrostatic and magnetic trapping mechanisms.

Gauge Fields in Homogeneous and Inhomogeneous Cosmologies

NASA Astrophysics Data System (ADS)

Darian, Bahman K.

Despite its formidable appearance, the study of classical Yang-Mills (YM) fields on homogeneous cosmologies is amenable to a formal treatment. This dissertation is a report on a systematic approach to the general construction of invariant YM fields on homogeneous cosmologies undertaken for the first time in this context. This construction is subsequently followed by the investigation of the behavior of YM field variables for the most simple of self-gravitating YM fields. Particularly interesting was a dynamical system analysis and the discovery of chaotic signature in the axially symmetric Bianchi I-YM cosmology. Homogeneous YM fields are well studied and are known to have chaotic properties. The chaotic behavior of YM field variables in homogeneous cosmologies might eventually lead to an invariant definition of chaos in (general) relativistic cosmological models. By choosing the gauge fields to be Abelian, the construction and the field equations presented so far reduce to that of electromagnetic field in homogeneous cosmologies. A perturbative analysis of gravitationally interacting electromagnetic and scalar fields in inhomogeneous cosmologies is performed via the Hamilton-Jacobi formulation of general relativity. An essential feature of this analysis is the spatial gradient expansion of the generating functional (Hamilton principal function) to solve the Hamiltonian constraint. Perturbations of a spatially flat Friedman-Robertson-Walker cosmology with an exponential potential for the scalar field are presented.

Small collision systems: Theory overview on cold nuclear matter effects

NASA Astrophysics Data System (ADS)

Armesto, Néstor

2018-02-01

Many observables measured at the Relativistic Heavy Ion Collider and the Large Hadron Collider show a smooth transition between proton-proton and protonnucleus collisions (small systems), and nucleus-nucleus collisions (large systems), when represented versus some variable like the multiplicity in the event. In this contribution I review some of the physics mechanisms, named cold nuclear matter effects, that may lead to a collective-like behaviour in small systems beyond the macroscopic description provided by relativistic hydrodynamics. I focus on the nuclear modification of parton densities, single inclusive particle production and correlations.

Numerical implementation of equations for photon motion in Kerr spacetime

NASA Astrophysics Data System (ADS)

Bursa, Michal

2017-12-01

Raytracing is one of the essential tools for accurate modeling of spectra and variability of various astrophysical objects. It has a major importance in relativistic environments, where light endures to a number of relativistic effects. Because the trajectories of light rays in curved spacetimes, and in Kerr spacetime in particular, are highly non-trivial, we summarize the equations governing the motion of photon (or any other zero rest mass particle) and give analytic solution of the equations that can be further used in practical computer implementations.

Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

NASA Astrophysics Data System (ADS)

Dvoeglazov, V. V.

Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric tensor fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the quantum field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric tensor of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.

Stationary equatorial MHD flows in general relativity

NASA Astrophysics Data System (ADS)

Daigne, F.; Drenkhahn, G.

2002-01-01

We derive a new formulation of the fully general relativistic equations describing a stationary equatorial MHD outflow from a rotating central object. The wind solution appears as a level contour of a ``Bernoulli'' function fixed by the requirements that it must pass through the slow and fast critical points. This approach is the general relativistic extension to the classical treatment of Sakurai (\\cite{sakurai:85}). We discuss in details how the efficiency of the magnetic to kinetic energy conversion depends mainly on the geometry of the flux tubes and show that the magnetic acceleration can work very well under some conditions. We show how this tool can be used for the study of several astrophysical phenomena, among which gamma-ray bursts.

Generating perfect fluid spheres in general relativity

NASA Astrophysics Data System (ADS)

Boonserm, Petarpa; Visser, Matt; Weinfurtner, Silke

2005-06-01

Ever since Karl Schwarzschild’s 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star—a static spherically symmetric blob of fluid with position-independent density—the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.

Solution of Supplee's submarine paradox through special and general relativity

NASA Astrophysics Data System (ADS)

Vieira, R. S.

2016-12-01

In 1989 Supplee described an apparent relativistic paradox on which a submarine seems to sink to observers at rest within the ocean, but it rather seems to float in the submarine proper frame. In this letter, we show that the paradox arises from a misuse of the Archimedes principle in the relativistic case. Considering first the special relativity, we show that any relativistic force field can be written in the Lorentz form, so that it can always be decomposed into a static (electric-like) and a dynamic (magnetic-like) part. These gravitomagnetic effects provide a relativistic formulation of Archimedes principle, from which the paradox is explained. Besides, if the curved spacetime on the vicinity of the Earth is taken into account, we show that the gravitational force exerted by the Earth on a moving body must increase with the speed of the body. The submarine paradox is then analyzed again with this speed-dependent gravitational force.

Relativistic elliptic matrix tops and finite Fourier transformations

NASA Astrophysics Data System (ADS)

Zotov, A.

2017-10-01

We consider a family of classical elliptic integrable systems including (relativistic) tops and their matrix extensions of different types. These models can be obtained from the “off-shell” Lax pairs, which do not satisfy the Lax equations in general case but become true Lax pairs under various conditions (reductions). At the level of the off-shell Lax matrix, there is a natural symmetry between the spectral parameter z and relativistic parameter η. It is generated by the finite Fourier transformation, which we describe in detail. The symmetry allows one to consider z and η on an equal footing. Depending on the type of integrable reduction, any of the parameters can be chosen to be the spectral one. Then another one is the relativistic deformation parameter. As a by-product, we describe the model of N2 interacting GL(M) matrix tops and/or M2 interacting GL(N) matrix tops depending on a choice of the spectral parameter.

Application of Central Upwind Scheme for Solving Special Relativistic Hydrodynamic Equations

PubMed Central

Yousaf, Muhammad; Ghaffar, Tayabia; Qamar, Shamsul

2015-01-01

The accurate modeling of various features in high energy astrophysical scenarios requires the solution of the Einstein equations together with those of special relativistic hydrodynamics (SRHD). Such models are more complicated than the non-relativistic ones due to the nonlinear relations between the conserved and state variables. A high-resolution shock-capturing central upwind scheme is implemented to solve the given set of equations. The proposed technique uses the precise information of local propagation speeds to avoid the excessive numerical diffusion. The second order accuracy of the scheme is obtained with the use of MUSCL-type initial reconstruction and Runge-Kutta time stepping method. After a discussion of the equations solved and of the techniques employed, a series of one and two-dimensional test problems are carried out. To validate the method and assess its accuracy, the staggered central and the kinetic flux-vector splitting schemes are also applied to the same model. The scheme is robust and efficient. Its results are comparable to those obtained from the sophisticated algorithms, even in the case of highly relativistic two-dimensional test problems. PMID:26070067

Computerized series solution of relativistic equations of motion.

NASA Technical Reports Server (NTRS)

Broucke, R.

1971-01-01

A method of solution of the equations of planetary motion is described. It consists of the use of numerical general perturbations in orbital elements and in rectangular coordinates. The solution is expanded in Fourier series in the mean anomaly with the aid of harmonic analysis and computerized series manipulation techniques. A detailed application to the relativistic motion of the planet Mercury is described both for Schwarzschild and isotropic coordinates.

Influence of the geometric configuration of accretion flow on the black hole spin dependence of relativistic acoustic geometry

NASA Astrophysics Data System (ADS)

Tarafdar, Pratik; Das, Tapas K.

Linear perturbation of general relativistic accretion of low angular momentum hydrodynamic fluid onto a Kerr black hole leads to the formation of curved acoustic geometry embedded within the background flow. Characteristic features of such sonic geometry depend on the black hole spin. Such dependence can be probed by studying the correlation of the acoustic surface gravity κ with the Kerr parameter a. The κ-a relationship further gets influenced by the geometric configuration of the accretion flow structure. In this work, such influence has been studied for multitransonic shocked accretion where linear perturbation of general relativistic flow profile leads to the formation of two analogue black hole-type horizons formed at the sonic points and one analogue white hole-type horizon which is formed at the shock location producing divergent acoustic surface gravity. Dependence of the κ-a relationship on the geometric configuration has also been studied for monotransonic accretion, over the entire span of the Kerr parameter including retrograde flow. For accreting astrophysical black holes, the present work thus investigates how the salient features of the embedded relativistic sonic geometry may be determined not only by the background spacetime, but also by the flow configuration of the embedding matter.

The lifespan of 3D radial solutions to the non-isentropic relativistic Euler equations

NASA Astrophysics Data System (ADS)

Wei, Changhua

2017-10-01

This paper investigates the lower bound of the lifespan of three-dimensional spherically symmetric solutions to the non-isentropic relativistic Euler equations, when the initial data are prescribed as a small perturbation with compact support to a constant state. Based on the structure of the hyperbolic system, we show the almost global existence of the smooth solutions to Eulerian flows (polytropic gases and generalized Chaplygin gases) with genuinely nonlinear characteristics. While for the Eulerian flows (Chaplygin gas and stiff matter) with mild linearly degenerate characteristics, we show the global existence of the radial solutions, moreover, for the non-strictly hyperbolic system (pressureless perfect fluid) satisfying the mild linearly degenerate condition, we prove the blowup phenomenon of the radial solutions and show that the lifespan of the solutions is of order O(ɛ ^{-1}), where ɛ denotes the width of the perturbation. This work can be seen as a complement of our work (Lei and Wei in Math Ann 367:1363-1401, 2017) for relativistic Chaplygin gas and can also be seen as a generalization of the classical Eulerian fluids (Godin in Arch Ration Mech Anal 177:497-511, 2005, J Math Pures Appl 87:91-117, 2007) to the relativistic Eulerian fluids.

Simulations of recoiling black holes: adaptive mesh refinement and radiative transfer

NASA Astrophysics Data System (ADS)

Meliani, Zakaria; Mizuno, Yosuke; Olivares, Hector; Porth, Oliver; Rezzolla, Luciano; Younsi, Ziri

2017-02-01

Context. In many astrophysical phenomena, and especially in those that involve the high-energy regimes that always accompany the astronomical phenomenology of black holes and neutron stars, physical conditions that are achieved are extreme in terms of speeds, temperatures, and gravitational fields. In such relativistic regimes, numerical calculations are the only tool to accurately model the dynamics of the flows and the transport of radiation in the accreting matter. Aims: We here continue our effort of modelling the behaviour of matter when it orbits or is accreted onto a generic black hole by developing a new numerical code that employs advanced techniques geared towards solving the equations of general-relativistic hydrodynamics. Methods: More specifically, the new code employs a number of high-resolution shock-capturing Riemann solvers and reconstruction algorithms, exploiting the enhanced accuracy and the reduced computational cost of adaptive mesh-refinement (AMR) techniques. In addition, the code makes use of sophisticated ray-tracing libraries that, coupled with general-relativistic radiation-transfer calculations, allow us to accurately compute the electromagnetic emissions from such accretion flows. Results: We validate the new code by presenting an extensive series of stationary accretion flows either in spherical or axial symmetry that are performed either in two or three spatial dimensions. In addition, we consider the highly nonlinear scenario of a recoiling black hole produced in the merger of a supermassive black-hole binary interacting with the surrounding circumbinary disc. In this way, we can present for the first time ray-traced images of the shocked fluid and the light curve resulting from consistent general-relativistic radiation-transport calculations from this process. Conclusions: The work presented here lays the ground for the development of a generic computational infrastructure employing AMR techniques to accurately and self-consistently calculate general-relativistic accretion flows onto compact objects. In addition to the accurate handling of the matter, we provide a self-consistent electromagnetic emission from these scenarios by solving the associated radiative-transfer problem. While magnetic fields are currently excluded from our analysis, the tools presented here can have a number of applications to study accretion flows onto black holes or neutron stars.

Fast Variability and Millimeter/IR Flares in GRMHD Models of Sgr A* from Strong-field Gravitational Lensing

NASA Astrophysics Data System (ADS)

Chan, Chi-kwan; Psaltis, Dimitrios; Özel, Feryal; Medeiros, Lia; Marrone, Daniel; Saḑowski, Aleksander; Narayan, Ramesh

2015-10-01

We explore the variability properties of long, high-cadence general relativistic magnetohydrodynamic (GRMHD) simulations across the electromagnetic spectrum using an efficient, GPU-based radiative transfer algorithm. We focus on both standard and normal evolution (SANE) and magnetically arrested disk (MAD) simulations with parameters that successfully reproduce the time-averaged spectral properties of Sgr A* and the size of its image at 1.3 mm. We find that the SANE models produce short-timescale variability with amplitudes and power spectra that closely resemble those inferred observationally. In contrast, MAD models generate only slow variability at lower flux levels. Neither set of models shows any X-ray flares, which most likely indicates that additional physics, such as particle acceleration mechanisms, need to be incorporated into the GRMHD simulations to account for them. The SANE models show strong, short-lived millimeter/infrared (IR) flares, with short (≲1 hr) time lags between the millimeter and IR wavelengths, that arise from the combination of short-lived magnetic flux tubes and strong-field gravitational lensing near the horizon. Such events provide a natural explanation for the observed IR flares with no X-ray counterparts.

FAST VARIABILITY AND MILLIMETER/IR FLARES IN GRMHD MODELS OF Sgr A* FROM STRONG-FIELD GRAVITATIONAL LENSING

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chan, Chi-kwan; Psaltis, Dimitrios; Özel, Feryal

2015-10-20

We explore the variability properties of long, high-cadence general relativistic magnetohydrodynamic (GRMHD) simulations across the electromagnetic spectrum using an efficient, GPU-based radiative transfer algorithm. We focus on both standard and normal evolution (SANE) and magnetically arrested disk (MAD) simulations with parameters that successfully reproduce the time-averaged spectral properties of Sgr A* and the size of its image at 1.3 mm. We find that the SANE models produce short-timescale variability with amplitudes and power spectra that closely resemble those inferred observationally. In contrast, MAD models generate only slow variability at lower flux levels. Neither set of models shows any X-ray flares,more » which most likely indicates that additional physics, such as particle acceleration mechanisms, need to be incorporated into the GRMHD simulations to account for them. The SANE models show strong, short-lived millimeter/infrared (IR) flares, with short (≲1 hr) time lags between the millimeter and IR wavelengths, that arise from the combination of short-lived magnetic flux tubes and strong-field gravitational lensing near the horizon. Such events provide a natural explanation for the observed IR flares with no X-ray counterparts.« less

CosmosDG: An hp -adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anninos, Peter; Lau, Cheuk; Bryant, Colton

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge–Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performedmore » separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.« less

CosmosDG: An hp-adaptive Discontinuous Galerkin Code for Hyper-resolved Relativistic MHD

NASA Astrophysics Data System (ADS)

Anninos, Peter; Bryant, Colton; Fragile, P. Chris; Holgado, A. Miguel; Lau, Cheuk; Nemergut, Daniel

2017-08-01

We have extended Cosmos++, a multidimensional unstructured adaptive mesh code for solving the covariant Newtonian and general relativistic radiation magnetohydrodynamic (MHD) equations, to accommodate both discrete finite volume and arbitrarily high-order finite element structures. The new finite element implementation, called CosmosDG, is based on a discontinuous Galerkin (DG) formulation, using both entropy-based artificial viscosity and slope limiting procedures for the regularization of shocks. High-order multistage forward Euler and strong-stability preserving Runge-Kutta time integration options complement high-order spatial discretization. We have also added flexibility in the code infrastructure allowing for both adaptive mesh and adaptive basis order refinement to be performed separately or simultaneously in a local (cell-by-cell) manner. We discuss in this report the DG formulation and present tests demonstrating the robustness, accuracy, and convergence of our numerical methods applied to special and general relativistic MHD, although we note that an equivalent capability currently also exists in CosmosDG for Newtonian systems.

Relativistic effects in the double S- and P-wave charmonium production in e{sup +}e{sup -} annihilation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Elekina, E. N.; Martynenko, A. P.

2010-03-01

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the pair production of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and P-wave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy {radical}(s) up to the secondmore » order. The relativistic treatment of the wave functions makes all such second order terms convergent, thus allowing the reliable calculation of their contributions to the production cross section. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the QCD generalization of the standard Breit potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the reaction e{sup +}+e{sup -{yields}}J/{Psi}({eta}{sub c})+{chi}{sub cJ}(h{sub c}) at the center-of-mass energy {radical}(s)=10.6 GeV.« less

General relativistic corrections in density-shear correlations

NASA Astrophysics Data System (ADS)

Ghosh, Basundhara; Durrer, Ruth; Sellentin, Elena

2018-06-01

We investigate the corrections which relativistic light-cone computations induce on the correlation of the tangential shear with galaxy number counts, also known as galaxy-galaxy lensing. The standard-approach to galaxy-galaxy lensing treats the number density of sources in a foreground bin as observable, whereas it is in reality unobservable due to the presence of relativistic corrections. We find that already in the redshift range covered by the DES first year data, these currently neglected relativistic terms lead to a systematic correction of up to 50% in the density-shear correlation function for the highest redshift bins. This correction is dominated by the fact that a redshift bin of number counts does not only lens sources in a background bin, but is itself again lensed by all masses between the observer and the counted source population. Relativistic corrections are currently ignored in the standard galaxy-galaxy analyses, and the additional lensing of a counted source populations is only included in the error budget (via the covariance matrix). At increasingly higher redshifts and larger scales, these relativistic and lensing corrections become however increasingly more important, and we here argue that it is then more efficient, and also cleaner, to account for these corrections in the density-shear correlations.

Self-gravitating axially symmetric disks in general-relativistic rotation

NASA Astrophysics Data System (ADS)

Karkowski, Janusz; Kulczycki, Wojciech; Mach, Patryk; Malec, Edward; Odrzywołek, Andrzej; Piróg, Michał

2018-05-01

We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata, but contains important new ingredients. We derive a new general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. Former results concerning rotation around spinless black holes emerge in the limit of a vanishing spin parameter. These rotation curves might be used for the description of rotating stars, after appropriate modification around the symmetry axis. They can be applied to the description of compact torus-black hole configurations, including active galactic nuclei or products of coalescences of two neutron stars.

General relativistic spectra of accretion discs around rapidly rotating neutron stars: effect of light bending

NASA Astrophysics Data System (ADS)

Bhattacharyya, Sudip; Bhattacharya, Dipankar; Thampan, Arun V.

2001-08-01

We present computed spectra, as seen by a distant observer, from the accretion disc around a rapidly rotating neutron star. Our calculations are carried out in a fully general relativistic framework, with an exact treatment of rotation. We take into account the Doppler shift, gravitational redshift and light-bending effects in order to compute the observed spectrum. We find that light bending significantly modifies the high-energy part of the spectrum. Computed spectra for slowly rotating neutron stars are also presented. These results would be important for modelling the observed X-ray spectra of low-mass X-ray binaries containing fast-spinning neutron stars.

Lagrangian theory of structure formation in relativistic cosmology. IV. Lagrangian approach to gravitational waves

NASA Astrophysics Data System (ADS)

Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander

2017-12-01

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of Lagrangian-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the Lagrangian perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to Eulerian background coordinates with truncation of nonlinear terms.

Estimation of mass outflow rates from viscous relativistic accretion discs around black holes

NASA Astrophysics Data System (ADS)

Chattopadhyay, Indranil; Kumar, Rajiv

2016-07-01

We investigated flow in Schwarzschild metric, around a non-rotating black hole and obtained self-consistent accretion-ejection solution in full general relativity. We covered the whole of parameter space in the advective regime to obtain shocked, as well as, shock-free accretion solution. We computed the jet streamline using von Zeipel surfaces and projected the jet equations of motion on to the streamline and solved them simultaneously with the accretion disc equations of motion. We found that steady shock cannot exist beyond α ≳ 0.06 in the general relativistic prescription, but is lower if mass-loss is considered too. We showed that for fixed outer boundary, the shock moves closer to the horizon with increasing viscosity parameter. The mass outflow rate increases as the shock moves closer to the black hole, but eventually decreases, maximizing at some intermediate value of shock location. The jet terminal speed increases with stronger shocks; quantitatively speaking, the terminal speed of jets vj∞ > 0.1 if rsh < 20rg. The maximum of the outflow rate obtained in the general relativistic regime is less than 6 per cent of the mass accretion rate.

Some classes of gravitational shock waves from higher order theories of gravity

NASA Astrophysics Data System (ADS)

Oikonomou, V. K.

2017-02-01

We study the gravitational shock wave generated by a massless high energy particle in the context of higher order gravities of the form F(R,R_{μν}R^{μν},R_{μναβ}R^{μν αβ}). In the case of F(R) gravity, we investigate the gravitational shock wave solutions corresponding to various cosmologically viable gravities, and as we demonstrate the solutions are rescaled versions of the Einstein-Hilbert gravity solution. Interestingly enough, other higher order gravities result to the general relativistic solution, except for some specific gravities of the form F(R_{μν}R^{μν}) and F(R,R_{μν}R^{μν}), which we study in detail. In addition, when realistic Gauss-Bonnet gravities of the form R+F(G) are considered, the gravitational shock wave solutions are identical to the general relativistic solution. Finally, the singularity structure of the gravitational shock waves solutions is studied, and it is shown that the effect of higher order gravities makes the singularities milder in comparison to the general relativistic solutions, and in some particular cases the singularities seem to be absent.

Hyperscaling-violating Lifshitz hydrodynamics from black-holes: part II

NASA Astrophysics Data System (ADS)

Kiritsis, Elias; Matsuo, Yoshinori

2017-03-01

The derivation of Lifshitz-invariant hydrodynamics from holography, presented in [1] is generalized to arbitrary hyperscaling violating Lifshitz scaling theories with an unbroken U(1) symmetry. The hydrodynamics emerging is non-relativistic with scalar "forcing". By a redefinition of the pressure it becomes standard non-relativistic hydrodynamics in the presence of specific chemical potential for the mass current. The hydrodynamics is compatible with the scaling theory of Lifshitz invariance with hyperscaling violation. The bulk viscosity vanishes while the shear viscosity to entropy ratio is the same as in the relativistic case. We also consider the dimensional reduction ansatz for the hydrodynamics and clarify the difference with previous results suggesting a non-vanishing bulk viscosity.

HEROIC: 3D general relativistic radiative post-processor with comptonization for black hole accretion discs

NASA Astrophysics Data System (ADS)

Narayan, Ramesh; Zhu, Yucong; Psaltis, Dimitrios; Saḑowski, Aleksander

2016-03-01

We describe Hybrid Evaluator for Radiative Objects Including Comptonization (HEROIC), an upgraded version of the relativistic radiative post-processor code HERO described in a previous paper, but which now Includes Comptonization. HEROIC models Comptonization via the Kompaneets equation, using a quadratic approximation for the source function in a short characteristics radiation solver. It employs a simple form of accelerated lambda iteration to handle regions of high scattering opacity. In addition to solving for the radiation field, HEROIC also solves for the gas temperature by applying the condition of radiative equilibrium. We present benchmarks and tests of the Comptonization module in HEROIC with simple 1D and 3D scattering problems. We also test the ability of the code to handle various relativistic effects using model atmospheres and accretion flows in a black hole space-time. We present two applications of HEROIC to general relativistic magnetohydrodynamics simulations of accretion discs. One application is to a thin accretion disc around a black hole. We find that the gas below the photosphere in the multidimensional HEROIC solution is nearly isothermal, quite different from previous solutions based on 1D plane parallel atmospheres. The second application is to a geometrically thick radiation-dominated accretion disc accreting at 11 times the Eddington rate. Here, the multidimensional HEROIC solution shows that, for observers who are on axis and look down the polar funnel, the isotropic equivalent luminosity could be more than 10 times the Eddington limit, even though the spectrum might still look thermal and show no signs of relativistic beaming.

General relativistic screening in cosmological simulations

NASA Astrophysics Data System (ADS)

Hahn, Oliver; Paranjape, Aseem

2016-10-01

We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large-scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential ψ that lead on large scales to the correct, fully relativistic description of density perturbations in the Newtonian gauge. We note that the relativistic constraint equation for ψ can be cast as a diffusion equation, with a diffusion length scale determined by the expansion of the Universe. Exploiting the weak time evolution of ψ in all regimes of interest, this equation can be further accurately approximated as a Helmholtz equation, with an effective relativistic "screening" scale ℓ related to the Hubble radius. We demonstrate that it is thus possible to carry out N-body simulations in the Newtonian gauge by replacing Poisson's equation with this Helmholtz equation, involving a trivial change in the Green's function kernel. Our results also motivate a simple, approximate (but very accurate) gauge transformation—δN(k )≈δsim(k )×(k2+ℓ-2)/k2 —to convert the density field δsim of standard collisionless N -body simulations (initialized in the comoving synchronous gauge) into the Newtonian gauge density δN at arbitrary times. A similar conversion can also be written in terms of particle positions. Our results can be interpreted in terms of a Jeans stability criterion induced by the expansion of the Universe. The appearance of the screening scale ℓ in the evolution of ψ , in particular, leads to a natural resolution of the "Jeans swindle" in the presence of superhorizon modes.

Compact stars in the braneworld: A new branch of stellar configurations with arbitrarily large mass

NASA Astrophysics Data System (ADS)

Lugones, Germán; Arbañil, José D. V.

2017-03-01

We study the properties of compact stars in the Randall-Sundrum type-II braneworld (BW) model. To this end, we solve the braneworld generalization of the stellar structure equations for a static fluid distribution with spherical symmetry considering that the spacetime outside the star is described by a Schwarzschild metric. First, the stellar structure equations are integrated employing the so-called causal limit equation of state (EOS), which is constructed using a well-established EOS at densities below a fiducial density, and the causal EOS P =ρ above it. It is a standard procedure in general relativistic stellar structure calculations to use such EOSs for obtaining a limit in the mass radius diagram, known as the causal limit, above which no stellar configurations are possible if the EOS fulfills the condition that the sound velocity is smaller than the speed of light. We find that the equilibrium solutions in the braneworld model can violate the general relativistic causal limit, and for sufficiently large mass they approach asymptotically to the Schwarzschild limit M =2 R . Then, we investigate the properties of hadronic and strange quark stars using two typical EOSs: a nonlinear relativistic mean-field model for hadronic matter and the Massachusetts Institute of Technology (MIT) bag model for quark matter. For masses below ˜1.5 M⊙- 2 M⊙ , the mass versus radius curves show the typical behavior found within the frame of general relativity. However, we also find a new branch of stellar configurations that can violate the general relativistic causal limit and that, in principle, may have an arbitrarily large mass. The stars belonging to this new branch are supported against collapse by the nonlocal effects of the bulk on the brane. We also show that these stars are always stable under small radial perturbations. These results support the idea that traces of extra dimensions might be found in astrophysics, specifically through the analysis of masses and radii of compact objects.

Absolute NMR shielding scales and nuclear spin–rotation constants in {sup 175}LuX and {sup 197}AuX (X = {sup 19}F, {sup 35}Cl, {sup 79}Br and {sup 127}I)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Demissie, Taye B., E-mail: taye.b.demissie@uit.no; Komorovsky, Stanislav; Repisky, Michal

2015-10-28

We present nuclear spin–rotation constants, absolute nuclear magnetic resonance (NMR) shielding constants, and shielding spans of all the nuclei in {sup 175}LuX and {sup 197}AuX (X = {sup 19}F, {sup 35}Cl, {sup 79}Br, {sup 127}I), calculated using coupled-cluster singles-and-doubles with a perturbative triples (CCSD(T)) correction theory, four-component relativistic density functional theory (relativistic DFT), and non-relativistic DFT. The total nuclear spin–rotation constants determined by adding the relativistic corrections obtained from DFT calculations to the CCSD(T) values are in general in agreement with available experimental data, indicating that the computational approach followed in this study allows us to predict reliable results formore » the unknown spin–rotation constants in these molecules. The total NMR absolute shielding constants are determined for all the nuclei following the same approach as that applied for the nuclear spin–rotation constants. In most of the molecules, relativistic effects significantly change the computed shielding constants, demonstrating that straightforward application of the non-relativistic formula relating the electronic contribution to the nuclear spin–rotation constants and the paramagnetic contribution to the shielding constants does not yield correct results. We also analyze the origin of the unusually large absolute shielding constant and its relativistic correction of gold in AuF compared to the other gold monohalides.« less

Effect of EMIC Wave Normal Angle Distribution on Relativistic Electron Scattering

NASA Technical Reports Server (NTRS)

Gamayunov, K. V.; Khazanov, G. V.

2006-01-01

The flux level of outer-zone relativistic electrons (above 1 MeV) is extremely variable during geomagnetic storms, and controlled by a competition between acceleration and loss. Precipitation of these electrons due to resonant pitch-angle scattering by electromagnetic ion cyclotron (EMIC) waves is considered one of the major loss mechanisms. This mechanism was suggested in early theoretical studies more than three decades ago. However, direct experimental evidence of the wave role in relativistic electrons precipitation is difficult to obtain because of lack of concurrent measurements of precipitating electrons at low altitudes and the waves in a magnetically conjugate equatorial region. Recently, the data from balloon-borne X-ray instruments provided indirect but strong evidence on an efficiency of the EMIC wave induced loss for the outer-zone relativistic electrons. These observations stimulated theoretical studies that, particularly, demonstrated that EMIC wave induced pitch-angle diffusion of MeV electrons can operate in the strong diffusion limit and this mechanism can compete with relativistic electron depletion caused by the Dst effect during the initial and main phases of storm. Although an effectiveness of relativistic electron scattering by EMIC waves depends strongly on the wave spectral properties, the most favorable assumptions regarding wave characteristics has been made in all previous theoretical studies. Particularly, only quasi field-aligned EMIC waves have been considered as a driver for relativistic electron loss. At the same time, there is growing experimental and theoretical evidence that these waves can be highly oblique; EMIC wave energy can occupy not only the region of generation, i.e. the region of small wave normal angles, but also the entire wave normal angle region, and even only the region near 90 degrees. The latter can dramatically change he effectiveness of relativistic electron scattering by EMIC waves. In the present study, we calculate the pitch-angle diffusion coefficients using the typical wave normal distributions obtained from our self-consistent ring current-EMIC wave model, and try to quantify the effect of EMIC wave normal angle characteristics on relativistic electron scattering.

General-relativistic Simulations of Four States of Accretion onto Millisecond Pulsars

NASA Astrophysics Data System (ADS)

Parfrey, Kyle; Tchekhovskoy, Alexander

2017-12-01

Accreting neutron stars can power a wide range of astrophysical phenomena including short- and long-duration gamma-ray bursts, ultra-luminous X-ray sources, and X-ray binaries. Numerical simulations are a valuable tool for studying the accretion-disk–magnetosphere interaction that is central to these problems, most clearly for the recently discovered transitional millisecond pulsars. However, magnetohydrodynamic (MHD) methods, widely used for simulating accretion, have difficulty in highly magnetized stellar magnetospheres, while force-free methods, suitable for such regions, cannot include the accreting gas. We present an MHD method that can stably evolve essentially force-free, highly magnetized regions, and describe the first time-dependent relativistic simulations of magnetized accretion onto millisecond pulsars. Our axisymmetric general-relativistic MHD simulations for the first time demonstrate how the interaction of a turbulent accretion flow with a pulsar’s electromagnetic wind can lead to the transition of an isolated pulsar to the accreting state. This transition naturally leads to the formation of relativistic jets, whose power can greatly exceed the power of the isolated pulsar’s wind. If the accretion rate is below a critical value, the pulsar instead expels the accretion stream. More generally, our simulations produce for the first time the four possible accretion regimes, in order of decreasing mass accretion rate: (a) crushed magnetosphere and direct accretion; (b) magnetically channeled accretion onto the stellar poles; (c) the propeller state, where material enters through the light cylinder but is prevented from accreting by the centrifugal barrier; (d) almost perfect exclusion of the accretion flow from the light cylinder by the pulsar wind.

Relativistic Jets on all Scales in Accreting Black Holes: Contributions from Simbol-X

NASA Astrophysics Data System (ADS)

Corbel, Stéphane

2009-05-01

In the last several years, multiwavelength observations of accreting black holes have allowed a general characterisation of black holes properties as they evolve along the course of their outburst cycles. Relativistic jets, in their multiple forms, have profoundly impacted our perception and understanding of emission processes in these systems. In these Proceedings, I will highlight some possible contributions from Simbol-X related to jets in accreting sources.

Relativistic sonic geometry for isothermal accretion in the Kerr metric

NASA Astrophysics Data System (ADS)

Arif Shaikh, Md

2018-03-01

We linearly perturb advective isothermal transonic accretion onto rotating astrophysical black holes to study the emergence of the relativistic acoustic spacetime and to investigate how the salient features of this spacetime is influenced by the spin angular momentum of the black hole. We have perturbed three different quantities—the velocity potential, the mass accretion rate and the relativistic Bernoulli’s constant to show that the acoustic metric obtained for these three cases are the same up to a conformal factor. By constructing the required causal structures, it has been demonstrated that the acoustic black holes are formed at the transonic points of the flow and the acoustic white holes are formed at the shock location. The corresponding acoustic surface gravity has been computed in terms of the relevant accretion variables and the background metric elements. We have performed a linear stability analysis of the background stationary flow.

Minidisks in Binary Black Hole Accretion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryan, Geoffrey; MacFadyen, Andrew, E-mail: gsr257@nyu.edu

Newtonian simulations have demonstrated that accretion onto binary black holes produces accretion disks around each black hole (“minidisks”), fed by gas streams flowing through the circumbinary cavity from the surrounding circumbinary disk. We study the dynamics and radiation of an individual black hole minidisk using 2D hydrodynamical simulations performed with a new general relativistic version of the moving-mesh code Disco. We introduce a comoving energy variable that enables highly accurate integration of these high Mach number flows. Tidally induced spiral shock waves are excited in the disk and propagate through the innermost stable circular orbit, providing a Reynolds stress thatmore » causes efficient accretion by purely hydrodynamic means and producing a radiative signature brighter in hard X-rays than the Novikov–Thorne model. Disk cooling is provided by a local blackbody prescription that allows the disk to evolve self-consistently to a temperature profile where hydrodynamic heating is balanced by radiative cooling. We find that the spiral shock structure is in agreement with the relativistic dispersion relation for tightly wound linear waves. We measure the shock-induced dissipation and find outward angular momentum transport corresponding to an effective alpha parameter of order 0.01. We perform ray-tracing image calculations from the simulations to produce theoretical minidisk spectra and viewing-angle-dependent images for comparison with observations.« less

Theories of Matter, Space and Time; Classical theories

NASA Astrophysics Data System (ADS)

Evans, N.; King, S. F.

2017-12-01

This book and its sequel ('Theories of Matter Space and Time: Quantum Theories') are taken from third and fourth year undergraduate Physics courses at Southampton University, UK. The aim of both books is to move beyond the initial courses in classical mechanics, special relativity, electromagnetism, and quantum theory to more sophisticated views of these subjects and their interdependence. The goal is to guide undergraduates through some of the trickier areas of theoretical physics with concise analysis while revealing the key elegance of each subject. The first chapter introduces the key areas of the principle of least action, an alternative treatment of Newtownian dynamics, that provides new understanding of conservation laws. In particular, it shows how the formalism evolved from Fermat's principle of least time in optics. The second introduces special relativity leading quickly to the need and form of four-vectors. It develops four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment; then returns to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again, it then returns to the action principle to formulate minimal substitution for an electrically charged particle.

Theories of Variable Mass Particles and Low Energy Nuclear Phenomena

NASA Astrophysics Data System (ADS)

Davidson, Mark

2014-02-01

Variable particle masses have sometimes been invoked to explain observed anomalies in low energy nuclear reactions (LENR). Such behavior has never been observed directly, and is not considered possible in theoretical nuclear physics. Nevertheless, there are covariant off-mass-shell theories of relativistic particle dynamics, based on works by Fock, Stueckelberg, Feynman, Greenberger, Horwitz, and others. We review some of these and we also consider virtual particles that arise in conventional Feynman diagrams in relativistic field theories. Effective Lagrangian models incorporating variable mass particle theories might be useful in describing anomalous nuclear reactions by combining mass shifts together with resonant tunneling and other effects. A detailed model for resonant fusion in a deuterium molecule with off-shell deuterons and electrons is presented as an example. Experimental means of observing such off-shell behavior directly, if it exists, is proposed and described. Brief explanations for elemental transmutation and formation of micro-craters are also given, and an alternative mechanism for the mass shift in the Widom-Larsen theory is presented. If variable mass theories were to find experimental support from LENR, then they would undoubtedly have important implications for the foundations of quantum mechanics, and practical applications may arise.

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

NASA Astrophysics Data System (ADS)

Wu, Kailiang; Tang, Huazhong

2018-06-01

The paper studies the physical-constraints-preserving (PCP) schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state (EOS) on more general meshes. It is an extension of the work (Wu and Tang in Math. Models Methods Appl. Sci. 27:1871-1928, 2017) which focuses on the ideal EOS and uniform Cartesian meshes. The general EOS without a special expression poses some additional difficulties in discussing the mathematical properties of admissible state set with the physical constraints on the fluid velocity, density and pressure. Rigorous analyses are provided for the PCP property of finite volume or discontinuous Galerkin schemes with the Lax-Friedrichs (LxF)-type flux on a general mesh with non-self-intersecting polytopes. Those are built on a more general form of generalized LxF splitting property and a different convex decomposition technique. It is shown in theory that the PCP property is closely connected with a discrete divergence-free condition, which is proposed on the general mesh and milder than that in Wu and Tang (2017).

CGRO Guest Investigator Program

NASA Technical Reports Server (NTRS)

Begelman, Mitchell C.

1997-01-01

The following are highlights from the research supported by this grant: (1) Theory of gamma-ray blazars: We studied the theory of gamma-ray blazars, being among the first investigators to propose that the GeV emission arises from Comptonization of diffuse radiation surrounding the jet, rather than from the synchrotron-self-Compton mechanism. In related work, we uncovered possible connections between the mechanisms of gamma-ray blazars and those of intraday radio variability, and have conducted a general study of the role of Compton radiation drag on the dynamics of relativistic jets. (2) A Nonlinear Monte Carlo code for gamma-ray spectrum formation: We developed, tested, and applied the first Nonlinear Monte Carlo (NLMC) code for simulating gamma-ray production and transfer under much more general (and realistic) conditions than are accessible with other techniques. The present version of the code is designed to simulate conditions thought to be present in active galactic nuclei and certain types of X-ray binaries, and includes the physics needed to model thermal and nonthermal electron-positron pair cascades. Unlike traditional Monte-Carlo techniques, our method can accurately handle highly non-linear systems in which the radiation and particle backgrounds must be determined self-consistently and in which the particle energies span many orders of magnitude. Unlike models based on kinetic equations, our code can handle arbitrary source geometries and relativistic kinematic effects In its first important application following testing, we showed that popular semi-analytic accretion disk corona models for Seyfert spectra are seriously in error, and demonstrated how the spectra can be simulated if the disk is sparsely covered by localized 'flares'.

General relativistic effects in the structure of massive white dwarfs

NASA Astrophysics Data System (ADS)

Carvalho, G. A.; Marinho, R. M.; Malheiro, M.

2018-04-01

In this work we investigate the structure of white dwarfs using the Tolman-Oppenheimer-Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of general relativity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs (M>1.3M_{⊙ }) are overestimated in comparison with GR outcomes. For a mass of 1.415M_{⊙ } the white dwarf radius predicted by GR is about 33% smaller than the Newtonian one. Hence, in this case, for the surface gravity the difference between the general relativistic and Newtonian outcomes is about 65%. We depict the general relativistic mass-radius diagrams as M/M_{⊙ }=R/(a+bR+cR^2+dR^3+kR^4), where a, b, c and d are parameters obtained from a fitting procedure of the numerical results and k=(2.08× 10^{-6}R_{⊙ })^{-1}, being R_{⊙ } the radius of the Sun in km. Lastly, we point out that GR plays an important role to determine any physical quantity that depends, simultaneously, on the mass and radius of massive white dwarfs.

Interpretation of Mössbauer experiment in a rotating system: A new proof for general relativity

NASA Astrophysics Data System (ADS)

Corda, Christian

2015-04-01

A historical experiment by Kündig on the transverse Doppler shift in a rotating system measured with the Mössbauer effect (Mössbauer rotor experiment) has been recently first re-analyzed and then replied by an experimental research group. The results of re-analyzing the experiment have shown that a correct re-processing of Kündig's experimental data gives an interesting deviation of a relative redshift between emission and absorption resonant lines from the standard prediction based on the relativistic dilatation of time. That prediction gives a redshift ∇E/E ≃ -1/2 v2/c2 where v is the tangential velocity of the absorber of resonant radiation, c is the velocity of light in vacuum and the result is given to the accuracy of first-order in v2/c2. Data re-processing gave ∇E/E ≃ - kv2/c2 with k = 0.596 ± 0.006. Subsequent new experimental results by the reply of Kündig experiment have shown a redshift with k = 0.68 ± 0.03 instead. By using Einstein Equivalence Principle, which states the equivalence between the gravitational "force" and the pseudo-force experienced by an observer in a non-inertial frame of reference (included a rotating frame of reference) here we re-analyze the theoretical framework of Mössbauer rotor experiments directly in the rotating frame of reference by using a general relativistic treatment. It will be shown that previous analyses missed an important effect of clock synchronization and that the correct general relativistic prevision in the rotating frame gives k ≃ 2/3 in perfect agreement with the new experimental results. Such an effect of clock synchronization has been missed in various papers in the literature with some subsequent claim of invalidity of relativity theory and/or some attempts to explain the experimental results through "exotic" effects. Our general relativistic interpretation shows, instead, that the new experimental results of the Mössbauer rotor experiment are a new, strong and independent, proof of Einstein general relativity. In the final section of the paper we discuss an analogy with the use of General Relativity in Global Positioning Systems.

Relativistic diffusion processes and random walk models

NASA Astrophysics Data System (ADS)

Dunkel, Jörn; Talkner, Peter; Hänggi, Peter

2007-02-01

The nonrelativistic standard model for a continuous, one-parameter diffusion process in position space is the Wiener process. As is well known, the Gaussian transition probability density function (PDF) of this process is in conflict with special relativity, as it permits particles to propagate faster than the speed of light. A frequently considered alternative is provided by the telegraph equation, whose solutions avoid superluminal propagation speeds but suffer from singular (noncontinuous) diffusion fronts on the light cone, which are unlikely to exist for massive particles. It is therefore advisable to explore other alternatives as well. In this paper, a generalized Wiener process is proposed that is continuous, avoids superluminal propagation, and reduces to the standard Wiener process in the nonrelativistic limit. The corresponding relativistic diffusion propagator is obtained directly from the nonrelativistic Wiener propagator, by rewriting the latter in terms of an integral over actions. The resulting relativistic process is non-Markovian, in accordance with the known fact that nontrivial continuous, relativistic Markov processes in position space cannot exist. Hence, the proposed process defines a consistent relativistic diffusion model for massive particles and provides a viable alternative to the solutions of the telegraph equation.

Is Space Really Expanding? A Counterexample

NASA Astrophysics Data System (ADS)

Chodorowski, Michał J.

2007-03-01

In all Friedman models, the cosmological redshift is widely interpreted as a consequence of the general-relativistic phenomenon of expansion of space. Other commonly believed consequences of this phenomenon are superluminal recession velocities of distant galaxies, and the distance to the particle horizon greater than ct (where t is the age of the Universe), in apparent conflict with special relativity. Here, we study a particular Friedman model: empty universe. This model exhibits both cosmological redshift, superluminal velocities and infinite distance to the horizon. However, we show that the cosmological redshift is there simply a relativistic Doppler shift. Moreover, apparently superluminal velocities and ‘acausal’ distance to the horizon are in fact a direct consequence of special-relativistic phenomenon of time dilation, as well as of the adopted definition of distance in cosmology. There is no conflict with special relativity, whatsoever. In particular, inertial recession velocities are subluminal. Since in the real Universe, sufficiently distant galaxies recede with relativistic velocities, these special-relativistic effects must be at least partly responsible for the cosmological redshift and the aforementioned ‘superluminalities’, commonly attributed to the expansion of space. Let us finish with a question resembling a Buddhism-Zen ‘koan’: in an empty universe, what is expanding?

Relativistic interpretation of Newtonian simulations for cosmic structure formation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fidler, Christian; Tram, Thomas; Crittenden, Robert

2016-09-01

The standard numerical tools for studying non-linear collapse of matter are Newtonian N -body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation theory, provided that the effects from radiation can be neglected. In this paper we show that the present day matter density receives more than 1% corrections from radiation on large scales if Newtonian simulations are initialised before z =50. We provide a relativistic framework in which unmodified Newtonian simulations are compatible with linear GR even in the presence of radiation. Our idea is to usemore » GR perturbation theory to keep track of the evolution of relativistic species and the relativistic space-time consistent with the Newtonian trajectories computed in N -body simulations. If metric potentials are sufficiently small, they can be computed using a first-order Einstein–Boltzmann code such as CLASS. We make this idea rigorous by defining a class of GR gauges, the Newtonian motion gauges, which are defined such that matter particles follow Newtonian trajectories. We construct a simple example of a relativistic space-time within which unmodified Newtonian simulations can be interpreted.« less

A relativistic signature in large-scale structure

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Bertacca, Daniele; Bruni, Marco; Koyama, Kazuya; Maartens, Roy; Matarrese, Sabino; Sasaki, Misao; Verde, Licia; Wands, David

2016-09-01

In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales-even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.

Quantum theory of atoms in molecules: results for the SR-ZORA Hamiltonian.

PubMed

Anderson, James S M; Ayers, Paul W

2011-11-17

The quantum theory of atoms in molecules (QTAIM) is generalized to include relativistic effects using the popular scalar-relativistic zeroth-order regular approximation (SR-ZORA). It is usually assumed that the definition of the atom as a volume bounded by a zero-flux surface of the electron density is closely linked to the form of the kinetic energy, so it is somewhat surprising that the atoms corresponding to the relativistic kinetic-energy operator in the SR-ZORA Hamiltonian are also bounded by zero-flux surfaces. The SR-ZORA Hamiltonian should be sufficient for qualitative descriptions of molecular electronic structure across the periodic table, which suggests that QTAIM-based analysis can be useful for molecules and solids containing heavy atoms.

From N=4 Galilean superparticle to three-dimensional non-relativistic N=4 superfields

NASA Astrophysics Data System (ADS)

Fedoruk, Sergey; Ivanov, Evgeny; Lukierski, Jerzy

2018-05-01

We consider the general N=4 , d = 3 Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization techniques, we introduce a class of actions for N=4 three-dimensional non-relativistic superparticle, such that they are linear in the central charge Maurer-Cartan one-forms. As a prerequisite to the quantization, we analyze the phase space constraints structure of our model for various choices of the central charges. The first class constraints generate gauge transformations, involving fermionic κ-gauge transformations. The quantization of the model gives rise to the collection of free N=4 , d = 3 Galilean superfields, which can be further employed, e.g., for description of three-dimensional non-relativistic N=4 supersymmetric theories.

bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport

DOE PAGES

Ryan, Benjamin R; Dolence, Joshua C.; Gammie, Charles F.

2015-06-25

We present bhlight, a numerical scheme for solving the equations of general relativistic radiation magnetohydrodynamics using a direct Monte Carlo solution of the frequency-dependent radiative transport equation. bhlight is designed to evolve black hole accretion flows at intermediate accretion rate, in the regime between the classical radiatively efficient disk and the radiatively inefficient accretion flow (RIAF), in which global radiative effects play a sub-dominant but non-negligible role in disk dynamics. We describe the governing equations, numerical method, idiosyncrasies of our implementation, and a suite of test and convergence results. We also describe example applications to radiative Bondi accretion and tomore » a slowly accreting Kerr black hole in axisymmetry.« less

Gravitomagnetic acceleration from black hole accretion disks

NASA Astrophysics Data System (ADS)

Poirier, J.; Mathews, G. J.

2016-05-01

We demonstrate how the motion of the neutral masses in an accretion disk orbiting a black hole creates a general-relativistic magnetic-like (gravitomagnetic) field that vertically accelerates neutral particles near an accretion disk upward and then inward toward the axis of the accretion disk. Even though this gravitomagnetic field is not the only mechanism contributing to the production of jets, it presents a novel means to identify one general relativistic effect from a much more complicated problem. In addition, as the accelerated material above or below the accretion disk nears the axis with a nearly vertical direction, a frame-dragging effect twists the trajectories around the axis thus contributing to the collimation of the jet.

Deflection of jets induced by jet-cloud and jet-galaxy interactions

NASA Astrophysics Data System (ADS)

Mendoza, S.; Longair, M. S.

2001-06-01

The model first introduced by Raga & Cantó in which astrophysical jets are deflected on passing through an isothermal high-density region is generalized by taking into account gravitational effects on the motion of the jet as it crosses the high-density cloud. The problem is also generalized for relativistic jets in which gravitational effects induced by the cloud are neglected. Two further cases, classical and relativistic, are discussed for the cases in which the jet is deflected on passing through the interstellar gas of a galaxy in which a dark matter halo dominates the gravitational potential. The criteria for the stability of jets due to the formation of internal shocks are also discussed.

General Relativistic Magnetohydrodynamics Simulations of Tilted Black Hole Accretion Flows and Their Radiative Properties

NASA Astrophysics Data System (ADS)

Shiokawa, Hotaka; Gammie, C. F.; Dolence, J.; Noble, S. C.

2013-01-01

We perform global General Relativistic Magnetohydrodynamics (GRMHD) simulations of non-radiative, magnetized disks that are initially tilted with respect to the black hole's spin axis. We run the simulations with different size and tilt angle of the tori for 2 different resolutions. We also perform radiative transfer using Monte Carlo based code that includes synchrotron emission, absorption and Compton scattering to obtain spectral energy distribution and light curves. Similar work was done by Fragile et al. (2007) and Dexter & Fragile (2012) to model the super massive black hole SgrA* with tilted accretion disks. We compare our results of fully conservative hydrodynamic code and spectra that include X-ray, with their results.

Thermal noise in a boost-invariant matter expansion in relativistic heavy-ion collisions

NASA Astrophysics Data System (ADS)

Chattopadhyay, Chandrodoy; Bhalerao, Rajeev S.; Pal, Subrata

2018-05-01

We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice quantum chromodynamics equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.

Test of Relativistic Gravity for Propulsion at the Large Hadron Collider

NASA Astrophysics Data System (ADS)

Felber, Franklin

2010-01-01

A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. An exact time-dependent solution of Einstein's gravitational field equation confirms that even the weak field of a mass moving at relativistic speeds could serve as a driver to accelerate a much lighter payload from rest to a good fraction of the speed of light. The time-dependent field of ultrarelativistic particles in a collider ring is calculated. An experiment is proposed as the first test of the predictions of general relativity in the ultrarelativistic limit by measuring the repulsive gravitational field of bunches of protons in the Large Hadron Collider (LHC). The estimated `antigravity beam' signal strength at a resonant detector of each proton bunch is 3 nm/s2 for 2 ns during each revolution of the LHC. This experiment can be performed off-line, without interfering with the normal operations of the LHC.

Probing relativistic effects in the central engine of AGN

NASA Astrophysics Data System (ADS)

Sanfrutos, M.; Miniutti, G.

2017-03-01

Active Galactic Nuclei (AGN) are perfect laboratories to check General Relativity (GR) effects by using Broad Line Region (BLR) clouds eclipses to probe the innermost regions of the accretion disk. A new relativistic X-ray spectral model for X-ray eclipses is introduced. First we present the different observables that are involved in X-ray eclipses, including the X-ray emitting regions size, the emissivity index, the cloud's column density, ionization, size and velocity, the black hole spin, and the system's inclination. Then we highlight some theoretical predictions on the observables by using XMM-Newton simulations, finding that absorption varies depending on the photons' energy range, being maximum when the approaching side of the X-ray-emitting region is covered. Finally, we fit our relativistic model to actual XMM-Newton data from a long observation of the NLS1 galaxy SWIFT J2127.4+5654, and compare our results with a previous work, in which we addressed the BLR cloud eclipse from a non-relativistic prespective.

Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

NASA Technical Reports Server (NTRS)

Maung, Khin Maung; Kahana, David E.; Norbury, John W.

1992-01-01

Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

Toward an absolute NMR shielding scale using the spin-rotation tensor within a relativistic framework.

PubMed

Aucar, I Agustín; Gomez, Sergio S; Giribet, Claudia G; Aucar, Gustavo A

2016-08-24

One of the most influential articles showing the best way to get the absolute values of NMR magnetic shieldings, σ (non-measurables) from both accurate measurements and theoretical calculations, was published a long time ago by Flygare. His model was shown to break down when heavy atoms are involved. This fact motivated the development of new theories of nuclear spin-rotation (SR) tensors, which consider electronic relativistic effects. One was published recently by some of us. In this article we take another step further and propose three different models that generalize Flygare's model. All of them are written using four-component relativistic expressions, though the two-component relativistic SO-S term also appears in one. The first clues for these developments were built from the relationship among σ and the SR tensors within the two-component relativistic LRESC model. Besides, we had to introduce a few other well defined assumptions: (i) relativistic corrections must be included in a way to best reproduce the relationship among the (e-e) term (called "paramagnetic" within the non-relativistic domain) of σ and its equivalent part of the SR tensor, (ii) as happens in Flygare's rule, the shielding of free atoms shall be included to improve accuracy. In the highest accurate model, a new term known as Spin-orbit due to spin, SO-S (in this mechanism the spin-Zeeman Hamiltonian replaces the orbital-Zeeman Hamiltonian), is included. We show the results of the application of those models to halogen containing linear molecules.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ko, Sung Moon; Park, Jeong-Hyuck; Suh, Minwoo, E-mail: sinsmk2003@sogang.ac.kr, E-mail: park@sogang.ac.kr, E-mail: minsuh@usc.edu

Double Field Theory suggests to view the whole massless sector of closed strings as the gravitational unity. The fundamental symmetries therein, including the O( D , D ) covariance, can determine unambiguously how the Standard Model as well as a relativistic point particle should couple to the closed string massless sector. The theory also refines the notion of singularity. We consider the most general, spherically symmetric, asymptotically flat, static vacuum solution to D =4 Double Field Theory, which contains three free parameters and consequently generalizes the Schwarzschild geometry. Analyzing the circular geodesic of a point particle in string frame, wemore » obtain the orbital velocity as a function of R /( M {sub ∞} G ) which is the dimensionless radial variable normalized by mass. The rotation curve generically features a maximum and thus non-Keplerian over a finite range, while becoming asymptotically Keplerian at infinity, R /( M {sub ∞} G )→ ∞. The adoption of the string frame rather than Einstein frame is the consequence of the fundamental symmetry principle. Our result opens up a new scheme to solve the dark matter/energy problems by modifying General Relativity at 'short' range of R /( M {sub ∞} G ).« less

On relativistic spin network vertices

NASA Astrophysics Data System (ADS)

Reisenberger, Michael P.

1999-04-01

Barrett and Crane have proposed a model of simplicial Euclidean quantum gravity in which a central role is played by a class of Spin(4) spin networks called "relativistic spin networks" which satisfy a series of physically motivated constraints. Here a proof is presented that demonstrates that the intertwiner of a vertex of such a spin network is uniquely determined, up to normalization, by the representations on the incident edges and the constraints. Moreover, the constraints, which were formulated for four valent spin networks only, are extended to networks of arbitrary valence, and the generalized relativistic spin networks proposed by Yetter are shown to form the entire solution set (mod normalization) of the extended constraints. Finally, using the extended constraints, the Barrett-Crane model is generalized to arbitrary polyhedral complexes (instead of just simplicial complexes) representing space-time. It is explained how this model, like the Barret-Crane model can be derived from BF theory, a simple topological field theory [G. Horowitz, Commun. Math. Phys. 125, 417 (1989)], by restricting the sum over histories to ones in which the left-handed and right-handed areas of any 2-surface are equal. It is known that the solutions of classical Euclidean general relativity form a branch of the stationary points of the BF action with respect to variations preserving this condition.

Theory of relativistic Brownian motion in the presence of electromagnetic field in (1+1) dimension

NASA Astrophysics Data System (ADS)

Mukhopadhyay, Annesh; Bandyopadhyay, M.; Bhamidipati, C.

2018-04-01

In this work, we consider the relativistic generalization of the theory of Brownian motion for the (1+1) dimensional case, which is again consistent with Einstein's special theory of relativity and reduces to standard Brownian motion in the Newtonian limit. All the generalizations are made considering Special theory of relativity into account. The particle under consideration has a velocity close to the speed of light and is a free Brownian particle suspended in a heat bath. With this generalization the velocity probability density functions are also obtained using Ito, Stratonovich and Hanggi-Klimontovich approach of pre-point, mid-point and post-point discretization rule. Subsequently, in our work, we have obtained the relativistic Langevin equations in the presence of an electromagnetic field. Finally, taking a special case of a constant vector potential and a constant electric field into account the Langevin equations are solved for the momentum and subsequently the velocity of the particle. Using a similar approach to the Fokker-planck equations of motion, the velocity distributions are also obtained in the presence of a constant vector potential and are plotted, which shows essential deviations from the one obtained without a potential. Our constant potential model can be realized in an optical potential.

The lunar orbit as probe of relativistic gravity.

NASA Astrophysics Data System (ADS)

Nordtvedt, K.

The author has analytically determined in a unified treament all general relativistic corrections to the Moon's orbit observable by present-day laser ranging data. Because the solar tidal deformation of the lunar orbit plays such a central role in altering the amplitudes and frequencies of lunar motion, the post-Newtonian equations of motion are solved using procedures similar to those Hill introduced into classical lunar theory and which treat the orbit's tidal deformation in a partially non-perturbative manner. The amplitudes of all perturbations of monthly period are found to be significantly amplified by interaction with the orbit's tidal deformation. In particular, this enhances the sensitivity of the lunar orbit as an observational probe of the gravitational to inertial mass ratio of the Earth (and Moon). The "evection" amplitude is altered by general relativity at an observationally significant level. Relativistic corrections to the perigee precession rate are found to include not only the "de Sitter" term, but also corrections from the solar tidal force which are 10% as large. Lunar laser ranging presently provides the most precise measurements of not only general relativity's "space geometry" and non-linear coupling structures, but also the comparison of free fall rates of two different bodies (Earth and Moon) toward a third body (Sun).

Carter separable electromagnetic fields

NASA Astrophysics Data System (ADS)

Lynden-Bell, D.

2000-02-01

The purely electromagnetic analogue in flat space of Kerr's metric in general relativity is only rarely considered. Here we carry out in flat space a programme similar to Carter's investigation of metrics in general relativity in which the motion of a charged particle is separable. We concentrate on the separability of the motion (be it classical, relativistic or quantum) of a charged particle in electromagnetic fields that lie in planes through an axis of symmetry. In cylindrical polar coordinates (t,R,φ,z) the four-vector potential takes the form [formmu2] is the unit toroidal vector. The forms of the functions Φ(R,z) and A(R,z) are sought that allow separable motion. This occurs for relativistic motion only when AR,Φ and A2-Φ2 are all of the separable form ζ(λ)-η(μ)]/(λ-μ), where ζ and η are arbitrary functions, and λ and μ are spheroidal coordinates or degenerations thereof. The special forms of A and Φ that allow this are deduced. They include the Kerr metric analogue, with E+iB=-∇{q[(r-ia).(r-ia)]-1/2}. Rather more general electromagnetic fields allow separation when the motion is non-relativistic. The investigation is extended to fields that lie in parallel planes. Connections to Larmor's theorem are remarked upon.

General relativistic viscous hydrodynamics of differentially rotating neutron stars

NASA Astrophysics Data System (ADS)

Shibata, Masaru; Kiuchi, Kenta; Sekiguchi, Yu-ichiro

2017-04-01

Employing a simplified version of the Israel-Stewart formalism for general-relativistic shear-viscous hydrodynamics, we perform axisymmetric general-relativistic simulations for a rotating neutron star surrounded by a massive torus, which can be formed from differentially rotating stars. We show that with our choice of a shear-viscous hydrodynamics formalism, the simulations can be stably performed for a long time scale. We also demonstrate that with a possibly high shear-viscous coefficient, not only viscous angular momentum transport works but also an outflow could be driven from a hot envelope around the neutron star for a time scale ≳100 ms with the ejecta mass ≳10-2 M⊙ , which is comparable to the typical mass for dynamical ejecta of binary neutron-star mergers. This suggests that massive neutron stars surrounded by a massive torus, which are typical outcomes formed after the merger of binary neutron stars, could be the dominant source for providing neutron-rich ejecta, if the effective shear viscosity is sufficiently high, i.e., if the viscous α parameter is ≳10-2. The present numerical result indicates the importance of a future high-resolution magnetohydrodynamics simulation that is the unique approach to clarify the viscous effect in the merger remnants of binary neutron stars by the first-principle manner.

General relativistic dynamics of an extreme mass-ratio binary interacting with an external body

NASA Astrophysics Data System (ADS)

Yang, Huan; Casals, Marc

2017-10-01

We study the dynamics of a hierarchical three-body system in the general relativistic regime: an extreme mass-ratio inner binary under the tidal influence of an external body. The inner binary consists of a central Schwarzschild black hole and a test body moving around it. We discuss three types of tidal effects on the orbit of the test body. First, the angular momentum of the inner binary precesses around the angular momentum of the outer binary. Second, the tidal field drives a "transient resonance" when the radial and azimuthal frequencies are commensurable. In contrast with resonances driven by the gravitational self-force, this tidal-driven resonance may boost the orbital angular momentum and eccentricity (a relativistic version of the Kozai-Lidov effect). Finally, for an orbit-dynamical effect during the nonresonant phase, we calculate the correction to the innermost stable circular (mean) orbit due to the tidal interaction. Hierarchical three-body systems are potential sources for future space-based gravitational wave missions, and the tidal effects that we find could contribute significantly to their waveform.

Space-Time, Relativity, and Cosmology

NASA Astrophysics Data System (ADS)

Wudka, Jose

2006-07-01

Space-Time, Relativity and Cosmology provides a historical introduction to modern relativistic cosmology and traces its historical roots and evolution from antiquity to Einstein. The topics are presented in a non-mathematical manner, with the emphasis on the ideas that underlie each theory rather than their detailed quantitative consequences. A significant part of the book focuses on the Special and General theories of relativity. The tests and experimental evidence supporting the theories are explained together with their predictions and their confirmation. Other topics include a discussion of modern relativistic cosmology, the consequences of Hubble's observations leading to the Big Bang hypothesis, and an overview of the most exciting research topics in relativistic cosmology. This textbook is intended for introductory undergraduate courses on the foundations of modern physics. It is also accessible to advanced high school students, as well as non-science majors who are concerned with science issues.• Uses a historical perspective to describe the evolution of modern ideas about space and time • The main arguments are described using a completely non-mathematical approach • Ideal for physics undergraduates and high-school students, non-science majors and general readers

Energy distribution of relativistic electrons in the kiloparsec scale jet of M 87 with Chandra

NASA Astrophysics Data System (ADS)

Sun, Xiao-Na; Yang, Rui-Zhi; Rieger, Frank M.; Liu, Ruo-Yu; Aharonian, Felix

2018-05-01

The X-ray emission from the jets in active galactic nuclei (AGN) carries important information on the distributions of relativistic electrons and magnetic fields on large scales. We reanalysed archival Chandra observations on the jet of M 87 from 2000 to 2016 with a total exposure of 1460 kiloseconds to explore the X-ray emission characteristics along the jet. We investigated the variability behaviours of the nucleus and the inner jet component HST-1, and confirm indications for day-scale X-ray variability in the nucleus contemporaneous to the 2010 high TeV γ-ray state. HST-1 shows a general decline in X-ray flux over the last few years consistent with its synchrotron interpretation. We extracted the X-ray spectra for the nucleus and all knots in the jet, showing that they are compatible with a single power law within the X-ray band. There are indications that the resultant X-ray photon index exhibit a trend, with slight but significant index variations ranging from ≃ 2.2 (e.g. in knot D) to ≃ 2.4-2.6 (in the outer knots F, A, and B). When viewed in a multiwavelength context, a more complex situation can be seen. Fitting the radio to X-ray spectral energy distributions (SEDs) assuming a synchrotron origin, we show that a broken power-law electron spectrum with break energy Eb around 1 (300 μG/B)1/2 TeV allows a satisfactory description of the multiband SEDs for most of the knots. However, in the case of knots B, C, and D we find indications that an additional high-energy component is needed to adequately reproduce the broad-band SEDs. We discuss the implications and suggest that a stratified jet model may account for the differences.

GRMHD and GRPIC Simulations

NASA Technical Reports Server (NTRS)

Nishikawa, K.-I.; Mizuno, Y.; Watson, M.; Fuerst, S.; Wu, K.; Hardee, P.; Fishman, G. J.

2007-01-01

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous code. The simulation results show the jet formations from a geometrically thin accretion disk near a nonrotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field configuration including issues for future research. A General Relativistic Particle-in-Cell Code (GRPIC) has been developed using the Kerr-Schild metric. The code includes kinetic effects, and is in accordance with GRMHD code. Since the gravitational force acting on particles is extreme near black holes, there are some difficulties in numerically describing these processes. The preliminary code consists of an accretion disk and free-falling corona. Results indicate that particles are ejected from the black hole. These results are consistent with other GRMHD simulations. The GRPIC simulation results will be presented, along with some remarks and future improvements. The emission is calculated from relativistic flows in black hole systems using a fully general relativistic radiative transfer formulation, with flow structures obtained by GRMHD simulations considering thermal free-free emission and thermal synchrotron emission. Bright filament-like features protrude (visually) from the accretion disk surface, which are enhancements of synchrotron emission where the magnetic field roughly aligns with the line-of-sight in the co-moving frame. The features move back and forth as the accretion flow evolves, but their visibility and morphology are robust. We would like to extend this research using GRPIC simulations and examine a possible new mechanism for certain X-ray quasi-periodic oscillations (QPOs) observed in blackhole X-ray binaries.

BBN constraints on MeV-scale dark sectors. Part I. Sterile decays

NASA Astrophysics Data System (ADS)

Hufnagel, Marco; Schmidt-Hoberg, Kai; Wild, Sebastian

2018-02-01

We study constraints from Big Bang Nucleosynthesis on inert particles in a dark sector which contribute to the Hubble rate and therefore change the predictions of the primordial nuclear abundances. We pay special attention to the case of MeV-scale particles decaying into dark radiation, which are neither fully relativistic nor non-relativistic during all temperatures relevant to Big Bang Nucleosynthesis. As an application we discuss the implications of our general results for models of self-interacting dark matter with light mediators.

A note on blowup of smooth solutions for relativistic Euler equations with infinite initial energy

NASA Astrophysics Data System (ADS)

Dong, Jianwei; Zhu, Junhui

2018-04-01

We study the singularity formation of smooth solutions of the relativistic Euler equations in (3+1)-dimensional spacetime for infinite initial energy. We prove that the smooth solution blows up in finite time provided that the radial component of the initial generalized momentum is sufficiently large without the conditions M(0)>0 and s2<1/3c2 , which were two key constraints stated in Pan and Smoller (Commun Math Phys 262:729-755, 2006).

Unified space--time trigonometry and its applications to relativistic kinematics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jaccarini, A.

1973-06-15

A geometrical approach to relativistic kinematics is presented. Owing to a unified space-time trigonometry, the spherical trigonometry formalism may be used to describe and study the kinematics of any collision process. Lorentz transformations may thus lie treated as purely geometrical problems. A different way to define a unified trigonometry is also proposed, which is based on the spinor representation of the Lorentz group. This leads to a different and more general formalism than the former one. (auth)

Relativistic algorithm for time transfer in Mars missions under IAU Resolutions: an analytic approach

NASA Astrophysics Data System (ADS)

Pan, Jun-Yang; Xie, Yi

2015-02-01

With tremendous advances in modern techniques, Einstein's general relativity has become an inevitable part of deep space missions. We investigate the relativistic algorithm for time transfer between the proper time τ of the onboard clock and the Geocentric Coordinate Time, which extends some previous works by including the effects of propagation of electromagnetic signals. In order to evaluate the implicit algebraic equations and integrals in the model, we take an analytic approach to work out their approximate values. This analytic model might be used in an onboard computer because of its limited capability to perform calculations. Taking an orbiter like Yinghuo-1 as an example, we find that the contributions of the Sun, the ground station and the spacecraft dominate the outcomes of the relativistic corrections to the model.

DISCOVERY OF A PSEUDOBULGE GALAXY LAUNCHING POWERFUL RELATIVISTIC JETS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kotilainen, Jari K.; Olguín-Iglesias, Alejandro; León-Tavares, Jonathan

Supermassive black holes launching plasma jets at close to the speed of light, producing gamma-rays, have ubiquitously been found to be hosted by massive elliptical galaxies. Since elliptical galaxies are generally believed to be built through galaxy mergers, active galactic nuclei (AGN) launching relativistic jets are associated with the latest stages of galaxy evolution. We have discovered a pseudobulge morphology in the host galaxy of the gamma-ray AGN PKS 2004-447. This is the first gamma-ray emitter radio-loud AGN found to have been launched from a system where both the black hole and host galaxy have been actively growing via secularmore » processes. This is evidence of an alternative black hole–galaxy co-evolutionary path to develop powerful relativistic jets, which is not merger driven.« less

Quantifying Intrinsic Variability of Sagittarius A* Using Closure Phase Measurements of the Event Horizon Telescope

NASA Astrophysics Data System (ADS)

Roelofs, Freek; Johnson, Michael D.; Shiokawa, Hotaka; Doeleman, Sheperd S.; Falcke, Heino

2017-09-01

General relativistic magnetohydrodynamic (GRMHD) simulations of accretion disks and jets associated with supermassive black holes show variability on a wide range of timescales. On timescales comparable to or longer than the gravitational timescale {t}G={GM}/{c}3, variation may be dominated by orbital dynamics of the inhomogeneous accretion flow. Turbulent evolution within the accretion disk is expected on timescales comparable to the orbital period, typically an order of magnitude larger than t G . For Sgr A*, t G is much shorter than the typical duration of a VLBI experiment, enabling us to study this variability within a single observation. Closure phases, the sum of interferometric visibility phases on a triangle of baselines, are particularly useful for studying this variability. In addition to a changing source structure, variations in observed closure phase can also be due to interstellar scattering, thermal noise, and the changing geometry of projected baselines over time due to Earth rotation. We present a metric that is able to distinguish the latter two from intrinsic or scattering variability. This metric is validated using synthetic observations of GRMHD simulations of Sgr A*. When applied to existing multi-epoch EHT data of Sgr A*, this metric shows that the data are most consistent with source models containing intrinsic variability from source dynamics, interstellar scattering, or a combination of those. The effects of black hole inclination, orientation, spin, and morphology (disk or jet) on the expected closure phase variability are also discussed.

Mass Function of Galaxy Clusters in Relativistic Inhomogeneous Cosmology

NASA Astrophysics Data System (ADS)

Ostrowski, Jan J.; Buchert, Thomas; Roukema, Boudewijn F.

The current cosmological model (ΛCDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress-energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for more than 20 years. Here we present one of the methods to tackle this problem, i.e. averaging the scalar parts of the Einstein equations, together with its application, the cosmological mass function of galaxy clusters.

Sonic black holes in a one-dimensional relativistic flow

NASA Astrophysics Data System (ADS)

Carbonaro, P.

2015-09-01

The analogy between sound propagation in a fluid background and light propagation in a curved spacetime, discovered by Unruh in 1981, does not work in general when considering the motion of a fluid which is confined in one spatial dimension being unable in (1+1) dimensions to introduce in a coherent manner an effective acoustic metric, barring some exceptional cases. In this paper a relativistic fluid is considered and the general condition for the existence of an acoustic metric in strictly one-dimensional systems is found. Attention is also paid to the physical meaning of the equations of state characterizing such systems and to the remarkable symmetry of structure taken by the basic equations. Finally the Hawking temperature is calculated in an artificial de Laval nozzle.

Review of gravitomagnetic acceleration from accretion disks

NASA Astrophysics Data System (ADS)

Poirier, J.; Mathews, G. J.

2015-11-01

We review the development of the equations of gravitoelectromagnetism and summarize how the motion of the neutral masses in an accretion disk orbiting a black hole creates a general-relativistic magnetic-like (gravitomagnetic) field that vertically accelerates neutral particles near the accretion disk upward and then inward toward the axis of the accretion disk. Even though this gravitomagnetic field is not the only mechanism to produce collimated jets, it is a novel means to identify one general relativistic effect from a much more complicated problem. In addition, as the accelerated material above or below the accretion disk nears the axis with a nearly vertical direction, a frame-dragging effect twists the trajectories around the axis thus contributing to the collimation of the jet.

Four-Component Relativistic Density-Functional Theory Calculations of Nuclear Spin-Rotation Constants: Relativistic Effects in p-Block Hydrides.

PubMed

Komorovsky, Stanislav; Repisky, Michal; Malkin, Elena; Demissie, Taye B; Ruud, Kenneth

2015-08-11

We present an implementation of the nuclear spin-rotation (SR) constants based on the relativistic four-component Dirac-Coulomb Hamiltonian. This formalism has been implemented in the framework of the Hartree-Fock and Kohn-Sham theory, allowing assessment of both pure and hybrid exchange-correlation functionals. In the density-functional theory (DFT) implementation of the response equations, a noncollinear generalized gradient approximation (GGA) has been used. The present approach enforces a restricted kinetic balance condition for the small-component basis at the integral level, leading to very efficient calculations of the property. We apply the methodology to study relativistic effects on the spin-rotation constants by performing calculations on XHn (n = 1-4) for all elements X in the p-block of the periodic table and comparing the effects of relativity on the nuclear SR tensors to that observed for the nuclear magnetic shielding tensors. Correlation effects as described by the density-functional theory are shown to be significant for the spin-rotation constants, whereas the differences between the use of GGA and hybrid density functionals are much smaller. Our calculated relativistic spin-rotation constants at the DFT level of theory are only in fair agreement with available experimental data. It is shown that the scaling of the relativistic effects for the spin-rotation constants (varying between Z(3.8) and Z(4.5)) is as strong as for the chemical shieldings but with a much smaller prefactor.

A relativistically interacting exactly solvable multi-time model for two massless Dirac particles in 1 + 1 dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lienert, Matthias, E-mail: lienert@math.lmu.de

2015-04-15

The question how to Lorentz transform an N-particle wave function naturally leads to the concept of a so-called multi-time wave function, i.e., a map from (space-time){sup N} to a spin space. This concept was originally proposed by Dirac as the basis of relativistic quantum mechanics. In such a view, interaction potentials are mathematically inconsistent. This fact motivates the search for new mechanisms for relativistic interactions. In this paper, we explore the idea that relativistic interaction can be described by boundary conditions on the set of coincidence points of two particles in space-time. This extends ideas from zero-range physics to amore » relativistic setting. We illustrate the idea at the simplest model which still possesses essential physical properties like Lorentz invariance and a positive definite density: two-time equations for massless Dirac particles in 1 + 1 dimensions. In order to deal with a spatio-temporally non-trivial domain, a necessity in the multi-time picture, we develop a new method to prove existence and uniqueness of classical solutions: a generalized version of the method of characteristics. Both mathematical and physical considerations are combined to precisely formulate and answer the questions of probability conservation, Lorentz invariance, interaction, and antisymmetry.« less

Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers.

PubMed

Jankowska, Marzena; Kupka, Teobald; Stobiński, Leszek; Faber, Rasmus; Lacerda, Evanildo G; Sauer, Stephan P A

2016-02-05

Hartree-Fock and density functional theory with the hybrid B3LYP and general gradient KT2 exchange-correlation functionals were used for nonrelativistic and relativistic nuclear magnetic shielding calculations of helium, neon, argon, krypton, and xenon dimers and free atoms. Relativistic corrections were calculated with the scalar and spin-orbit zeroth-order regular approximation Hamiltonian in combination with the large Slater-type basis set QZ4P as well as with the four-component Dirac-Coulomb Hamiltonian using Dyall's acv4z basis sets. The relativistic corrections to the nuclear magnetic shieldings and chemical shifts are combined with nonrelativistic coupled cluster singles and doubles with noniterative triple excitations [CCSD(T)] calculations using the very large polarization-consistent basis sets aug-pcSseg-4 for He, Ne and Ar, aug-pcSseg-3 for Kr, and the AQZP basis set for Xe. For the dimers also, zero-point vibrational (ZPV) corrections are obtained at the CCSD(T) level with the same basis sets were added. Best estimates of the dimer chemical shifts are generated from these nuclear magnetic shieldings and the relative importance of electron correlation, ZPV, and relativistic corrections for the shieldings and chemical shifts is analyzed. © 2015 Wiley Periodicals, Inc.

Molecular dynamics approach to dissipative relativistic hydrodynamics: Propagation of fluctuations

NASA Astrophysics Data System (ADS)

Shahsavar, Leila; Ghodrat, Malihe; Montakhab, Afshin

2016-12-01

Relativistic generalization of hydrodynamic theory has attracted much attention from a theoretical point of view. However, it has many important practical applications in high energy as well as astrophysical contexts. Despite various attempts to formulate relativistic hydrodynamics, no definitive consensus has been achieved. In this work, we propose to test the predictions of four types of first-order hydrodynamic theories for nonperfect fluids in the light of numerically exact molecular dynamics simulations of a fully relativistic particle system in the low density regime. In this regard, we study the propagation of density, velocity, and heat fluctuations in a wide range of temperatures using extensive simulations and compare them to the corresponding analytic expressions we obtain for each of the proposed theories. As expected, in the low temperature classical regime all theories give the same results, consistent with the numerics. In the high temperature extremely relativistic regime, not all considered theories are distinguishable from one another. However, in the intermediate regime, a meaningful distinction exists in the predictions of various theories considered here. We find that the predictions of the recent formulation due to Tsumura, Kunihiro, and Ohnishi are more consistent with our numerical results than the traditional theories: the Meixner, modified Eckart, and modified Marle-Stewart theories.

On the acceleration of charged particles at relativistic shock fronts

NASA Technical Reports Server (NTRS)

Kirk, J. G.; Schneider, P.

1987-01-01

The diffusive acceleration of highly relativistic particles at a shock is reconsidered. Using the same physical assumptions as Blandford and Ostriker (1978), but dropping the restriction to nonrelativistic shock velocities, the authors find approximate solutions of the particle kinetic equation by generalizing the diffusion approximation to higher order terms in the anisotropy of the particle distribution. The general solution of the transport equation on either side of the shock is constructed, which involves the solution of an eigenvalue problem. By matching the two solutions at the shock, the spectral index of the resulting power law is found by taking into account a sufficiently large number of eigenfunctions. Low-order truncation corresponds to the standard diffusion approximation and to a somewhat more general method described by Peacock (1981). In addition to the energy spectrum, the method yields the angular distribution of the particles and its spatial dependence.

Exact general relativistic disks with magnetic fields

NASA Astrophysics Data System (ADS)

Letelier, Patricio S.

1999-11-01

The well-known ``displace, cut, and reflect'' method used to generate cold disks from given solutions of Einstein equations is extended to solutions of Einstein-Maxwell equations. Four exact solutions of the these last equations are used to construct models of hot disks with surface density, azimuthal pressure, and azimuthal current. The solutions are closely related to Kerr, Taub-NUT, Lynden-Bell-Pinault, and to a one-soliton solution. We find that the presence of the magnetic field can change in a nontrivial way the different properties of the disks. In particular, the pure general relativistic instability studied by Bic̆ák, Lynden-Bell, and Katz [Phys. Rev. D 47, 4334 (1993)] can be enhanced or cured by different distributions of currents inside the disk. These currents, outside the disk, generate a variety of axial symmetric magnetic fields. As far as we know these are the first models of hot disks studied in the context of general relativity.

To the memory of A. A. Logunov: General relativity theory and the relativistic theory of gravity

NASA Astrophysics Data System (ADS)

Gershtein, S. S.

2017-05-01

We briefly review the contributions of A. A. Logunov to understanding the problems of general relativity and gravity with special attention to the issue of the possibility of a catastrophic stellar collapse forming a "black hole."

Entanglement of quantum clocks through gravity

NASA Astrophysics Data System (ADS)

Castro Ruiz, Esteban; Giacomini, Flaminia; Brukner, Časlav

2017-03-01

In general relativity, the picture of space-time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.

Entanglement of quantum clocks through gravity.

PubMed

Castro Ruiz, Esteban; Giacomini, Flaminia; Brukner, Časlav

2017-03-21

In general relativity, the picture of space-time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.

Entanglement of quantum clocks through gravity

PubMed Central

Castro Ruiz, Esteban; Giacomini, Flaminia; Brukner, Časlav

2017-01-01

In general relativity, the picture of space–time assigns an ideal clock to each world line. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby world lines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is, at most, a convenient fiction. Specifically, we show that the general relativistic mass–energy equivalence implies gravitational interaction between the clocks, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well defined. However, the general relativistic notion of time is recovered in the classical limit of clocks. PMID:28270623

Relativistic apsidal motion in eccentric eclipsing binaries

NASA Astrophysics Data System (ADS)

Wolf, M.; Claret, A.; Kotková, L.; Kučáková, H.; Kocián, R.; Brát, L.; Svoboda, P.; Šmelcer, L.

2010-01-01

Context. The study of apsidal motion in detached eclipsing binary systems is known to be an important source of information about stellar internal structure as well as the possibility of verifying of General Relativity outside the Solar System. Aims: As part of the long-term Ondřejov and Ostrava observational projects, we aim to measure precise times of minima for eccentric eclipsing binaries, needed for the accurate determination of apsidal motion, providing a suitable test of the effects of General Relativity. Methods: About seventy new times of minimum light recorded with photoelectric or CCD photometers were obtained for ten eccentric-orbit eclipsing binaries with significant relativistic apsidal motion. Their O-C diagrams were analysed using all reliable timings found in the literature, and new or improved elements of apsidal motion were obtained. Results: We confirm very long periods of apsidal motion for all systems. For BF Dra and V1094 Tau, we present the first apsidal-motion solution. The relativistic effects are dominant, representing up to 100% of the total observable apsidal-motion rate in several systems. The theoretical and observed values of the internal structure constant k 2 were compared for systems with lower relativistic contribution. Using the light-time effect solution, we predict a faint third component for V1094 Tau orbiting with a short period of about 8 years. Partly based on photoelectric observations secured at the Hvar Observatory, Faculty of Geodesy, Zagreb, Croatia, in October 2008.

HERO - A 3D general relativistic radiative post-processor for accretion discs around black holes

NASA Astrophysics Data System (ADS)

Zhu, Yucong; Narayan, Ramesh; Sadowski, Aleksander; Psaltis, Dimitrios

2015-08-01

HERO (Hybrid Evaluator for Radiative Objects) is a 3D general relativistic radiative transfer code which has been tailored to the problem of analysing radiation from simulations of relativistic accretion discs around black holes. HERO is designed to be used as a post-processor. Given some fixed fluid structure for the disc (i.e. density and velocity as a function of position from a hydrodynamic or magnetohydrodynamic simulation), the code obtains a self-consistent solution for the radiation field and for the gas temperatures using the condition of radiative equilibrium. The novel aspect of HERO is that it combines two techniques: (1) a short-characteristics (SC) solver that quickly converges to a self-consistent disc temperature and radiation field, with (2) a long-characteristics (LC) solver that provides a more accurate solution for the radiation near the photosphere and in the optically thin regions. By combining these two techniques, we gain both the computational speed of SC and the high accuracy of LC. We present tests of HERO on a range of 1D, 2D, and 3D problems in flat space and show that the results agree well with both analytical and benchmark solutions. We also test the ability of the code to handle relativistic problems in curved space. Finally, we discuss the important topic of ray defects, a major limitation of the SC method, and describe our strategy for minimizing the induced error.

X-Ray Quasi-periodic Oscillations in the Lense–Thirring Precession Model. I. Variability of Relativistic Continuum

NASA Astrophysics Data System (ADS)

You, Bei; Bursa, Michal; Życki, Piotr T.

2018-05-01

We develop a Monte Carlo code to compute the Compton-scattered X-ray flux arising from a hot inner flow that undergoes Lense–Thirring precession. The hot flow intercepts seed photons from an outer truncated thin disk. A fraction of the Comptonized photons will illuminate the disk, and the reflected/reprocessed photons will contribute to the observed spectrum. The total spectrum, including disk thermal emission, hot flow Comptonization, and disk reflection, is modeled within the framework of general relativity, taking light bending and gravitational redshift into account. The simulations are performed in the context of the Lense–Thirring precession model for the low-frequency quasi-periodic oscillations, so the inner flow is assumed to precess, leading to periodic modulation of the emitted radiation. In this work, we concentrate on the energy-dependent X-ray variability of the model and, in particular, on the evolution of the variability during the spectral transition from hard to soft state, which is implemented by the decrease of the truncation radius of the outer disk toward the innermost stable circular orbit. In the hard state, where the Comptonizing flow is geometrically thick, the Comptonization is weakly variable with a fractional variability amplitude of ≤10% in the soft state, where the Comptonizing flow is cooled down and thus becomes geometrically thin, the fractional variability of the Comptonization is highly variable, increasing with photon energy. The fractional variability of the reflection increases with energy, and the reflection emission for low spin is counterintuitively more variable than the one for high spin.

Nonradial and nonpolytropic astrophysical outflows. X. Relativistic MHD rotating spine jets in Kerr metric

NASA Astrophysics Data System (ADS)

Chantry, L.; Cayatte, V.; Sauty, C.; Vlahakis, N.; Tsinganos, K.

2018-04-01

Context. High-resolution radio imaging of active galactic nuclei (AGN) has revealed that the jets of some sources present superluminal knots and transverse stratification. Recent observational projects, such as ALMA and γ-ray telescopes, such as HESS and HESS2 have provided new observational constraints on the central regions of rotating black holes in AGN, suggesting that there is an inner- or spine-jet surrounded by a disk wind. This relativistic spine-jet is likely to be composed of electron-positron pairs extracting energy from the black hole and will be explored by the future γ-ray telescope CTA. Aims: In this article we present an extension to and generalization of relativistic jets in Kerr metric of the Newtonian meridional self-similar mechanism. We aim at modeling the inner spine-jet of AGN as a relativistic light outflow emerging from a spherical corona surrounding a Kerr black hole and its inner accretion disk. Methods: The model is built by expanding the metric and the forces with colatitude to first order in the magnetic flux function. As a result of the expansion, all colatitudinal variations of the physical quantities are quantified by a unique parameter. Unlike previous models, effects of the light cylinder are not neglected. Results: Solutions with high Lorentz factors are obtained and provide spine-jet models up to the polar axis. As in previous publications, we calculate the magnetic collimation efficiency parameter, which measures the variation of the available energy across the field lines. This collimation efficiency is an integral part of the model, generalizing the classical magnetic rotator efficiency criterion to Kerr metric. We study the variation of the magnetic efficiency and acceleration with the spin of the black hole and show their high sensitivity to this integral. Conclusions: These new solutions model collimated or radial, relativistic or ultra-relativistic outflows in AGN or γ-ray bursts. In particular, we discuss the relevance of our solutions to modeling the M 87 spine-jet. We study the efficiency of the central black hole spin to collimate a spine-jet and show that the jet power is of the same order as that determined by numerical simulations.

Analysis of Microvariable Activity of BL Lacertae

NASA Astrophysics Data System (ADS)

Sadun, Alberto C.; Asadi-Zeydabadi, Masoud; Hindman, Lauren; Moody, J. Ward

2018-06-01

BL Lac is a low-frequency peaked blazar (LBL) which emits synchrotron radiation at near-IR and optical wavelengths. Therefore optical observations are helpful in, among other things, studying the acceleration and cooling timescales of the electrons in the relativistic jets. We have made very high cadence observations of BL Lac over a number of nights with the Remote Observatory for Variable Object Research (ROVOR). Each night shows secular drift as well as a number of microvariable events lasting only a few minutes each. These data were then processed, compiled, and analyzed in order to examine the underlying mechanism that resulted in such activity. A geometric model is introduced that has worked well in the past on other similar sources.Our relativistic jet model consists of a slowly varying beamed source that already appears bright because it lies nearly to our line of sight. From this, individual relativistic components are ejected a few degrees relative to the aforementioned beaming angle. This is what we believe is responsible for the microvariability emission.

The Euler-Poisson-Darboux equation for relativists

NASA Astrophysics Data System (ADS)

Stewart, John M.

2009-09-01

The Euler-Poisson-Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space-time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space-times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm.

A novel quantum-mechanical interpretation of the Dirac equation

NASA Astrophysics Data System (ADS)

K-H Kiessling, M.; Tahvildar-Zadeh, A. S.

2016-04-01

A novel interpretation is given of Dirac’s ‘wave equation for the relativistic electron’ as a quantum-mechanical one-particle equation. In this interpretation the electron and the positron are merely the two different ‘topological spin’ states of a single more fundamental particle, not distinct particles in their own right. The new interpretation is backed up by the existence of such ‘bi-particle’ structures in general relativity, in particular the ring singularity present in any spacelike section of the spacetime singularity of the maximal-analytically extended, topologically non-trivial, electromagnetic Kerr-Newman (KN)spacetime in the zero-gravity limit (here, ‘zero-gravity’ means the limit G\\to 0, where G is Newton’s constant of universal gravitation). This novel interpretation resolves the dilemma that Dirac’s wave equation seems to be capable of describing both the electron and the positron in ‘external’ fields in many relevant situations, while the bi-spinorial wave function has only a single position variable in its argument, not two—as it should if it were a quantum-mechanical two-particle wave equation. A Dirac equation is formulated for such a ring-like bi-particle which interacts with a static point charge located elsewhere in the topologically non-trivial physical space associated with the moving ring particle, the motion being governed by a de Broglie-Bohm type law extracted from the Dirac equation. As an application, the pertinent general-relativistic zero-gravity hydrogen problem is studied in the usual Born-Oppenheimer approximation. Its spectral results suggest that the zero-G KN magnetic moment be identified with the so-called ‘anomalous magnetic moment of the physical electron,’ not with the Bohr magneton, so that the ring radius is only a tiny fraction of the electron’s reduced Compton wavelength.

Quantum And Relativistic Protocols For Secure Multi-Party Computation

NASA Astrophysics Data System (ADS)

Colbeck, Roger

2009-11-01

After a general introduction, the thesis is divided into four parts. In the first, we discuss the task of coin tossing, principally in order to highlight the effect different physical theories have on security in a straightforward manner, but, also, to introduce a new protocol for non-relativistic strong coin tossing. This protocol matches the security of the best protocol known to date while using a conceptually different approach to achieve the task. In the second part variable bias coin tossing is introduced. This is a variant of coin tossing in which one party secretly chooses one of two biased coins to toss. It is shown that this can be achieved with unconditional security for a specified range of biases, and with cheat-evident security for any bias. We also discuss two further protocols which are conjectured to be unconditionally secure for any bias. The third section looks at other two-party secure computations for which, prior to our work, protocols and no-go theorems were unknown. We introduce a general model for such computations, and show that, within this model, a wide range of functions are impossible to compute securely. We give explicit cheating attacks for such functions. In the final chapter we discuss the task of expanding a private random string, while dropping the usual assumption that the protocol's user trusts her devices. Instead we assume that all quantum devices are supplied by an arbitrarily malicious adversary. We give two protocols that we conjecture securely perform this task. The first allows a private random string to be expanded by a finite amount, while the second generates an arbitrarily large expansion of such a string.

Magnetohydrodynamic waves with relativistic electrons and positrons in degenerate spin-1/2 astrophysical plasmas

NASA Astrophysics Data System (ADS)

Maroof, R.; Ali, S.; Mushtaq, A.; Qamar, A.

2015-11-01

Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.

The NASA Neutron Star Grand Challenge: The coalescences of Neutron Star Binary System

NASA Astrophysics Data System (ADS)

Suen, Wai-Mo

1998-04-01

NASA funded a Grand Challenge Project (9/1996-1999) for the development of a multi-purpose numerical treatment for relativistic astrophysics and gravitational wave astronomy. The coalescence of binary neutron stars is chosen as the model problem for the code development. The institutes involved in it are the Argonne Lab, Livermore lab, Max-Planck Institute at Potsdam, StonyBrook, U of Illinois and Washington U. We have recently succeeded in constructing a highly optimized parallel code which is capable of solving the full Einstein equations coupled with relativistic hydrodynamics, running at over 50 GFLOPS on a T3E (the second milestone point of the project). We are presently working on the head-on collisions of two neutron stars, and the inclusion of realistic equations of state into the code. The code will be released to the relativity and astrophysics community in April of 1998. With the full dynamics of the spacetime, relativistic hydro and microphysics all combined into a unified 3D code for the first time, many interesting large scale calculations in general relativistic astrophysics can now be carried out on massively parallel computers.

Relativistic N-body simulations with massive neutrinos

NASA Astrophysics Data System (ADS)

Adamek, Julian; Durrer, Ruth; Kunz, Martin

2017-11-01

Some of the dark matter in the Universe is made up of massive neutrinos. Their impact on the formation of large scale structure can be used to determine their absolute mass scale from cosmology, but to this end accurate numerical simulations have to be developed. Due to their relativistic nature, neutrinos pose additional challenges when one tries to include them in N-body simulations that are traditionally based on Newtonian physics. Here we present the first numerical study of massive neutrinos that uses a fully relativistic approach. Our N-body code, gevolution, is based on a weak-field formulation of general relativity that naturally provides a self-consistent framework for relativistic particle species. This allows us to model neutrinos from first principles, without invoking any ad-hoc recipes. Our simulation suite comprises some of the largest neutrino simulations performed to date. We study the effect of massive neutrinos on the nonlinear power spectra and the halo mass function, focusing on the interesting mass range between 0.06 eV and 0.3 eV and including a case for an inverted mass hierarchy.

Non-linear hydrodynamical evolution of rotating relativistic stars: numerical methods and code tests

NASA Astrophysics Data System (ADS)

Font, José A.; Stergioulas, Nikolaos; Kokkotas, Kostas D.

2000-04-01

We present numerical hydrodynamical evolutions of rapidly rotating relativistic stars, using an axisymmetric, non-linear relativistic hydrodynamics code. We use four different high-resolution shock-capturing (HRSC) finite-difference schemes (based on approximate Riemann solvers) and compare their accuracy in preserving uniformly rotating stationary initial configurations in long-term evolutions. Among these four schemes, we find that the third-order piecewise parabolic method scheme is superior in maintaining the initial rotation law in long-term evolutions, especially near the surface of the star. It is further shown that HRSC schemes are suitable for the evolution of perturbed neutron stars and for the accurate identification (via Fourier transforms) of normal modes of oscillation. This is demonstrated for radial and quadrupolar pulsations in the non-rotating limit, where we find good agreement with frequencies obtained with a linear perturbation code. The code can be used for studying small-amplitude or non-linear pulsations of differentially rotating neutron stars, while our present results serve as testbed computations for three-dimensional general-relativistic evolution codes.

Statistical mechanics in the context of special relativity. II.

PubMed

Kaniadakis, G

2005-09-01

The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g., momentum, energy, etc.), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E 66, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits us to construct a coherent and self-consistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which is recovered in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore, this statistical mechanics can be obtained as the stationary case of a generalized kinetic theory governed by an evolution equation obeying the H theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.

General-relativistic pulsar magnetospheric emission

NASA Astrophysics Data System (ADS)

Pétri, J.

2018-06-01

Most current pulsar emission models assume photon production and emission within the magnetosphere. Low-frequency radiation is preferentially produced in the vicinity of the polar caps, whereas the high-energy tail is shifted to regions closer but still inside the light cylinder. We conducted a systematic study of the merit of several popular radiation sites like the polar cap, the outer gap, and the slot gap. We computed sky maps emanating from each emission site according to a prescribed distribution function for the emitting particles made of an electron/positron mixture. Calculations are performed using a three-dimensional integration of the plasma emissivity in the vacuum electromagnetic field of a rotating and centred general-relativistic dipole. We compare Newtonian electromagnetic fields to their general-relativistic counterpart. In the latter case, light bending is also taken into account. As a typical example, light curves and sky maps are plotted for several power-law indices of the particle distribution function. The detailed pulse profiles strongly depend on the underlying assumption about the fluid motion subject to strong electromagnetic fields. This electromagnetic topology enforces the photon propagation direction directly, or indirectly, from aberration effects. We also discuss the implication of a net stellar electric charge on to sky maps. Taking into account, the electric field strongly affects the light curves originating close to the light cylinder, where the electric field strength becomes comparable to the magnetic field strength.

Microlensing of Relativistic Knots in the Quasar HE 1104-1805 AB

NASA Astrophysics Data System (ADS)

Schechter, Paul L.; Udalski, A.; Szymański, M.; Kubiak, M.; Pietrzyński, G.; Soszyński, I.; Woźniak, P.; Żebruń, K.; Szewczyk, O.; Wyrzykowski, Ł.

2003-02-01

We present 3 years of photometry of the ``Double Hamburger'' lensed quasar, HE 1104-1805 AB, obtained on 102 separate nights using the Optical Gravitational Lensing Experiment 1.3 m telescope. Both the A and B images show variations, but with substantial differences in the light curves at all time delays. At the 310 day delay reported by Wisotzki and collaborators, the difference light curve has an rms amplitude of 0.060 mag. The structure functions for the A and B images are quite different, with image A more than twice as variable as image B (a factor of 4 in structure function) on timescales of less than a month. Adopting microlensing as a working hypothesis for the uncorrelated variability, the short timescale argues for the relativistic motion of one or more components of the source. We argue that the small amplitude of the fluctuations is due to the finite size of the source with respect to the microlenses.

Fluid dynamical description of relativistic nuclear collisions

NASA Technical Reports Server (NTRS)

Nix, J. R.; Strottman, D.

1982-01-01

On the basis of both a conventional relativistic nuclear fluid dynamic model and a two fluid generalization that takes into account the interpenetration of the target and projectile upon contact, collisions between heavy nuclei moving at relativistic speeds are calculated. This is done by solving the relevant equations of motion numerically in three spatial dimensions by use of particle in cell finite difference computing techniques. The effect of incorporating a density isomer, or quasistable state, in the nuclear equation of state at three times normal nuclear density, and the effect of doubling the nuclear compressibility coefficient are studied. For the reaction 20Ne + 238U at a laboratory bombarding energy per nucleon of 393 MeV, the calculated distributions in energy and angle of outgoing charged particles are compared with recent experimental data both integrated over all impact parameters and for nearly central collisions.

Relativistic jet models for the BL Lacertae object Mrk 421 during three epochs of observation

NASA Technical Reports Server (NTRS)

Mufson, S. L.; Hutter, D. J.; Kondo, Y.; Wisniewski, W. Z.

1988-01-01

Coordinated observation of the nearby BL Lacertae object Mrk 421 obtained during May 1980, January 1984, and March 1984 are described. These observations give a time-frozen picture of the continuous spectrum of Mrk 421 at X-ray, ultraviolet, optical, and radio wavelengths. The observed spectra have been fitted to an inhomogeneous relativistic jet model. In general, the models reproduce the data well. Many of the observed differences during the three epochs can be attributed to variations in the opening angle of the jet and in the angle that the jet makes to the line of sight. The jet models obtained here are compared with the homogeneous, spherically symmetric, synchrotron self-Compton models for this source. The models are also compared with the relativistic jet models obtained for other active galactic nuclei.

Simulation of Relativistic Shocks and Associated Self-Consistent Radiation

NASA Technical Reports Server (NTRS)

Nishikawa, K.-I.; Niemiec, J.; Medvedev, M.; Zhang, B.; Hardee, P.; Mizuno, Y.; Nordlund, A.; Frederiksen, J.; Sol, H.; Pohl, M.;

Relativistic corrections to the form factors of Bc into P-wave orbitally excited charmonium

NASA Astrophysics Data System (ADS)

Zhu, Ruilin

2018-06-01

We investigated the form factors of the Bc meson into P-wave orbitally excited charmonium using the nonrelativistic QCD effective theory. Through the analytic computation, the next-to-leading order relativistic corrections to the form factors were obtained, and the asymptotic expressions were studied in the infinite bottom quark mass limit. Employing the general form factors, we discussed the exclusive decays of the Bc meson into P-wave orbitally excited charmonium and a light meson. We found that the relativistic corrections lead to a large correction for the form factors, which makes the branching ratios of the decay channels B (Bc ± →χcJ (hc) +π± (K±)) larger. These results are useful for the phenomenological analysis of the Bc meson decays into P-wave charmonium, which shall be tested in the LHCb experiments.

Simulation of Relativistic Shocks and Associated Radiation from Turbulent Magnetic Fields

NASA Technical Reports Server (NTRS)

Nishikawa, K.-I.; Mizuno, Y.; Niemiec, J.; Medvedev, M.; Zhang, B.; Hardee, P.; Frederiksen, J.; Sol, H.; Pohl, M.; Hartmann, D. H.;

Relativity in the Global Positioning System.

PubMed

Ashby, Neil

2003-01-01

The Global Positioning System (GPS) uses accurate, stable atomic clocks in satellites and on the ground to provide world-wide position and time determination. These clocks have gravitational and motional frequency shifts which are so large that, without carefully accounting for numerous relativistic effects, the system would not work. This paper discusses the conceptual basis, founded on special and general relativity, for navigation using GPS. Relativistic principles and effects which must be considered include the constancy of the speed of light, the equivalence principle, the Sagnac effect, time dilation, gravitational frequency shifts, and relativity of synchronization. Experimental tests of relativity obtained with a GPS receiver aboard the TOPEX/POSEIDON satellite will be discussed. Recently frequency jumps arising from satellite orbit adjustments have been identified as relativistic effects. These will be explained and some interesting applications of GPS will be discussed.

Relativistic cosmic-ray spectra in the fully nonlinear theory of shock acceleration

NASA Technical Reports Server (NTRS)

Ellison, D. C.; Eichler, D.

1985-01-01

The non-linear theory of shock acceleration was generalized to include wave dynamics. In the limit of rapid wave damping, it is found that a finite wave velocity tempers the acceleration of high Mach number shocks and limits the maximum compression ratio even when energy loss is important. For a given spectrum, the efficiency of relativistic particle production is essentially independent of v sub Ph. For the three families shown, the percentage of kinetic energy flux going into relativistic particles is (1) 72 percent, (2) 44 percent, and (3) 26 percent (this includes the energy loss at the upper energy cutoff). Even small v sub ph, typical of the HISM, produce quasi-universal spectra that depend only weakly on the acoustic Mach number. These spectra should be close enough to e(-2) to satisfy cosmic ray source requirements.

A SCILAB Program for Computing General-Relativistic Models of Rotating Neutron Stars by Implementing Hartle's Perturbation Method

NASA Astrophysics Data System (ADS)

Papasotiriou, P. J.; Geroyannis, V. S.

We implement Hartle's perturbation method to the computation of relativistic rigidly rotating neutron star models. The program has been written in SCILAB (© INRIA ENPC), a matrix-oriented high-level programming language. The numerical method is described in very detail and is applied to many models in slow or fast rotation. We show that, although the method is perturbative, it gives accurate results for all practical purposes and it should prove an efficient tool for computing rapidly rotating pulsars.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations

NASA Astrophysics Data System (ADS)

de Wijs, G. A.; Laskowski, R.; Blaha, P.; Havenith, R. W. A.; Kresse, G.; Marsman, M.

2017-02-01

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

NMR shieldings from density functional perturbation theory: GIPAW versus all-electron calculations.

PubMed

de Wijs, G A; Laskowski, R; Blaha, P; Havenith, R W A; Kresse, G; Marsman, M

2017-02-14

We present a benchmark of the density functional linear response calculation of NMR shieldings within the gauge-including projector-augmented-wave method against all-electron augmented-plane-wave+local-orbital and uncontracted Gaussian basis set results for NMR shieldings in molecular and solid state systems. In general, excellent agreement between the aforementioned methods is obtained. Scalar relativistic effects are shown to be quite large for nuclei in molecules in the deshielded limit. The small component makes up a substantial part of the relativistic corrections.

Dilational symmetry-breaking in thermodynamics

NASA Astrophysics Data System (ADS)

Lin, Chris L.; Ordóñez, Carlos R.

2017-04-01

Using thermodynamic relations and dimensional analysis we derive a general formula for the thermodynamical trace 2{ E}-DP for nonrelativistic systems and { E}-DP for relativistic systems, where D is the number of spatial dimensions, in terms of the microscopic scales of the system within the grand canonical ensemble. We demonstrate the formula for several cases, including anomalous systems which develop scales through dimensional transmutation. Using this relation, we make explicit the connection between dimensional analysis and the virial theorem. This paper is focused mainly on the non-relativistic aspects of this relation.

Open/closed string duality and relativistic fluids

NASA Astrophysics Data System (ADS)

Niarchos, Vasilis

2016-07-01

We propose an open/closed string duality in general backgrounds extending previous ideas about open string completeness by Ashoke Sen. Our proposal sets up a general version of holography that works in gravity as a tomographic principle. We argue, in particular, that previous expectations of a supergravity/Dirac-Born-Infeld (DBI) correspondence are naturally embedded in this conjecture and can be tested in a well-defined manner. As an example, we consider the correspondence between open string field theories on extremal D-brane setups in flat space in the large-N , large 't Hooft limit, and asymptotically flat solutions in ten-dimensional type II supergravity. We focus on a convenient long-wavelength regime, where specific effects of higher-spin open string modes can be traced explicitly in the dual supergravity computation. For instance, in this regime we show how the full Abelian DBI action arises from supergravity as a straightforward reformulation of relativistic hydrodynamics. In the example of a (2 +1 )-dimensional open string theory this reformulation involves an Abelian Hodge duality. We also point out how different deformations of the DBI action, related to higher-derivative corrections and non-Abelian effects, can arise in this context as deformations in corresponding relativistic hydrodynamics.

Radiation from Accelerated Particles in Shocks and Reconnections

NASA Technical Reports Server (NTRS)

Nishikawa, K.-I.; Zhang, B.; Niemiec, J.; Medvedev, M.; Hardee, P.; Mizuno, Y.; Nordlund, A.; Frederiksen, J. T.; Sol, H.; Pohl, M.;

Rigorous coupled wave analysis of acousto-optics with relativistic considerations.

PubMed

Xia, Guoqiang; Zheng, Weijian; Lei, Zhenggang; Zhang, Ruolan

2015-09-01

A relativistic analysis of acousto-optics is presented, and a rigorous coupled wave analysis is generalized for the diffraction of the acousto-optical effect. An acoustic wave generates a grating with temporally and spatially modulated permittivity, hindering direct applications of the rigorous coupled wave analysis for the acousto-optical effect. In a reference frame which moves with the acoustic wave, the grating is static, the medium moves, and the coupled wave equations for the static grating may be derived. Floquet's theorem is then applied to cast these equations into an eigenproblem. Using a Lorentz transformation, the electromagnetic fields in the grating region are transformed to the lab frame where the medium is at rest, and relativistic Doppler frequency shifts are introduced into various diffraction orders. In the lab frame, the boundary conditions are considered and the diffraction efficiencies of various orders are determined. This method is rigorous and general, and the plane waves in the resulting expansion satisfy the dispersion relation of the medium and are propagation modes. Properties of various Bragg diffractions are results, rather than preconditions, of this method. Simulations of an acousto-optical tunable filter made by paratellurite, TeO(2), are given as examples.

PHYSICAL-CONSTRAINT-PRESERVING CENTRAL DISCONTINUOUS GALERKIN METHODS FOR SPECIAL RELATIVISTIC HYDRODYNAMICS WITH A GENERAL EQUATION OF STATE

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Kailiang; Tang, Huazhong, E-mail: wukl@pku.edu.cn, E-mail: hztang@math.pku.edu.cn

The ideal gas equation of state (EOS) with a constant adiabatic index is a poor approximation for most relativistic astrophysical flows, although it is commonly used in relativistic hydrodynamics (RHD). This paper develops high-order accurate, physical-constraints-preserving (PCP), central, discontinuous Galerkin (DG) methods for the one- and two-dimensional special RHD equations with a general EOS. It is built on our theoretical analysis of the admissible states for RHD and the PCP limiting procedure that enforce the admissibility of central DG solutions. The convexity, scaling invariance, orthogonal invariance, and Lax–Friedrichs splitting property of the admissible state set are first proved with themore » aid of its equivalent form. Then, the high-order central DG methods with the PCP limiting procedure and strong stability-preserving time discretization are proved, to preserve the positivity of the density, pressure, specific internal energy, and the bound of the fluid velocity, maintain high-order accuracy, and be L {sup 1}-stable. The accuracy, robustness, and effectiveness of the proposed methods are demonstrated by several 1D and 2D numerical examples involving large Lorentz factor, strong discontinuities, or low density/pressure, etc.« less

Irradiation of an Accretion Disc by a Jet: General Properties and Implications for Spin Measurements of Black Holes

NASA Technical Reports Server (NTRS)

T.Dauser; Garcia, J.; Wilms, J.; Boeck, M.; Brenneman, L. W.; Falanga, M.; Fukumura, Keigo; Reynolds, C. S.

2013-01-01

X-ray irradiation of the accretion disc leads to strong reflection features, which are then broadened and distorted by relativistic effects. We present a detailed, general relativistic approach to model this irradiation for different geometries of the primary X-ray source. These geometries include the standard point source on the rotational axis as well as more jet-like sources, which are radially elongated and accelerating. Incorporating this code in the RELLINE model for relativistic line emission, the line shape for any configuration can be predicted. We study how different irradiation geometries affect the determination of the spin of the black hole. Broad emission lines are produced only for compact irradiating sources situated close to the black hole. This is the only case where the black hole spin can be unambiguously determined. In all other cases the line shape is narrower, which could either be explained by a low spin or an elongated source. We conclude that for those cases and independent of the quality of the data, no unique solution for the spin exists and therefore only a lower limit of the spin value can be given

Outflows in X-ray binaries

NASA Astrophysics Data System (ADS)

Diaz Trigo, M.

2017-10-01

Accretion onto neutron stars and black holes powers the most luminous phenomena in the Universe. Associated to it is the existence of outflows, in the form of uncollimated winds or highly collimated relativistic jets. The origin of outflows and their feedback to the environment is one of the most debated topics in astrophysics today. In this talk I will review the current understanding of accretion disc winds in X-ray binaries, their launching mechanism and their relation to specific accretion states. I will also discuss the potential interplay between the appearance/disappearance of such winds and relativistic jets and the insight gained with ongoing multi-wavelength observational programmes focused on the variability of such phenomena.

Exact Solution of Klein-Gordon and Dirac Equations with Snyder-de Sitter Algebra

NASA Astrophysics Data System (ADS)

Merad, M.; Hadj Moussa, M.

2018-01-01

In this paper, we present the exact solution of the (1+1)-dimensional relativistic Klein-Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder-de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen-Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for α 1 and α 2 → 0 and are compared with those of literature.

ASTRORAY: General relativistic polarized radiative transfer code

NASA Astrophysics Data System (ADS)

Shcherbakov, Roman V.

2014-07-01

ASTRORAY employs a method of ray tracing and performs polarized radiative transfer of (cyclo-)synchrotron radiation. The radiative transfer is conducted in curved space-time near rotating black holes described by Kerr-Schild metric. Three-dimensional general relativistic magneto hydrodynamic (3D GRMHD) simulations, in particular performed with variations of the HARM code, serve as an input to ASTRORAY. The code has been applied to reproduce the sub-mm synchrotron bump in the spectrum of Sgr A*, and to test the detectability of quasi-periodic oscillations in its light curve. ASTRORAY can be readily applied to model radio/sub-mm polarized spectra of jets and cores of other low-luminosity active galactic nuclei. For example, ASTRORAY is uniquely suitable to self-consistently model Faraday rotation measure and circular polarization fraction in jets.

High order volume-preserving algorithms for relativistic charged particles in general electromagnetic fields

NASA Astrophysics Data System (ADS)

He, Yang; Sun, Yajuan; Zhang, Ruili; Wang, Yulei; Liu, Jian; Qin, Hong

2016-09-01

We construct high order symmetric volume-preserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volume-preserving methods that can be applied to systems with time-dependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracy-enhancing processing technique, the explicit methods obtain high-order accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations.

Probing the magnetic field structure in Sgr A* on Black Hole Horizon Scales with Polarized Radiative Transfer Simulations

NASA Astrophysics Data System (ADS)

Gold, Roman; McKinney, Jonathan; Johnson, Michael; Doeleman, Sheperd; Event Horizon Telescope Collaboration

2016-03-01

Accreting black holes (BHs) are at the core of relativistic astrophysics as messengers of the strong-field regime of General Relativity and prime targets of several observational campaigns, including imaging the black hole shadow in SagA* and M87 with the Event Horizon Telescope. I will present results from general-relativistic, polarized radiatiative transfer models for the inner accretion flow in Sgr A*. The models use time dependent, global GRMHD simulations of hot accretion flows including standard-and-normal-evolution (SANE) and magnetically arrested disks (MAD). I present comparisons of these synthetic data sets to the most recent observations with the Event Horizon Telescope and show how the data distinguishes the models and probes the magnetic field structure.

Fragments of Science: Festschrift for Mendel Sachs

NASA Astrophysics Data System (ADS)

Ram, Michael

1999-11-01

The Table of Contents for the full book PDF is as follows: * Preface * Sketches at a Symposium * For Mendel Sachs * The Constancy of an Angular Point of View * Information-Theoretic Logic and Transformation-Theoretic Logic * The Invention of the Transistor and the Realization of the Hole * Mach's Principle, Newtonian Gravitation, Absolute Space, and Einstein * The Sun, Our Variable Star * The Inconstant Sun: Symbiosis of Time Variations of Sunspots, Atmospheric Radiocarbon, Aurorae, and Tree Ring Growth * Other Worlds * Super-Classical Quantum Mechanics * A Probabilistic Approach to the Phase Problem of X-Ray Crystallography * A Nonlinear Twist on Inertia Gives Unified Electroweak Gravitation * Neutrino Oscillations * On an Incompleteness in the General-Relativistic Description of Gravitation * All Truth is One * Ideas of Physics: Correspondence between Colleagues * The Influence of the Physics and Philosophy of Einstein's Relativity on My Attitudes in Science: An Autobiography

Unitary Quantum Relativity. (Work in Progress)

NASA Astrophysics Data System (ADS)

Finkelstein, David Ritz

2017-01-01

A quantum universe is expressed as a finite unitary relativistic quantum computer network. Its addresses are subject to quantum superposition as well as its memory. It has no exact mathematical model. It Its Hilbert space of input processes is also a Clifford algebra with a modular architecture of many ranks. A fundamental fermion is a quantum computer element whose quantum address belongs to the rank below. The least significant figures of its address define its spin and flavor. The most significant figures of it adress define its orbital variables. Gauging arises from the same quantification as space-time. This blurs star images only slightly, but perhaps measurably. General relativity is an approximation that splits nature into an emptiness with a high symmetry that is broken by a filling of lower symmetry. Action principles result from self-organization pf the vacuum.

Hamiltonian dynamics of extended objects

NASA Astrophysics Data System (ADS)

Capovilla, R.; Guven, J.; Rojas, E.

2004-12-01

We consider relativistic extended objects described by a reparametrization-invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the dynamics of such higher derivative models which is motivated by the ADM formulation of general relativity. The canonical momenta are identified by looking at boundary behaviour under small deformations of the action; the relationship between the momentum conjugate to the embedding functions and the conserved momentum density is established. The canonical Hamiltonian is constructed explicitly; the constraints on the phase space, both primary and secondary, are identified and the role they play in the theory is described. The multipliers implementing the primary constraints are identified in terms of the ADM lapse and shift variables and Hamilton's equations are shown to be consistent with the Euler Lagrange equations.

Optical Variability of BL Lacertae During the Major Outburst of 1997

NASA Technical Reports Server (NTRS)

Ghosh, K. K.; Ramsey, B. D.; Sadun, A. C.; Soundararajaperumal, S.; Wang, J.

2000-01-01

We have undertaken an investigation of recent flux variability in BL Lac. We present optical observations taken over 22 nights documenting major as well as minor outbursts. This has been combined, for purposes of multifrequency analysis, with published X-ray and T-ray data taken for an additional single night, On two nights in particular, including the night of the X-ray observations, a major outburst of about a full magnitude of variation was recorded. All the data have been analyzed with theoretical models. Attempts were made to use synchrotron self-Compton and external Comptonization models to explain the data; however, both classes of models were found lacking. More satisfactory results were obtained using an analytical model proposed by Wang et al. that involves the evolution of synchrotron spectra in a homogeneous jet due to the injection of relativistic electrons, taking into account radiation losses during the outbursts. It is hoped that the results of this study of BL Lac, an archetype for the class of blazars in general, represent a more generic phenomenon applicable to the entire class.

Optical Variability of BL Lacertae During the Major Outburst of 1997

NASA Technical Reports Server (NTRS)

Ghosh, K. K.; Ramsey, B. D.; Sadun, A. C.; Soundarajaperumal, S.; Wang, J.

1999-01-01

We have undertaken an investigation of recent flux variability in BL Lac. We present optical observations taken over 12 nights documenting major as well as minor outbursts. This has been combined, for purposes of multifrequency analysis, with published X-ray and gamma ray data taken for an additional single night. On two nights in particular, which includes the night of the X-ray observations, a major outburst of about a full magnitude of variation was recorded. All the data have been analyzed with theoretical models. Attempts were made to use synchrotron self-Compton and external Comptonization models to explain the data; however both classes of models were found lacking. More satisfactory results were obtained using an analytical model proposed by Wang et al. that involves the evolution of synchrotron spectra in a homogeneous jet due to the injection of relativistic electrons, taking into account radiation losses during the outbursts. It is hoped that the results of this study of BL Lac, an archetype for the class of blazars in general, represent a more generic phenomenon applicable to the entire class.

Quantum effects in the cosmic microwave background radiation

NASA Astrophysics Data System (ADS)

Messer, J.

1990-11-01

Based on the quantum correlated general relativistic Vlasov equations in an Einstein-de Sitter universe, we show that quantum effects are beyond measurability in the cosmic microwave background radiation.

Gravitational Stokes parameters. [for electromagnetic and gravitational radiation in relativity

NASA Technical Reports Server (NTRS)

Anile, A. M.; Breuer, R. A.

1974-01-01

The electromagnetic and gravitational Stokes parameters are defined in the general theory of relativity. The general-relativistic equation of radiative transfer for polarized radiation is then derived in terms of the Stokes parameters for both high-frequency electromagnetic and gravitational waves. The concept of Stokes parameters is generalized for the most general class of metric theories of gravity, where six (instead of two) independent states of polarization are present.

Relativistic Outflows from Advection-dominated Accretion Disks around Black Holes

NASA Astrophysics Data System (ADS)

Becker, Peter A.; Subramanian, Prasad; Kazanas, Demosthenes

2001-05-01

Advection-dominated accretion flows (ADAFs) have a positive Bernoulli parameter and are therefore gravitationally unbound. The Newtonian ADAF model has been generalized recently to obtain the ADIOS model that includes outflows of energy and angular momentum, thereby allowing accretion to proceed self-consistently. However, the utilization of a Newtonian gravitational potential limits the ability of this model to describe the inner region of the disk, where any relativistic outflows are likely to originate. In this paper we modify the ADIOS scenario to incorporate a pseudo-Newtonian potential, which approximates the effects of general relativity. The analysis yields a unique, self-similar solution for the structure of the coupled disk/wind system. Interesting features of the new solution include the relativistic character of the outflow in the vicinity of the radius of marginal stability, which represents the inner edge of the quasi-Keplerian disk in our model. Hence, our self-similar solution may help to explain the origin of relativistic jets in active galaxies. At large distances the radial dependence of the accretion rate approaches the unique form M~r1/2, with an associated density variation given by ρ~r-1. This density variation agrees with that implied by the dependence of the hard X-ray time lags on the Fourier frequency for a number of accreting galactic black hole candidates. While intriguing, the predictions made using our self-similar solution need to be confirmed in the future using a detailed model that includes a physical description of the energization mechanism that drives the outflow, which is likely to be powered by the shear of the underlying accretion disk.

Relativistic Outflows from ADAFs

NASA Astrophysics Data System (ADS)

Becker, Peter; Subramanian, Prasad; Kazanas, Demosthenes

2001-04-01

Advection-dominated accretion flows (ADAFs) have a positive Bernoulli parameter, and are therefore gravitationally bound. The Newtonian ADAF model has been generalized recently to obtain the ADIOS model that includes outflows of energy and angular momentum, thereby allowing accretion to proceed self-consistently. However, the utilization of a Newtonian gravitational potential limits the ability of this model to describe the inner region of the disk, where any relativistic outflows are likely to originate. In this paper we modify the ADIOS scenario to incorporate a seudo - Newtonian potential, which approximates the effects of general relativity. The analysis yields a unique, self - similar solution for the structure of the coupled disk/wind system. Interesting features of the new solution include the relativistic character of the outflow in the vicinity of the radius of marginal stability, which represents the inner edge of the quasi-Keplerian disk in our model. Our self - similar model may therefore help to explain the origin of relativistic jets in active galaxies. At large distances the radial dependence of the accretion rate approachs the unique form dot M ∝ r^1/2, with an associated density variation given by ρ ∝ r-1. This density variation agrees with that implied by the dependence of the X-ray hard time lags on the Fourier frequency for a number of accreting galactic black hole candidates. While intriguing, the results of our self-similar model need to be confirmed in the future by incorporating a detailed physical description of the energization mechanism that drives the outflow, which is likely to be powered by the shear of the underlying accretion disk.

The behavior of beams of relativistic non-thermal electrons under the influence of collisions and synchrotron losses

NASA Technical Reports Server (NTRS)

Mctiernan, James M.; Petrosian, Vahe

1989-01-01

For many astrophysical situations, such as in solar flares or cosmic gamma-ray bursts, continuum gamma rays with energies up to hundreds of MeV were observed, and can be interpreted to be due to bremsstrahlung radiation by relativistic electrons. The region of acceleration for these particles is not necessarily the same as the region in which the radiation is produced, and the effects of the transport of the electrons must be included in the general problem. Hence it is necessary to solve the kinetic equation for relativistic electrons, including all the interactions and loss mechanisms relevant at such energies. The resulting kinetic equation for non-thermal electrons, including the effects of Coulomb collisions and losses due to synchrotron emission, was solved analytically in some simple limiting cases, and numerically for the general cases including constant and varying background plasma density and magnetic field. New approximate analytic solutions are presented for collision dominated cases, for small pitch angles and all energies, synchrotron dominated cases, both steady-state and time dependent, for all pitch angles and energies, and for cases when both synchrotron and collisional energy losses are important, but for relativistic electrons. These analytic solutions are compared to the full numerical results in the proper limits. These results will be useful for calculation of spectra and angular distribution of the radiation (x rays, gamma-rays, and microwaves) emitted via synchrotron or bremsstrahlung processes by the electrons. These properties and their relevance to observations will be observed in subsequent papers.

Cosmic Extremes: Probing Energetic Transients with Radio Observations

NASA Astrophysics Data System (ADS)

Denham Alexander, Kate

2018-01-01

With the advent of sensitive facilities like the Karl G. Jansky Very Large Array (VLA) and planning well underway for vastly more powerful wide-field interferometers like the Square Kilometer Array, the study of radio astrophysical transients is poised for dramatic growth. Radio observations provide a unique window into a wide variety of transient events, from gamma-ray bursts (GRBs) to supernovae to tidal disruption events (TDEs) in which a star is torn apart by a supermassive black hole. In particular, GRBs and TDEs have emerged as valuable probes of some of the most extreme physics in the Universe. In these high-energy laboratories, the longer timescale of radio emission allows for extensive followup and characterization of the event energies and the densities of surrounding material. I will present high-cadence broadband radio studies of GRB afterglows and TDEs undertaken with the goal of learning more about their physical properties, the physics underlying the formation and growth of relativistic jets and outflows, and the environments in which these events occur. Our observations confirm that only a small fraction of TDEs produce relativistic jets but reveal low-luminosity, non-relativistic outflows in two nearby TDEs, allowing us to begin constraining the bulk of the TDE population. Our GRB radio observations reveal both intrinsic variability (reverse shocks) and extrinsic variability (interstellar scintillation). The insights derived from these studies will be invaluable for designing and interpreting the results from future radio transient surveys.

Lighthouse in the dust: infrared echoes of periodic emission from massive black hole binaries★

NASA Astrophysics Data System (ADS)

D'Orazio, Daniel J.; Haiman, Zoltán

2017-09-01

The optical and UV emission from sub-parsec massive black hole binaries (MBHBs) in active galactic nuclei (AGNs) is believed to vary periodically, on time-scales comparable to the binary's orbital time. If driven by accretion rate fluctuations, the variability could be isotropic. If dominated by relativistic Doppler modulation, the variability should instead be anisotropic, resembling a rotating forward-beamed lighthouse. We consider the infrared (IR) reverberation of either type of periodic emission by pc-scale circumbinary dust tori. We predict the phase and amplitude of IR variability as a function of the ratio of dust light crossing time to the source variability period, and of the torus inclination and opening angle. We enumerate several differences between the isotropic and anisotropic cases. Interestingly, for a nearly face-on binary with an inclined dust torus, the Doppler boost can produce IR variability without any observable optical/UV variability. Such orphan-IR variability would have been missed in optical searches for periodic AGNs. We apply our models to time-domain WISE IR data from the MBHB candidate PG 1302-102 and find consistency with dust reverberation by both isotropically emitting and Doppler-boosted sources in the shorter wavelength W1-W2 (2.8 → 5.3 μm) bands. We constrain the dust torus to be thin (aspect ratio ˜ 0.1), with an inner radius at 1-5 pc. More generally, our dust-echo models will aid in identifying new MBHB candidates, determining their nature and constraining the physical properties of MBHBs and their dust tori.

Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cardall, Christian Y.

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. Here, a relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal+kinetic energy in the appropriate limit—emerges naturally and self-consistently from themore » difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass m, when m is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.« less

Relativistic centrifugal instability

NASA Astrophysics Data System (ADS)

Gourgouliatos, Konstantinos N.; Komissarov, Serguei S.

2018-03-01

Near the central engine, many astrophysical jets are expected to rotate about their axis. Further out they are expected to go through the processes of reconfinement and recollimation. In both these cases, the flow streams along a concave surface and hence, it is subject to the centrifugal force. It is well known that such flows may experience the centrifugal instability (CFI), to which there are many laboratory examples. The recent computer simulations of relativistic jets from active galactic nuclei undergoing the process of reconfinement show that in such jets CFI may dominate over the Kelvin-Helmholtz instability associated with velocity shear (Gourgouliatos & Komissarov). In this letter, we generalize the Rayleigh criterion for CFI in rotating fluids to relativistic flows using a heuristic analysis. We also present the results of computer simulations which support our analytic criterion for the case of an interface separating two uniformly rotating cylindrical flows. We discuss the difference between CFI and the Rayleigh-Taylor instability in flows with curved streamlines.

Relativistic analogue of the Newtonian fluid energy equation with nucleosynthesis

DOE PAGES

Cardall, Christian Y.

2017-12-15

In Newtonian fluid dynamics simulations in which composition has been tracked by a nuclear reaction network, energy generation due to composition changes has generally been handled as a separate source term in the energy equation. Here, a relativistic equation in conservative form for total fluid energy, obtained from the spacetime divergence of the stress-energy tensor, in principle encompasses such energy generation; but it is not explicitly manifest. An alternative relativistic energy equation in conservative form—in which the nuclear energy generation appears explicitly, and that reduces directly to the Newtonian internal+kinetic energy in the appropriate limit—emerges naturally and self-consistently from themore » difference of the equation for total fluid energy and the equation for baryon number conservation multiplied by the average baryon mass m, when m is expressed in terms of contributions from the nuclear species in the fluid, and allowed to be mutable.« less

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star - I. Formulation of the equations

NASA Astrophysics Data System (ADS)

Rezzolla, L.; Ahmedov, B. J.; Miller, J. C.

2001-04-01

We present analytic solutions of Maxwell equations in the internal and external background space-time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space-time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space-time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.

Stationary phase method and delay times for relativistic and non-relativistic tunneling particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bernardini, A.E.

2009-06-15

The stationary phase method is frequently adopted for calculating tunneling phase times of analytically-continuous Gaussian or infinite-bandwidth step pulses which collide with a potential barrier. This report deals with the basic concepts on deducing transit times for quantum scattering: the stationary phase method and its relation with delay times for relativistic and non-relativistic tunneling particles. After reexamining the above-barrier diffusion problem, we notice that the applicability of this method is constrained by several subtleties in deriving the phase time that describes the localization of scattered wave packets. Using a recently developed procedure - multiple wave packet decomposition - for somemore » specifical colliding configurations, we demonstrate that the analytical difficulties arising when the stationary phase method is applied for obtaining phase (traversal) times are all overcome. In this case, we also investigate the general relation between phase times and dwell times for quantum tunneling/scattering. Considering a symmetrical collision of two identical wave packets with an one-dimensional barrier, we demonstrate that these two distinct transit time definitions are explicitly connected. The traversal times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Multiple wave packet decomposition shows us that the phase time (group delay) describes the exact position of the scattered particles and, in addition to the exact relation with the dwell time, leads to correct conceptual understanding of both transit time definitions. At last, we extend the non-relativistic formalism to the solutions for the tunneling zone of a one-dimensional electrostatic potential in the relativistic (Dirac to Klein-Gordon) wave equation where the incoming wave packet exhibits the possibility of being almost totally transmitted through the potential barrier. The conditions for the occurrence of accelerated and, eventually, superluminal tunneling transmission probabilities are all quantified and the problematic superluminal interpretation based on the non-relativistic tunneling dynamics is revisited. Lessons concerning the dynamics of relativistic tunneling and the mathematical structure of its solutions suggest revealing insights into mathematically analogous condensed-matter experiments using electrostatic barriers in single- and bi-layer graphene, for which the accelerated tunneling effect deserves a more careful investigation.« less

Normalizing a relativistic model of X-ray reflection. Definition of the reflection fraction and its implementation in relxill

NASA Astrophysics Data System (ADS)

Dauser, T.; García, J.; Walton, D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.

2016-05-01

Aims: The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods: The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results: Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model, namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions: Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name refl_frac in all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).

Normalizing a Relativistic Model of X-Ray Reflection Definition of the Reflection Fraction and Its Implementation in relxill

NASA Technical Reports Server (NTRS)

Dauser, T.; Garcia, J.; Walton, D. J.; Eikmann, W.; Kallman, T.; McClintock, J.; Wilms, J.

2016-01-01

Aims. The only relativistic reflection model that implements a parameter relating the intensity incident on an accretion disk to the observed intensity is relxill. The parameter used in earlier versions of this model, referred to as the reflection strength, is unsatisfactory; it has been superseded by a parameter that provides insight into the accretion geometry, namely the reflection fraction. The reflection fraction is defined as the ratio of the coronal intensity illuminating the disk to the coronal intensity that reaches the observer. Methods. The relxill model combines a general relativistic ray-tracing code and a photoionization code to compute the component of radiation reflected from an accretion that is illuminated by an external source. The reflection fraction is a particularly important parameter for relativistic models with well-defined geometry, such as the lamp post model, which is a focus of this paper. Results. Relativistic spectra are compared for three inclinations and for four values of the key parameter of the lamp post model,namely the height above the black hole of the illuminating, on-axis point source. In all cases, the strongest reflection is produced for low source heights and high spin. A low-spin black hole is shown to be incapable of producing enhanced relativistic reflection. Results for the relxill model are compared to those obtained with other models and a Monte Carlo simulation. Conclusions. Fitting data by using the relxill model and the recently implemented reflection fraction, the geometry of a system can be constrained. The reflection-fraction is independent of system parameters such as inclination and black hole spin. The reflection-fraction parameter was implemented with the name reflec_frac all flavours of the relxill model, and the non-relativistic reflection model xillver, in v0.4a (18 January 2016).

Core-dependent and ligand-dependent relativistic corrections to the nuclear magnetic shieldings in MH4-n Y n (n = 0-4; M = Si, Ge, Sn, and Y = H, F, Cl, Br, I) model compounds.

PubMed

Maldonado, Alejandro F; Aucar, Gustavo A; Melo, Juan I

2014-09-01

The nuclear magnetic shieldings of Si, Ge, and Sn in MH(4-n) Y(n) (M = Si, Ge, Sn; Y = F, Cl, Br, I and n = 1-4) molecular systems are highly influenced by the substitution of one or more hydrogens by heavy-halogen atoms. We applied the linear response elimination of small components (LRESC) formalism to calculate those shieldings and learn whether including only a few of the leading relativistic correction terms is sufficient to be able to quantitatively reproduce the full relativistic value. It was observed that the nuclear magnetic shieldings change as the number of heavy halogen substituents and their weights vary, and the pattern of σ(M) generally does not exhibit the normal halogen dependence (NHD) behavior that can be seen in similar molecular systems containing carbon atoms. We also analyzed each relativistic correction afforded by the LRESC method and split them in two: core-dependent and ligand-dependent contributions; we then looked for the electronic mechanisms involved in the different relativistic effects and in the total relativistic value. Based on this analysis, we were able to study the electronic mechanism involved in a recently proposed relativistic effect, the "heavy atom effect on vicinal heavy atom" (HAVHA), in more detail. We found that the main electronic mechanism is the spin-orbit or σ p (T(3)) correction, although other corrections such as σ p (S(1)) and σ p (S(3)) are also important. Finally, we analyzed proton magnetic shieldings and found that, for molecules containing Sn as the central atom, σ(H) decreases as the number of heavy halogen substituents (of the same type: either F, Cl, or Br) increases, albeit at different rates for different halogens. σ(H) only increase as the number of halogen substituents increases if the halogen is iodine.

A Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples.

NASA Astrophysics Data System (ADS)

Tate, Ranjeet Shekhar

1992-01-01

General relativity has two features in particular, which make it difficult to apply to it existing schemes for the quantization of constrained systems. First, there is no background structure in the theory, which could be used, e.g., to regularize constraint operators, to identify a "time" or to define an inner product on physical states. Second, in the Ashtekar formulation of general relativity, which is a promising avenue to quantum gravity, the natural variables for quantization are not canonical; and, classically, there are algebraic identities between them. Existing schemes are usually not concerned with such identities. Thus, from the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a general prescription to find the physical inner product, and is flexible enough to accommodate non -canonical variables. In this dissertation I present an algebraic formulation of the Dirac approach to the quantization of constrained systems. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to general relativity, and may give some insight into the pitfalls lurking in quantum gravity. The previous quantizations of one such model had many surprising features. When this model is quantized using the algebraic program, there is no longer any unexpected behaviour. I also construct the complete quantum theory for a previously unsolved relativistic cosmology. All these models indicate that the algebraic formulation provides powerful new tools for quantization. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such "dynamically constrained" systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.

Relativistic Theory of Gheorghe Zapan for Psychical Phenoma

NASA Astrophysics Data System (ADS)

Sofonea, Liviu

A biography and an account of main scientific research of a Psychologist, Mathematician, Cybernetician, Teacher, Army officer, Lawyer Gheorghe Zapan (1891-1976) and of his relation with Special and General Relativity is given.

Finite-Temperature Relativistic Time-Blocking Approximation for Nuclear Strength Functions

NASA Astrophysics Data System (ADS)

Wibowo, Herlik; Litvinova, Elena

2017-09-01

This work presents an extension of the relativistic nuclear field theory (RNFT) developed throughout the last decade as an approach to the nuclear many-body problem, based on QHD meson-nucleon Lagrangian and relativistic field theory. The unique feature of RNFT is a consistent connection of the high-energy scale of heavy mesons, the medium-energy range of pion, and the low-energy domain of emergent collective vibrations (phonons). RNFT has demonstrated a very good performance in various nuclear structure calculations across the nuclear chart and, in particular, provides a consistent input for description of the two phases of r-process nucleosynthesis: neutron capture and beta decay. Further inclusion of finite temperature effects presented here allows for an extension of the method to highly excited compound nuclei. The covariant response theory in the relativistic time-blocking approximation (RTBA) is generalized for thermal effects, adopting the Matsubara Green's function formalism to the RNFT framework. The finite-temperature RTBA is implemented numerically to calculate multipole strength functions in medium-mass and heavy nuclei. The obtained results will be discussed in comparison to available experimental data and in the context of possible consequences for astrophysics.

Cosmological measurements with general relativistic galaxy correlations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raccanelli, Alvise; Montanari, Francesco; Durrer, Ruth

We investigate the cosmological dependence and the constraining power of large-scale galaxy correlations, including all redshift-distortions, wide-angle, lensing and gravitational potential effects on linear scales. We analyze the cosmological information present in the lensing convergence and in the gravitational potential terms describing the so-called ''relativistic effects'', and we find that, while smaller than the information contained in intrinsic galaxy clustering, it is not negligible. We investigate how neglecting them does bias cosmological measurements performed by future spectroscopic and photometric large-scale surveys such as SKA and Euclid. We perform a Fisher analysis using the CLASS code, modified to include scale-dependent galaxymore » bias and redshift-dependent magnification and evolution bias. Our results show that neglecting relativistic terms, especially lensing convergence, introduces an error in the forecasted precision in measuring cosmological parameters of the order of a few tens of percent, in particular when measuring the matter content of the Universe and primordial non-Gaussianity parameters. The analysis suggests a possible substantial systematic error in cosmological parameter constraints. Therefore, we argue that radial correlations and integrated relativistic terms need to be taken into account when forecasting the constraining power of future large-scale number counts of galaxy surveys.« less

Exploring the propagation of relativistic quantum wavepackets in the trajectory-based formulation

NASA Astrophysics Data System (ADS)

Tsai, Hung-Ming; Poirier, Bill

2016-03-01

In the context of nonrelativistic quantum mechanics, Gaussian wavepacket solutions of the time-dependent Schrödinger equation provide useful physical insight. This is not the case for relativistic quantum mechanics, however, for which both the Klein-Gordon and Dirac wave equations result in strange and counterintuitive wavepacket behaviors, even for free-particle Gaussians. These behaviors include zitterbewegung and other interference effects. As a potential remedy, this paper explores a new trajectory-based formulation of quantum mechanics, in which the wavefunction plays no role [Phys. Rev. X, 4, 040002 (2014)]. Quantum states are represented as ensembles of trajectories, whose mutual interaction is the source of all quantum effects observed in nature—suggesting a “many interacting worlds” interpretation. It is shown that the relativistic generalization of the trajectory-based formulation results in well-behaved free-particle Gaussian wavepacket solutions. In particular, probability density is positive and well-localized everywhere, and its spatial integral is conserved over time—in any inertial frame. Finally, the ensemble-averaged wavepacket motion is along a straight line path through spacetime. In this manner, the pathologies of the wave-based relativistic quantum theory, as applied to wavepacket propagation, are avoided.

The chemistry of the superheavy elements. II. The stability of high oxidation states in group 11 elements: Relativistic coupled cluster calculations for the di-, tetra- and hexafluoro metallates of Cu, Ag, Au, and element 111

NASA Astrophysics Data System (ADS)

Seth, Michael; Cooke, Fiona; Schwerdtfeger, Peter; Heully, Jean-Louis; Pelissier, Michel

1998-09-01

The stability of the high oxidation states +3 and +5 in Group 11 fluorides is studied by relativistic Møller-Plesset (MP) and coupled cluster methods. Higher metal oxidation states are stabilized by relativistic effects. As a result, the hexafluoro complex of the Group 11 element with nuclear charge 111 and oxidation state +5 is the most stable compared to the other congeners. The results also suggest that AgF6- is thermodynamically stable and, therefore, it might be feasable to synthesize this compound. For the copper fluorides we observe very large oscillations in the Møller-Plesset series up to the fourth order. Nonrelativistic calculations lead to the expected trend in the metal-fluorine bond distances for the MF2- compounds, CuF2-

Relativistic boost as the cause of periodicity in a massive black-hole binary candidate.

PubMed

D'Orazio, Daniel J; Haiman, Zoltán; Schiminovich, David

2015-09-17

Because most large galaxies contain a central black hole, and galaxies often merge, black-hole binaries are expected to be common in galactic nuclei. Although they cannot be imaged, periodicities in the light curves of quasars have been interpreted as evidence for binaries, most recently in PG 1302-102, which has a short rest-frame optical period of four years (ref. 6). If the orbital period of the black-hole binary matches this value, then for the range of estimated black-hole masses, the components would be separated by 0.007-0.017 parsecs, implying relativistic orbital speeds. There has been much debate over whether black-hole orbits could be smaller than one parsec (ref. 7). Here we report that the amplitude and the sinusoid-like shape of the variability of the light curve of PG 1302-102 can be fitted by relativistic Doppler boosting of emission from a compact, steadily accreting, unequal-mass binary. We predict that brightness variations in the ultraviolet light curve track those in the optical, but with a two to three times larger amplitude. This prediction is relatively insensitive to the details of the emission process, and is consistent with archival ultraviolet data. Follow-up ultraviolet and optical observations in the next few years can further test this prediction and confirm the existence of a binary black hole in the relativistic regime.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Philippov, Alexander A.; Cerutti, Benoit; Spitkovsky, Anatoly

It has recently been demonstrated that self-consistent particle-in-cell simulations of low-obliquity pulsar magnetospheres in flat spacetime show weak particle acceleration and no pair production near the poles. We investigate the validity of this conclusion in a more realistic spacetime geometry via general-relativistic particle-in-cell simulations of the aligned pulsar magnetosphere with pair formation. We find that the addition of the frame-dragging effect makes the local current density along the magnetic field larger than the Goldreich–Julian value, which leads to unscreened parallel electric fields and the ignition of a pair cascade. When pair production is active, we observe field oscillations in themore » open field bundle, which could be related to pulsar radio emission. We conclude that general-relativistic effects are essential for the existence of the pulsar mechanism in low-obliquity rotators.« less

Inference of relativistic electron spectra from measurements of inverse Compton radiation

NASA Astrophysics Data System (ADS)

Craig, I. J. D.; Brown, J. C.

1980-07-01

The inference of relativistic electron spectra from spectral measurement of inverse Compton radiation is discussed for the case where the background photon spectrum is a Planck function. The problem is formulated in terms of an integral transform that relates the measured spectrum to the unknown electron distribution. A general inversion formula is used to provide a quantitative assessment of the information content of the spectral data. It is shown that the observations must generally be augmented by additional information if anything other than a rudimentary two or three parameter model of the source function is to be derived. It is also pointed out that since a similar equation governs the continuum spectra emitted by a distribution of black-body radiators, the analysis is relevant to the problem of stellar population synthesis from galactic spectra.

Generalized Case ``Van Kampen theory for electromagnetic oscillations in a magnetized plasma

NASA Astrophysics Data System (ADS)

Bairaktaris, F.; Hizanidis, K.; Ram, A. K.

2017-10-01

The Case-Van Kampen theory is set up to describe electrostatic oscillations in an unmagnetized plasma. Our generalization to electromagnetic oscillations in magnetized plasma is formulated in the relativistic position-momentum phase space of the particles. The relativistic Vlasov equation includes the ambient, homogeneous, magnetic field, and space-time dependent electromagnetic fields that satisfy Maxwell's equations. The standard linearization technique leads to an equation for the perturbed distribution function in terms of the electromagnetic fields. The eigenvalues and eigenfunctions are obtained from three integrals `` each integral being over two different components of the momentum vector. Results connecting phase velocity, frequency, and wave vector will be presented. Supported in part by the Hellenic National Programme on Controlled Thermonuclear Fusion associated with the EUROfusion Consortium, and by DoE Grant DE-FG02-91ER-54109.

Monte Carlo closure for moment-based transport schemes in general relativistic radiation hydrodynamic simulations

NASA Astrophysics Data System (ADS)

Foucart, Francois

2018-04-01

General relativistic radiation hydrodynamic simulations are necessary to accurately model a number of astrophysical systems involving black holes and neutron stars. Photon transport plays a crucial role in radiatively dominated accretion discs, while neutrino transport is critical to core-collapse supernovae and to the modelling of electromagnetic transients and nucleosynthesis in neutron star mergers. However, evolving the full Boltzmann equations of radiative transport is extremely expensive. Here, we describe the implementation in the general relativistic SPEC code of a cheaper radiation hydrodynamic method that theoretically converges to a solution of Boltzmann's equation in the limit of infinite numerical resources. The algorithm is based on a grey two-moment scheme, in which we evolve the energy density and momentum density of the radiation. Two-moment schemes require a closure that fills in missing information about the energy spectrum and higher order moments of the radiation. Instead of the approximate analytical closure currently used in core-collapse and merger simulations, we complement the two-moment scheme with a low-accuracy Monte Carlo evolution. The Monte Carlo results can provide any or all of the missing information in the evolution of the moments, as desired by the user. As a first test of our methods, we study a set of idealized problems demonstrating that our algorithm performs significantly better than existing analytical closures. We also discuss the current limitations of our method, in particular open questions regarding the stability of the fully coupled scheme.

Imprint of thawing scalar fields on the large scale galaxy overdensity

NASA Astrophysics Data System (ADS)

Dinda, Bikash R.; Sen, Anjan A.

2018-04-01

We investigate the observed galaxy power spectrum for the thawing class of scalar field models taking into account various general relativistic corrections that occur on very large scales. We consider the full general relativistic perturbation equations for the matter as well as the dark energy fluid. We form a single autonomous system of equations containing both the background and the perturbed equations of motion which we subsequently solve for different scalar field potentials. First we study the percentage deviation from the Λ CDM model for different cosmological parameters as well as in the observed galaxy power spectra on different scales in scalar field models for various choices of scalar field potentials. Interestingly the difference in background expansion results from the enhancement of power from Λ CDM on small scales, whereas the inclusion of general relativistic (GR) corrections results in the suppression of power from Λ CDM on large scales. This can be useful to distinguish scalar field models from Λ CDM with future optical/radio surveys. We also compare the observed galaxy power spectra for tracking and thawing types of scalar field using some particular choices for the scalar field potentials. We show that thawing and tracking models can have large differences in observed galaxy power spectra on large scales and for smaller redshifts due to different GR effects. But on smaller scales and for larger redshifts, the difference is small and is mainly due to the difference in background expansion.

General relativistic calculations for white dwarfs

NASA Astrophysics Data System (ADS)

Mathew, Arun; Nandy, Malay K.

2017-05-01

The mass-radius relations for white dwarfs are investigated by solving the Newtonian as well as Tolman-Oppenheimer-Volkoff (TOV) equations for hydrostatic equilibrium assuming the electron gas to be non-interacting. We find that the Newtonian limiting mass of 1.4562{M}⊙ is modified to 1.4166{M}⊙ in the general relativistic case for {}_2^4{{He}} (and {}_612{{C}}) white dwarfs. Using the same general relativistic treatment, the critical mass for {}2656{{Fe}} white dwarfs is obtained as 1.2230{M}⊙ . In addition, departure from the ideal degenerate equation of state (EoS) is accounted for by considering Salpeter’s EoS along with the TOV equation, yielding slightly lower values for the critical masses, namely 1.4081{M}⊙ for {}_2^4{{He}}, 1.3916{M}⊙ for {}_612{{C}} and 1.1565{M}⊙ for {}2656{{Fe}} white dwarfs. We also compare the critical densities for gravitational instability with the neutronization threshold densities to find that {}_2^4{{He}} and {}_612{{C}} white dwarfs are stable against neutronization with the critical values of 1.4081{M}⊙ and 1.3916{M}⊙ , respectively. However, the critical masses for {}_816{{O}}, {}1020{{Ne}}, {}1224{{Mg}}, {}1428{{Si}}, {}1632{{S}} and {}2656{{Fe}} white dwarfs are lower due to neutronization. Corresponding to their central densities for neutronization thresholds, we obtain their maximum stable masses due to neutronization by solving the TOV equation coupled with the Salpeter EoS.

ON THE MAGNETIC FIELD OF PULSARS WITH REALISTIC NEUTRON STAR CONFIGURATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belvedere, R.; Rueda, Jorge A.; Ruffini, R., E-mail: riccardo.belvedere@icra.it, E-mail: jorge.rueda@icra.it, E-mail: ruffini@icra.it

2015-01-20

We have recently developed a neutron star model fulfilling global and not local charge neutrality, both in the static and in the uniformly rotating cases. The model is described by the coupled Einstein-Maxwell-Thomas-Fermi equations, in which all fundamental interactions are accounted for in the framework of general relativity and relativistic mean field theory. Uniform rotation is introduced following Hartle's formalism. We show that the use of realistic parameters of rotating neutron stars, obtained from numerical integration of the self-consistent axisymmetric general relativistic equations of equilibrium, leads to values of the magnetic field and radiation efficiency of pulsars that are verymore » different from estimates based on fiducial parameters that assume a neutron star mass M = 1.4 M {sub ☉}, radius R = 10 km, and moment of inertia I = 10{sup 45} g cm{sup 2}. In addition, we compare and contrast the magnetic field inferred from the traditional Newtonian rotating magnetic dipole model with respect to the one obtained from its general relativistic analog, which takes into account the effect of the finite size of the source. We apply these considerations to the specific high-magnetic field pulsar class and show that, indeed, all of these sources can be described as canonical pulsars driven by the rotational energy of the neutron star, and have magnetic fields lower than the quantum critical field for any value of the neutron star mass.« less

Quantum work statistics of charged Dirac particles in time-dependent fields

DOE PAGES

Deffner, Sebastian; Saxena, Avadh

2015-09-28

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Thus, special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

CHARGED PARTICLE MULTIPLICITIES IN ULTRA-RELATIVISTIC AU+AU AND CU+CU COLLISIONS

NASA Astrophysics Data System (ADS)

Back, B. B.; Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Chetluru, V.; Decowski, M. P.; Garcia, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Harnarine, I.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holynski, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Richardson, E.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Szostak, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; Vannieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Willhelm, D.; Wolfs, F. L. H.; Wosiek, B.; Wozniak, K.; Wyngaardt, S.; Wyslouch, B.

The PHOBOS collaboration has carried out a systematic study of charged particle multiplicities in Cu+Cu and Au+Au collisions at the Relativistic Heavy-Ion Collider (RHIC) at Brookhaven National Laboratory. A unique feature of the PHOBOS detector is its ability to measure charged particles over a very wide angular range from 0.5° to 179.5° corresponding to |η| <5.4. The general features of the charged particle multiplicity distributions as a function of pseudo-rapidity, collision energy and centrality, as well as system size, are discussed.

Sterile neutrino dark matter with supersymmetry

NASA Astrophysics Data System (ADS)

Shakya, Bibhushan; Wells, James D.

2017-08-01

Sterile neutrino dark matter, a popular alternative to the WIMP paradigm, has generally been studied in non-supersymmetric setups. If the underlying theory is supersymmetric, we find that several interesting and novel dark matter features can arise. In particular, in scenarios of freeze-in production of sterile neutrino dark matter, its superpartner, the sterile sneutrino, can play a crucial role in early Universe cosmology as the dominant source of cold, warm, or hot dark matter, or of a subdominant relativistic population of sterile neutrinos that can contribute to the effective number of relativistic degrees of freedom Neff during big bang nucleosynthesis.

Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stanke, Monika, E-mail: monika@fizyka.umk.pl; Palikot, Ewa, E-mail: epalikot@doktorant.umk.pl; Adamowicz, Ludwik, E-mail: ludwik@email.arizona.edu

2016-05-07

Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H{sub 2} and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.

Relativistic properties of a molecule: energy, linear momentum, angular momentum and boost momentum to order 1/c 2

NASA Astrophysics Data System (ADS)

Cameron, Robert P.; Cotter, J. P.

2018-05-01

We give an explicit and general description of the energy, linear momentum, angular momentum and boost momentum of a molecule to order 1/c 2, where it necessary to take account of kinetic contributions made by the electrons and nuclei as well as electromagnetic contributions made by the intramolecular field. A wealth of interesting subtleties are encountered that are not seen at order 1/c 0, including relativistic Hall shifts, anomalous velocities and hidden momenta. Some of these have well known analogues in solid state physics.

On HQET and NRQCD operators of dimension 8 and above

DOE PAGES

Gunawardana, Ayesh; Paz, Gil

2017-07-27

Effective field theories such as Heavy Quark Effective Theory (HQET) and Non Relativistic Quantum Chromo-(Electro-) dynamics NRQCD (NRQED) are indispensable tools in controlling the effects of the strong interaction. The increasing experimental precision requires the knowledge of higher dimensional operators. We present a general method that allows for an easy construction of HQET or NRQCD (NRQED) operators that contain two heavy quark or non-relativistic fields and any number of covariant derivatives. As an application of our method, we list these terms in the 1/M 4 NRQCD Lagrangian, where M is the mass of of the spin-half field.

Larmor precession and barrier tunneling time of a neutral spinning particle

NASA Astrophysics Data System (ADS)

Li, Zhi-Jian; Liang, J. Q.; Kobe, D. H.

2001-10-01

The Larmor precession of a neutral spinning particle in a magnetic field confined to the region of a one-dimensional rectangular barrier is investigated for both a nonrelativistic and a relativistic incoming particle. The spin precession serves as a clock to measure the time spent by a quantum particle traversing a potential barrier. With the help of a general spin coherent state it is explicitly shown that the precession time is equal to the dwell time in both the nonrelativistic and relativistic cases. We also present a numerical estimation of the precession time showing an apparent superluminal tunneling.

Charge Dependence and Electric Quadrupole Effects on Single-Nucleon Removal in Relativistic and Intermediate Energy Nuclear Collisions

NASA Technical Reports Server (NTRS)

Norbury, John W.

1992-01-01

Single nucleon removal in relativistic and intermediate energy nucleus-nucleus collisions is studied using a generalization of Weizsacker-Williams theory that treats each electromagnetic multipole separately. Calculations are presented for electric dipole and quadrupole excitations and incorporate a realistic minimum impact parameter, Coulomb recoil corrections, and the uncertainties in the input photonuclear data. Discrepancies are discussed. The maximum quadrupole effect to be observed in future experiments is estimated and also an analysis of the charge dependence of the electromagnetic cross sections down to energies as low as 100 MeV/nucleon is made.

Charge dependence and electric quadrupole effects on single-nucleon removal in relativistic and intermediate energy nuclear collisions

NASA Technical Reports Server (NTRS)

Norbury, J. W.; Townsend, L. W. (Principal Investigator)

1990-01-01

Single-nucleon removal in relativistic and intermediate energy nucleus-nucleus collisions is studied using a generalization of Weizsacker-Williams theory that treats each electromagnetic multipole separately. Calculations are presented for electric dipole and quadrupole excitations and incorporate a realistic minimum impact parameter, Coulomb recoil corrections, and the uncertainties in the input photonuclear data. Discrepancies are discussed. The maximum quadrupole effect to be observed in future experiments is estimated and also an analysis of the charge dependence of the electromagnetic cross sections down to energies as low as 100 MeV/nucleon is made.

The stationary non-equilibrium plasma of cosmic-ray electrons and positrons

NASA Astrophysics Data System (ADS)

Tomaschitz, Roman

2016-06-01

The statistical properties of the two-component plasma of cosmic-ray electrons and positrons measured by the AMS-02 experiment on the International Space Station and the HESS array of imaging atmospheric Cherenkov telescopes are analyzed. Stationary non-equilibrium distributions defining the relativistic electron-positron plasma are derived semi-empirically by performing spectral fits to the flux data and reconstructing the spectral number densities of the electronic and positronic components in phase space. These distributions are relativistic power-law densities with exponential cutoff, admitting an extensive entropy variable and converging to the Maxwell-Boltzmann or Fermi-Dirac distributions in the non-relativistic limit. Cosmic-ray electrons and positrons constitute a classical (low-density high-temperature) plasma due to the low fugacity in the quantized partition function. The positron fraction is assembled from the flux densities inferred from least-squares fits to the electron and positron spectra and is subjected to test by comparing with the AMS-02 flux ratio measured in the GeV interval. The calculated positron fraction extends to TeV energies, predicting a broad spectral peak at about 1 TeV followed by exponential decay.

Characterizing Relativistic Electrons Flux Enhancement Events using sensors onboard SAMPEX and POLAR

NASA Astrophysics Data System (ADS)

Kanekal, S. G.; Selesnick, R. S.; Baker, D. N.; Blake, J. B.

2004-12-01

Relativistic electron fluxes in the Earth's outer Van Allen belt are highly variable with flux enhancements of several orders of magnitude occurring on time scales of a few days. Radiation belt electrons often are energized to relativistic energies when the magnetosphere is subjected to high solar wind speed and the southward turning of the interplanetary magnetic field. Characterization of electron acceleration properties such as electron spectra and flux isotropization are important in understanding acceleration models. We use sensors onboard SAMPEX and POLAR to measure and survey systematically these properties. SAMPEX measurements cover the entire outer zone for more than a decade from mid 1992 to mid 2004 and POLAR covers the time period from mid 1996 to the present. We use the pulse height analyzed data from the PET detector onboard SAMPEX to measure electron spectra. Fluxes measured by the HIST detector onboard POLAR together with the PET measurements are used to characterize isotropization times. This paper presents electron spectra and isotropization time scales for a few representative events. We will eventually extend these measurements and survey the entire solar cycle 23.

Relativistic theory of particles in a scattering flow I: basic equations, diffusion and drift.

NASA Astrophysics Data System (ADS)

Achterberg, A.; Norman, C. A.

2018-06-01

We reconsider the theory of particle transport in a scattering medium, allowing for relativistic flow velocities. The theory uses a mixed set of variables, with position and time measured in the Laboratory Frame, and particle energy and momentum measured in the Fluid Rest Frame, the reference frame where scattering is assumed to be elastic. We give a new derivation for the fictitious force terms in the equation of motion that are present if the Fluid Rest Frame is not an inertial frame. By using a 3+1 notation we discuss the physical interpretation of the different terms in the fictitious force. It is shown that different approaches to the problem of particle propagation in a magnetized medium due to Skilling (1975) and Kulsrud (1983) are largely equivalent. We extend known results for non-relativistic flows to include the effects of cross-field diffusion for cosmic rays in a magnetized plasma. We also carefully consider the correct form of the diffusion approximation for scattering, and show that the resulting equations can be cast in conservation form.

On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lusanna, Luca

2004-08-19

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are gauge variables, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the Dirac observables, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of causality dictates the choice of retarded solutions at the classical level. However both the problems of themore » classical theory of the electron, leading to the choice of (1/2) (retarded + advanced) solutions, and the regularization of quantum field theory, leading to the Feynman propagator, introduce anticipatory aspects. The determination of the relativistic Darwin potential as a semi-classical approximation to the Lienard-Wiechert solution for particles with Grassmann-valued electric charges, regularizing the Coulomb self-energies, shows that these anticipatory effects live beyond the semi-classical approximation (tree level) under the form of radiative corrections, at least for the electro-magnetic interaction.Talk and 'best contribution' at The Sixth International Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16, 2003.« less

Conservative, special-relativistic smoothed particle hydrodynamics

NASA Astrophysics Data System (ADS)

Rosswog, Stephan

2010-11-01

We present and test a new, special-relativistic formulation of smoothed particle hydrodynamics (SPH). Our approach benefits from several improvements with respect to earlier relativistic SPH formulations. It is self-consistently derived from the Lagrangian of an ideal fluid and accounts for the terms that stem from non-constant smoothing lengths, usually called “grad-h terms”. In our approach, we evolve the canonical momentum and the canonical energy per baryon and thus circumvent some of the problems that have plagued earlier formulations of relativistic SPH. We further use a much improved artificial viscosity prescription which uses the extreme local eigenvalues of the Euler equations and triggers selectively on (a) shocks and (b) velocity noise. The shock trigger accurately monitors the relative density slope and uses it to fine-tune the amount of artificial viscosity that is applied. This procedure substantially sharpens shock fronts while still avoiding post-shock noise. If not triggered, the viscosity parameter of each particle decays to zero. None of these viscosity triggers is specific to special relativity, both could also be applied in Newtonian SPH.The performance of the new scheme is explored in a large variety of benchmark tests where it delivers excellent results. Generally, the grad-h terms deliver minor, though worthwhile, improvements. As expected for a Lagrangian method, it performs close to perfect in supersonic advection tests, but also in strong relativistic shocks, usually considered a particular challenge for SPH, the method yields convincing results. For example, due to its perfect conservation properties, it is able to handle Lorentz factors as large as γ = 50,000 in the so-called wall shock test. Moreover, we find convincing results in a rarely shown, but challenging test that involves so-called relativistic simple waves and also in multi-dimensional shock tube tests.

Relativistic electron kinetic effects on laser diagnostics in burning plasmas

NASA Astrophysics Data System (ADS)

Mirnov, V. V.; Den Hartog, D. J.

2018-02-01

Toroidal interferometry/polarimetry (TIP), poloidal polarimetry (PoPola), and Thomson scattering systems (TS) are major optical diagnostics being designed and developed for ITER. Each of them relies upon a sophisticated quantitative understanding of the electron response to laser light propagating through a burning plasma. Review of the theoretical results for two different applications is presented: interferometry/polarimetry (I/P) and polarization of Thomson scattered light, unified by the importance of relativistic (quadratic in vTe/c) electron kinetic effects. For I/P applications, rigorous analytical results are obtained perturbatively by expansion in powers of the small parameter τ = Te/me c2, where Te is electron temperature and me is electron rest mass. Experimental validation of the analytical models has been made by analyzing data of more than 1200 pulses collected from high-Te JET discharges. Based on this validation the relativistic analytical expressions are included in the error analysis and design projects of the ITER TIP and PoPola systems. The polarization properties of incoherent Thomson scattered light are being examined as a method of Te measurement relevant to ITER operational regimes. The theory is based on Stokes vector transformation and Mueller matrices formalism. The general approach is subdivided into frequency-integrated and frequency-resolved cases. For each of them, the exact analytical relativistic solutions are presented in the form of Mueller matrix elements averaged over the relativistic Maxwellian distribution function. New results related to the detailed verification of the frequency-resolved solutions are reported. The precise analytic expressions provide output much more rapidly than relativistic kinetic numerical codes allowing for direct real-time feedback control of ITER device operation.

Frontiers in Relativistic Celestial Mechanics, Vol. 2, Applications and Experiments

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei

2014-08-01

Relativistic celestial mechanics - investigating the motion celestial bodies under the influence of general relativity - is a major tool of modern experimental gravitational physics. With a wide range of prominent authors from the field, this two-volume series consists of reviews on a multitude of advanced topics in the area of relativistic celestial mechanics - starting from more classical topics such as the regime of asymptotically-flat spacetime, light propagation and celestial ephemerides, but also including its role in cosmology and alternative theories of gravity as well as modern experiments in this area. This second volume of a two-volume series covers applications of the theory as well as experimental verifications. From tools to determine light travel times in curved space-time to laser ranging between earth and moon and between satellites, and impacts on the definition of time scales and clock comparison techniques, a variety of effects is discussed. On the occasion of his 80-th birthday, these two volumes honor V. A. Brumberg - one of the pioneers in modern relativistic celestial mechanics. Contributions include: J. Simon, A. Fienga: Victor Brumberg and the French school of analytical celestial mechanics T. Fukushima: Elliptic functions and elliptic integrals for celestial mechanics and dynamical astronomy P. Teyssandier: New tools for determining the light travel time in static, spherically symmetric spacetimes beyond the order G2 J. Müller, L. Biskupek, F. Hofmann and E. Mai: Lunar laser ranging and relativity N. Wex: Testing relativistic celestial mechanics with radio pulsars I. Ciufolini et al.: Dragging of inertial frames, fundamental physics, and satellite laser ranging G. Petit, P. Wolf, P. Delva: Atomic time, clocks, and clock comparisons in relativistic spacetime: a review

What is dynamics in quantum gravity?

NASA Astrophysics Data System (ADS)

Małkiewicz, Przemysław

2017-10-01

The appearance of the Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen internal degree of freedom, the so-called internal clock. We investigate the way in which the choice of internal clock determines the quantum dynamics and how much different quantum dynamics induced by different clocks are. We develop our method of comparison by extending the Hamilton-Jacobi theory of contact transformations to include a new type of transformation which transforms both the canonical variables and the internal clock. We employ our method to study the quantum dynamics of the Friedmann-Lemaitre model and obtain semiclassical corrections to the classical dynamics, which depend on the choice of internal clock. For a unique quantisation map we find the abundance of inequivalent semiclassical corrections induced by quantum dynamics taking place in different internal clocks. It follows that the concepts like minimal volume, maximal curvature and the number of quantum bounces, often used to describe quantum effects in cosmological models, depend on the choice of internal clock.

Can the relativistic light-bending model explain X-ray spectral variations of Seyfert galaxies?

NASA Astrophysics Data System (ADS)

Mizumoto, Misaki; Moriyama, Kotaro; Ebisawa, Ken; Mineshige, Shin; Kawanaka, Norita; Tsujimoto, Masahiro

2018-04-01

Many Seyfert galaxies are known to exhibit Fe-K broad emission line features in their X-ray energy spectra. The observed lines have three distinct features: (1) the line profiles are skewed and show significant low-energy tails, (2) the Fe-K band has low variability, which produces a broad and deep dip in the root-mean-square (rms) spectra, and (3) photons in this band have time lags behind those in the adjacent energy bands with amplitudes of several Rg/c, where Rg is the gravitational radius. The "relativistic light-bending model" is proposed to explain these observed features, where a compact X-ray source ("lamp post") above an extreme Kerr black hole illuminates the innermost area of the accretion disc. In this paper, we critically examine the relativistic light-bending model by computing the rms spectra and the lag features using a ray-tracing technique, when a lamp post moves vertically on the black hole spin axis. As a result, we found that the observed deep rms dip requires that the iron is extremely overabundant (≳10 solar), whereas the observed lag amplitude is consistent with the normal iron abundance. Furthermore, disappearance of the lag in the high-flux state requires a source height as high as ˜40 Rg, which contradicts the relativistically broad emission line feature. Our simulations agree with the data that the reverberation feature moves to lower frequencies with larger source height; however, if this scenario is correct, the simulations predict the detection of a clear Fe-K lag at low frequencies, which is not constrained in the data. Therefore, we conclude that the relativistic light-bending model may not explain the characteristic Fe-K spectral variations in Seyfert galaxies.

Can the relativistic light-bending model explain X-ray spectral variations of Seyfert galaxies?

NASA Astrophysics Data System (ADS)

Mizumoto, Misaki; Moriyama, Kotaro; Ebisawa, Ken; Mineshige, Shin; Kawanaka, Norita; Tsujimoto, Masahiro

2018-06-01

Many Seyfert galaxies are known to exhibit Fe-K broad emission line features in their X-ray energy spectra. The observed lines have three distinct features: (1) the line profiles are skewed and show significant low-energy tails, (2) the Fe-K band has low variability, which produces a broad and deep dip in the root-mean-square (rms) spectra, and (3) photons in this band have time lags behind those in the adjacent energy bands with amplitudes of several Rg/c, where Rg is the gravitational radius. The "relativistic light-bending model" is proposed to explain these observed features, where a compact X-ray source ("lamp post") above an extreme Kerr black hole illuminates the innermost area of the accretion disc. In this paper, we critically examine the relativistic light-bending model by computing the rms spectra and the lag features using a ray-tracing technique, when a lamp post moves vertically on the black hole spin axis. As a result, we found that the observed deep rms dip requires that the iron is extremely overabundant (≳10 solar), whereas the observed lag amplitude is consistent with the normal iron abundance. Furthermore, disappearance of the lag in the high-flux state requires a source height as high as ˜40 Rg, which contradicts the relativistically broad emission line feature. Our simulations agree with the data that the reverberation feature moves to lower frequencies with larger source height; however, if this scenario is correct, the simulations predict the detection of a clear Fe-K lag at low frequencies, which is not constrained in the data. Therefore, we conclude that the relativistic light-bending model may not explain the characteristic Fe-K spectral variations in Seyfert galaxies.

Relativistic effects in local inertial frames including parametrized-post-Newtonian effects

NASA Astrophysics Data System (ADS)

Shahid-Saless, Bahman; Ashby, Neil

1988-09-01

We use the concept of a generalized Fermi frame to describe relativistic effects, due to local and distant sources of gravitation, on a body placed in a local inertial frame of reference. In particular we have considered a model of two spherically symmetric gravitating point sources, moving in circular orbits around a common barycenter where one of the bodies is chosen to be the local and the other the distant one. This has been done using the slow-motion, weak-field approximation and including four of the parametrized-post-Newtonian (PPN) parameters. The position of the classical center of mass must be modified when the PPN parameter ζ2 is included. We show that the main relativistic effect on a local satellite is described by the Schwarzschild field of the local body and the nonlinear term corresponding to the self-interaction of the local source with itself. There are also much smaller terms that are proportional, respectively, to the product of the potentials of local and distant bodies and to the distant body's self-interactions. The spatial axes of the local frame undergo geodetic precession. In addition we have an acceleration of the order of 10-11 cm sec-2 that vanish in the case of general relativity, which is discussed in detail.

Formation of precessing jets by tilted black hole discs in 3D general relativistic MHD simulations

NASA Astrophysics Data System (ADS)

Liska, M.; Hesp, C.; Tchekhovskoy, A.; Ingram, A.; van der Klis, M.; Markoff, S.

2018-02-01

Gas falling into a black hole (BH) from large distances is unaware of BH spin direction, and misalignment between the accretion disc and BH spin is expected to be common. However, the physics of tilted discs (e.g. angular momentum transport and jet formation) is poorly understood. Using our new GPU-accelerated code H-AMR, we performed 3D general relativistic magnetohydrodynamic simulations of tilted thick accretion discs around rapidly spinning BHs, at the highest resolution to date. We explored the limit where disc thermal pressure dominates magnetic pressure, and showed for the first time that, for different magnetic field strengths on the BH, these flows launch magnetized relativistic jets propagating along the rotation axis of the tilted disc (rather than of the BH). If strong large-scale magnetic flux reaches the BH, it bends the inner few gravitational radii of the disc and jets into partial alignment with the BH spin. On longer time-scales, the simulated disc-jet system as a whole undergoes Lense-Thirring precession and approaches alignment, demonstrating for the first time that jets can be used as probes of disc precession. When the disc turbulence is well resolved, our isolated discs spread out, causing both the alignment and precession to slow down.

TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duffell, Paul C.; MacFadyen, Andrew I., E-mail: pcd233@nyu.edu, E-mail: macfadyen@nyu.edu

2011-12-01

We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluidsmore » on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.« less

Relativistic theory for syntonization of clocks in the vicinity of the Earth

NASA Technical Reports Server (NTRS)

Wolf, Peter; Petit, G.

1995-01-01

A well known prediction of Einstein's general theory of relativity states that two ideal clocks that move with a relative velocity, and are submitted to different gravitational fields will, in general, be observed to run at different rates. Similarly the rate of a clock with respect to the coordinate time of some spacetime reference system is dependent on the velocity of the clock in that reference system and on the gravitational fields it is submitted to. For the syntonization of clocks and the realization of coordinate times (like TAI) this rate shift has to be taken into account at an accuracy level which should be below the frequency stability of the clocks in question, i.e. all terms that are larger than the instability of the clocks should be corrected for. We present a theory for the calculation of the relativistic rate shift for clocks in the vicinity of the Earth, including all terms larger than one part in 10(exp 18). This, together with previous work on clock synchronization (Petit & Wolf 1993, 1994), amounts to a complete relativistic theory for the realization of coordinate time scales at picosecond synchronization and 10(exp -18) syntonization accuracy, which should be sufficient to accommodate future developments in time transfer and clock technology.

General relativistic satellite astrometry. II. Modeling parallax and proper motion

NASA Astrophysics Data System (ADS)

de Felice, F.; Bucciarelli, B.; Lattanzi, M. G.; Vecchiato, A.

2001-07-01

The non-perturbative general relativistic approach to global astrometry introduced by de Felice et al. (\\cite{defetal}) is here extended to account for the star motions on the Schwarzschild celestial sphere. A new expression of the observables, i.e. angular distances among stars, is provided, which takes into account the effects of parallax and proper motions. This dynamical model is then tested on an end-to-end simulation of the global astrometry mission GAIA. The results confirm the findings of our earlier work, which applied to the case of a static (angular coordinates only) sphere. In particular, measurements of large arcs among stars (each measurement good to ~ 100 mu arcsec, as expected for V ~ 17 mag stars) repeated over an observing period comparable to the mission lifetime foreseen for GAIA, can be modeled to yield estimates of positions, parallaxes, and annual proper motions good to ~ 15 mu arcsec. This second round of experiments confirms, within the limitations of the simulation and the assumptions of the current relativistic model, that the space-born global astrometry initiated with Hipparcos can be pushed down to the 10-5 arcsec accuracy level proposed with the GAIA mission. Finally, the simplified case we have solved can be used as reference for testing the limiting behavior of more realistic models as they become available.

Application of a relativistic accretion disc model to X-ray spectra of LMC X-1 and GRO J1655-40

NASA Astrophysics Data System (ADS)

Gierliński, Marek; Maciołek-Niedźwiecki, Andrzej; Ebisawa, Ken

2001-08-01

We present a general relativistic accretion disc model and its application to the soft-state X-ray spectra of black hole binaries. The model assumes a flat, optically thick disc around a rotating Kerr black hole. The disc locally radiates away the dissipated energy as a blackbody. Special and general relativistic effects influencing photons emitted by the disc are taken into account. The emerging spectrum, as seen by a distant observer, is parametrized by the black hole mass and spin, the accretion rate, the disc inclination angle and the inner disc radius. We fit the ASCA soft-state X-ray spectra of LMC X-1 and GRO J1655-40 by this model. We find that, having additional limits on the black hole mass and inclination angle from optical/UV observations, we can constrain the black hole spin from X-ray data. In LMC X-1 the constraint is weak, and we can only rule out the maximally rotating black hole. In GRO J1655-40 we can limit the spin much better, and we find 0.68<=a<=0.88. Accretion discs in both sources are radiation-pressure dominated. We do not find Compton reflection features in the spectra of any of these objects.

An X-ray survey of variable radio bright quasars

NASA Technical Reports Server (NTRS)

Henriksen, M. J.; Marshall, F. E.; Mushotzky, R. F.

1984-01-01

A sample consisting primarily of radio bright quasars was observed in X-rays with the Einstein Observatory for times ranging from 1500 to 5000 seconds. Detected sources had luminosities ranging from 0.2 to 41.0 x 10 to the 45th power ergs/sec in the 0.5 to 4.5 keV band. Three of the fourteen objects which were reobserved showed flux increases greater than a factor of two on a time scale greater than six months. No variability was detected during the individual observations. The optical and X-ray luminosities are correlated, which suggests a common origin. However, the relationship (L sub x is approximately L sub op to the (.89 + or - .15)) found for historic radio variables may be significantly different than that reported for other radio bright sources. Some of the observed X-ray fluxes were substantially below the predicted self-Compton flux, assuming incoherent synchrotron emission and using VLBI results to constrain the size of the emission region, which suggests relativistic expansion in these sources. Normal CIV emission in two of the sources with an overpredicted Compton component suggests that although they, like BL Lac objects, have highly relativistic material apparently moving at small angle to the line of sight, they have a smaller fraction of the continuum component in the beam.

Proof of the Spin Statistics Connection 2: Relativistic Theory

NASA Astrophysics Data System (ADS)

Santamato, Enrico; De Martini, Francesco

2017-12-01

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

Bonding and magnetic response properties of several toroid structures. Insights of the role of Ni2S2 as a building block from relativistic density functional theory calculations.

PubMed

Muñoz-Castro, Alvaro

2011-10-06

Relativistic density functional calculations were carried out on several nickel toroid mercaptides of the general formula [Ni(μ-SR)(2)](n), with the aim to characterize and analyze their stability and magnetic response properties, in order to gain more insights into their stabilization and size-dependent behavior. The Ni-ligand interaction has been studied by means projected density of states and energy decomposition analysis, which denotes its stabilizing character. The graphical representation of the response to an external magnetic field is applied for the very first time taking into account the spin-orbit term. This map allows one to clearly characterize the magnetic behavior inside and in the closeness of the toroid structure showing the prescence of paratropic ring currents inside the Ni(n) ring, and by contrast, diatropic currents confined in each Ni(2)S(2) motif denoting an aromatic behavior (in terms of magnetic criteria). The calculated data suggests that the Ni(2)S(2) moiety can be regarded as a stable constructing block, which can afford several toroid structures of different nuclearities in agreement with that reported in the experimental literature. In addition, the effects of the relativistic treatment over the magnetic response properties on these lighter compounds are denoted by comparing nonrelativistic, scalar relativistic, and scalar plus spin-orbit relativistic treatments, showing their acting, although nonpronunced, role.

SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shalaby, Mohamad; Broderick, Avery E.; Chang, Philip

Numerical heating in particle-in-cell (PIC) codes currently precludes the accurate simulation of cold, relativistic plasma over long periods, severely limiting their applications in astrophysical environments. We present a spatially higher-order accurate relativistic PIC algorithm in one spatial dimension, which conserves charge and momentum exactly. We utilize the smoothness implied by the usage of higher-order interpolation functions to achieve a spatially higher-order accurate algorithm (up to the fifth order). We validate our algorithm against several test problems—thermal stability of stationary plasma, stability of linear plasma waves, and two-stream instability in the relativistic and non-relativistic regimes. Comparing our simulations to exact solutionsmore » of the dispersion relations, we demonstrate that SHARP can quantitatively reproduce important kinetic features of the linear regime. Our simulations have a superior ability to control energy non-conservation and avoid numerical heating in comparison to common second-order schemes. We provide a natural definition for convergence of a general PIC algorithm: the complement of physical modes captured by the simulation, i.e., those that lie above the Poisson noise, must grow commensurately with the resolution. This implies that it is necessary to simultaneously increase the number of particles per cell and decrease the cell size. We demonstrate that traditional ways for testing for convergence fail, leading to plateauing of the energy error. This new PIC code enables us to faithfully study the long-term evolution of plasma problems that require absolute control of the energy and momentum conservation.« less

Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

NASA Technical Reports Server (NTRS)

Hizanidis, Kyriakos; Vlahos, L.; Polymilis, C.

1989-01-01

The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

Beyond ideal magnetohydrodynamics: from fibration to 3  +  1 foliation

NASA Astrophysics Data System (ADS)

Andersson, N.; Hawke, I.; Dionysopoulou, K.; Comer, G. L.

2017-06-01

We consider a resistive multi-fluid framework from the 3  +  1 space-time foliation point-of-view, paying particular attention to issues relating to the use of multi-parameter equations of state and the associated inversion from evolved to primitive variables. We highlight relevant numerical issues that arise for general systems with relative flows. As an application of the new formulation, we consider a three-component system relevant for hot neutron stars. In this case we let the baryons (neutrons and protons) move together, but allow heat and electrons to exhibit relative flow. This reduces the problem to three momentum equations; overall energy-momentum conservation, a generalised Ohm’s law and a heat equation. Our results provide a hierarchy of increasingly complex models and prepare the ground for new state-of-the-art simulations of relevant scenarios in relativistic astrophysics.

Impact of relativistic effects on cosmological parameter estimation

NASA Astrophysics Data System (ADS)

Lorenz, Christiane S.; Alonso, David; Ferreira, Pedro G.

2018-01-01

Future surveys will access large volumes of space and hence very long wavelength fluctuations of the matter density and gravitational field. It has been argued that the set of secondary effects that affect the galaxy distribution, relativistic in nature, will bring new, complementary cosmological constraints. We study this claim in detail by focusing on a subset of wide-area future surveys: Stage-4 cosmic microwave background experiments and photometric redshift surveys. In particular, we look at the magnification lensing contribution to galaxy clustering and general-relativistic corrections to all observables. We quantify the amount of information encoded in these effects in terms of the tightening of the final cosmological constraints as well as the potential bias in inferred parameters associated with neglecting them. We do so for a wide range of cosmological parameters, covering neutrino masses, standard dark-energy parametrizations and scalar-tensor gravity theories. Our results show that, while the effect of lensing magnification to number counts does not contain a significant amount of information when galaxy clustering is combined with cosmic shear measurements, this contribution does play a significant role in biasing estimates on a host of parameter families if unaccounted for. Since the amplitude of the magnification term is controlled by the slope of the source number counts with apparent magnitude, s (z ), we also estimate the accuracy to which this quantity must be known to avoid systematic parameter biases, finding that future surveys will need to determine s (z ) to the ˜5 %- 10 % level. On the contrary, large-scale general-relativistic corrections are irrelevant both in terms of information content and parameter bias for most cosmological parameters but significant for the level of primordial non-Gaussianity.

Confirmation of general relativity on large scales from weak lensing and galaxy velocities.

PubMed

Reyes, Reinabelle; Mandelbaum, Rachel; Seljak, Uros; Baldauf, Tobias; Gunn, James E; Lombriser, Lucas; Smith, Robert E

2010-03-11

Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, E(G), that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to 'galaxy bias' (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of E(G) different from the general relativistic prediction because, in these theories, the 'gravitational slip' (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure and the strength of the gravitational lensing effect. Here we report that E(G) = 0.39 +/- 0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of E(G) approximately 0.4. The measured value excludes a model within the tensor-vector-scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f(R) theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

Confirmation of general relativity on large scales from weak lensing and galaxy velocities

NASA Astrophysics Data System (ADS)

Reyes, Reinabelle; Mandelbaum, Rachel; Seljak, Uros; Baldauf, Tobias; Gunn, James E.; Lombriser, Lucas; Smith, Robert E.

2010-03-01

Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale gravitational lensing, galaxy clustering and structure growth rate. The combination is insensitive to `galaxy bias' (the difference between the clustering of visible galaxies and invisible dark matter) and is thus robust to the uncertainty in this parameter. Modified theories of gravity generally predict values of EG different from the general relativistic prediction because, in these theories, the `gravitational slip' (the difference between the two potentials that describe perturbations in the gravitational metric) is non-zero, which leads to changes in the growth of structure and the strength of the gravitational lensing effect. Here we report that EG = 0.39+/-0.06 on length scales of tens of megaparsecs, in agreement with the general relativistic prediction of EG~0.4. The measured value excludes a model within the tensor-vector-scalar gravity theory, which modifies both Newtonian and Einstein gravity. However, the relatively large uncertainty still permits models within f() theory, which is an extension of general relativity. A fivefold decrease in uncertainty is needed to rule out these models.

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balsara, Dinshaw S., E-mail: dbalsara@nd.edu; Amano, Takanobu, E-mail: amano@eps.s.u-tokyo.ac.jp; Garain, Sudip, E-mail: sgarain@nd.edu

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equationsmore » is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge–Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.« less

A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Amano, Takanobu; Garain, Sudip; Kim, Jinho

2016-08-01

In various astrophysics settings it is common to have a two-fluid relativistic plasma that interacts with the electromagnetic field. While it is common to ignore the displacement current in the ideal, classical magnetohydrodynamic limit, when the flows become relativistic this approximation is less than absolutely well-justified. In such a situation, it is more natural to consider a positively charged fluid made up of positrons or protons interacting with a negatively charged fluid made up of electrons. The two fluids interact collectively with the full set of Maxwell's equations. As a result, a solution strategy for that coupled system of equations is sought and found here. Our strategy extends to higher orders, providing increasing accuracy. The primary variables in the Maxwell solver are taken to be the facially-collocated components of the electric and magnetic fields. Consistent with such a collocation, three important innovations are reported here. The first two pertain to the Maxwell solver. In our first innovation, the magnetic field within each zone is reconstructed in a divergence-free fashion while the electric field within each zone is reconstructed in a form that is consistent with Gauss' law. In our second innovation, a multidimensionally upwinded strategy is presented which ensures that the magnetic field can be updated via a discrete interpretation of Faraday's law and the electric field can be updated via a discrete interpretation of the generalized Ampere's law. This multidimensional upwinding is achieved via a multidimensional Riemann solver. The multidimensional Riemann solver automatically provides edge-centered electric field components for the Stokes law-based update of the magnetic field. It also provides edge-centered magnetic field components for the Stokes law-based update of the electric field. The update strategy ensures that the electric field is always consistent with Gauss' law and the magnetic field is always divergence-free. This collocation also ensures that electromagnetic radiation that is propagating in a vacuum has both electric and magnetic fields that are exactly divergence-free. Coupled relativistic fluid dynamic equations are solved for the positively and negatively charged fluids. The fluids' numerical fluxes also provide a self-consistent current density for the update of the electric field. Our reconstruction strategy ensures that fluid velocities always remain sub-luminal. Our third innovation consists of an efficient design for several popular IMEX schemes so that they provide strong coupling between the finite-volume-based fluid solver and the electromagnetic fields at high order. This innovation makes it possible to efficiently utilize high order IMEX time update methods for stiff source terms in the update of high order finite-volume methods for hyperbolic conservation laws. We also show that this very general innovation should extend seamlessly to Runge-Kutta discontinuous Galerkin methods. The IMEX schemes enable us to use large CFL numbers even in the presence of stiff source terms. Several accuracy analyses are presented showing that our method meets its design accuracy in the MHD limit as well as in the limit of electromagnetic wave propagation. Several stringent test problems are also presented. We also present a relativistic version of the GEM problem, which shows that our algorithm can successfully adapt to challenging problems in high energy astrophysics.

Curvature-Squared Cosmology In The First-Order Formalism

NASA Technical Reports Server (NTRS)

Shahid-Saless, Bahman

1993-01-01

Paper presents theoretical study of some of general-relativistic ramifications of gravitational-field energy density proportional to R - alpha R(exp 2) (where R is local scalar curvature of space-time and alpha is a constant).

A pseudo energy-invariant method for relativistic wave equations with Riesz space-fractional derivatives

NASA Astrophysics Data System (ADS)

Macías-Díaz, J. E.; Hendy, A. S.; De Staelen, R. H.

2018-03-01

In this work, we investigate a general nonlinear wave equation with Riesz space-fractional derivatives that generalizes various classical hyperbolic models, including the sine-Gordon and the Klein-Gordon equations from relativistic quantum mechanics. A finite-difference discretization of the model is provided using fractional centered differences. The method is a technique that is capable of preserving an energy-like quantity at each iteration. Some computational comparisons against solutions available in the literature are performed in order to assess the capability of the method to preserve the invariant. Our experiments confirm that the technique yields good approximations to the solutions considered. As an application of our scheme, we provide simulations that confirm, for the first time in the literature, the presence of the phenomenon of nonlinear supratransmission in Riesz space-fractional Klein-Gordon equations driven by a harmonic perturbation at the boundary.

A new blackhole theorem and its applications to cosmology and astrophysics

NASA Astrophysics Data System (ADS)

Wang, Shouhong; Ma, Tian

2015-04-01

We shall present a blackhole theorem and a theorem on the structure of our Universe, proved in a recently published paper, based on 1) the Einstein general theory of relativity, and 2) the cosmological principle that the universe is homogeneous and isotropic. These two theorems are rigorously proved using astrophysical dynamical models coupling fluid dynamics and general relativity based on a symmetry-breaking principle. With the new blackhole theorem, we further demonstrate that both supernovae explosion and AGN jets, as well as many astronomical phenomena including e.g. the recent reported are due to combined relativistic, magnetic and thermal effects. The radial temperature gradient causes vertical Benard type convection cells, and the relativistic viscous force (via electromagnetic, the weak and the strong interactions) gives rise to a huge explosive radial force near the Schwarzschild radius, leading e.g. to supernovae explosion and AGN jets.

Static axisymmetric equilibria in general relativistic magnetohydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nunez, Manuel

2008-01-15

While the definition of static equilibria is not clear in a general relativistic context, in many cases of astrophysical interest a natural 3+1 split exists which allows us to define physically meaningful spatial and temporal coordinates. We study the possibility of axisymmetric magnetohydrodynamic equilibria in this setting. The presence of a nontrivial shift velocity provides a constraint not present in the Newtonian case, while the momentum equation may be set in a Grad-Shafranov-like form with the presence of additional terms involving the space-time metric coefficients. It is found that whenever the magnetic field or the shift velocity possesses poloidal component,more » the existence of even local static equilibria demands that the metric parameters satisfy such strong conditions that these equilibria are extremely unlikely. Only very particular cases such as purely toroidal fields and shifts yield existence of equilibria, provided we are able to choose arbitrarily the plasma pressure and density.« less

A field theory approach to the evolution of canonical helicity and energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

You, S.

A redefinition of the Lagrangian of a multi-particle system in fields reformulates the single-particle, kinetic, and fluid equations governing fluid and plasma dynamics as a single set of generalized Maxwell's equations and Ohm's law for canonical force-fields. The Lagrangian includes new terms representing the coupling between the motion of particle distributions, between distributions and electromagnetic fields, with relativistic contributions. The formulation shows that the concepts of self-organization and canonical helicity transport are applicable across single-particle, kinetic, and fluid regimes, at classical and relativistic scales. The theory gives the basis for comparing canonical helicity change to energy change in general systems.more » For example, in a fixed, isolated system subject to non-conservative forces, a species' canonical helicity changes less than total energy only if gradients in density or distribution function are shallow.« less

Anisotropic charged stellar models in Generalized Tolman IV spacetime

NASA Astrophysics Data System (ADS)

Murad, Mohammad Hassan; Fatema, Saba

2015-01-01

With the presence of electric charge and pressure anisotropy some anisotropic stellar models have been developed. An algorithm recently presented by Herrera et al. (Phys. Rev. D 77, 027502 (2008)) to generate static spherically symmetric anisotropic solutions of Einstein's equations has been used to derive relativistic anisotropic charged fluid spheres. In the absence of pressure anisotropy the fluid spheres reduce to some well-known Generalized Tolman IV exact metrics. The astrophysical significance of the resulting equations of state (EOS) for a particular case (Wyman-Leibovitz-Adler) for the anisotropic charged matter distribution has been discussed. Physical analysis shows that the relativistic stellar structure obtained in this work may reasonably model an electrically charged compact star, whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself like electrically charged bare strange quark stars.

Large-scale 3D galaxy correlation function and non-Gaussianity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raccanelli, Alvise; Doré, Olivier; Bertacca, Daniele

We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects --- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the gravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f{sub NL} is small), so that a relativistic approach is needed. Furthermore, we look at how large-scalemore » corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.« less

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

2017-12-01

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

Exploring Stability of General Relativistic Accretion Disks

NASA Astrophysics Data System (ADS)

Korobkin, Oleg; Abdikamalov, Ernazar; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard

2011-04-01

Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios, involving core collapse of massive stars and mergers of compact ob jects. I will present results on our recent study of the stability of such disks against runaway and non-axisymmetric instabilities, which we explore using three-dimensional hydrodynamics simulations in full general relativity. All of our models develop unstable non-axisymmetric modes on a dynamical timescale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the non-axisymmetric mode with azimuthal number m=1 is accompanied by an outspiraling motion of the black hole, which significantly amplifies the growth rate of the m=1 mode in some cases. We will discuss the types, growth rates and pattern speeds of the unstable modes, as well as the detectability of the gravitational waves from such objects.

Relativistic Celestial Mechanics of the Solar System

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei; Efroimsky, Michael; Kaplan, George

2011-09-01

The general theory of relativity was developed by Einstein a century ago. Since then, it has become the standard theory of gravity, especially important to the fields of fundamental astronomy, astrophysics, cosmology, and experimental gravitational physics. Today, the application of general relativity is also essential for many practical purposes involving astrometry, navigation, geodesy, and time synchronization. Numerous experiments have successfully tested general relativity to a remarkable level of precision. Exploring relativistic gravity in the solar system now involves a variety of high-accuracy techniques, for example, very long baseline radio interferometry, pulsar timing, spacecraft Doppler tracking, planetary radio ranging, lunar laser ranging, the global positioning system (GPS), torsion balances and atomic clocks. Over the last few decades, various groups within the International Astronomical Union have been active in exploring the application of the general theory of relativity to the modeling and interpretation of high-accuracy astronomical observations in the solar system and beyond. A Working Group on Relativity in Celestial Mechanics and Astrometry was formed in 1994 to define and implement a relativistic theory of reference frames and time scales. This task was successfully completed with the adoption of a series of resolutions on astronomical reference systems, time scales, and Earth rotation models by the 24th General Assembly of the IAU, held in Manchester, UK, in 2000. However, these resolutions only form a framework for the practical application of relativity theory, and there have been continuing questions on the details of the proper application of relativity theory to many common astronomical problems. To ensure that these questions are properly addressed, the 26th General Assembly of the IAU, held in Prague in August 2006, established the IAU Commission 52, "Relativity in Fundamental Astronomy". The general scientific goals of the new commission are to: * clarify the geometrical and dynamical concepts of fundamental astronomy within a relativistic framework, * provide adequate mathematical and physical formulations to be used in fundamental astronomy, * deepen the understanding of relativity among astronomers and students of astronomy, and * promote research needed to accomplish these tasks. The present book is intended to make a theoretical contribution to the efforts undertaken by this commission. The first three chapters of the book review the foundations of celestial mechanics as well as those of special and general relativity. Subsequent chapters discuss the theoretical and experimental principles of applied relativity in the solar system. The book is written for graduate students and researchers working in the area of gravitational physics and its applications inmodern astronomy. Chapters 1 to 3 were written by Michael Efroimsky and Sergei Kopeikin, Chapters 4 to 8 by Sergei Kopeikin, and Chapter 9 by George Kaplan. Sergei Kopeikin also edited the overall text. It hardly needs to be said that Newtonian celestial mechanics is a very broad area. In Chapter 1, we have concentrated on derivation of the basic equations, on explanation of the perturbed two-body problem in terms of osculating and nonosculating elements, and on discussion of the gauge freedom in the six-dimensional configuration space of the orbital parameters. The gauge freedom of the configuration space has many similarities to the gauge freedom of solutions of the Einstein field equations in general theory of relativity. It makes an important element of the Newtonian theory of gravity, which is often ignored in the books on classic celestial mechanics. Special relativity is discussed in Chapter 2. While our treatment is in many aspects similar to the other books on special relativity, we have carefully emphasised the explanation of the Lorentz and Poincaré transformations, and the appropriate transformation properties of geometric objects like vectors and tensors, for example, the velocity, acceleration, force, electromagnetic field, and so on. Chapter 3 is devoted to general relativity. It explains the main ideas of the tensor calculus on curved manifolds, the theory of the affine connection and parallel transport, and the mathematical and physical foundations of Einstein's approach to gravity. Within this chapter, we have also included topics which are not well covered in standard books on general relativity: namely, the variational analysis on manifolds and the multipolar expansion of gravitational radiation. Chapter 4 introduces a detailed theory of relativistic reference frames and time scales in an N-body system comprised of massive, extended bodies - like our own solar system. Here, we go beyond general relativity and base our analysis on the scalar-tensor theory of gravity. This allows us to extend the domain of applicability of the IAU resolutions on relativistic reference frames, which in their original form were applicable only in the framework of general relativity. We explain the principles of construction of reference frames, and explore their relationship with the solutions of the gravitational field equations. We also discuss the post-Newtonian multipolemoments of the gravitational field from the viewpoint of global and local coordinates. Chapter 5 discusses the principles of derivation of transformations between reference frames in relativistic celestial mechanics. The standard parameterized post-Newtonian (PPN) formalism by K. Nordtevdt and C. Will operates with a single coordinate frame covering the entire N-body system, but it is insufficient for discussion of more subtle relativistic effects showing up in orbital and rotational motion of extended bodies. Consideration of such effects require, besides the global frame, the introduction of a set of local frames needed to properly treat each body and its internal structure and dynamics. The entire set of global and local frames allows us to to discover and eliminate spurious coordinate effects that have no physical meaning. The basic mathematical technique used in our theoretical treatment is based on matching of asymptotic post-Newtonian expansions of the solutions of the gravity field equations. In Chapter 6, we discuss the principles of relativistic celestial mechanics of massive bodies and particles. We focus on derivation of the post-Newtonian equations of orbital and rotational motion of an extended body possessing multipolar moments. These moments couple with the tidal gravitational fields of other bodies, making the motion of the body under consideration very complicated. Simplification is possible if the body can be assumed spherically symmetric. We discuss the conditions under which this simplification can be afforded, and derive the equations of motion of spherically-symmetric bodies. These equations are solved in the case of the two-body problem, and we demonstrate the rich nature of the possible coordinate presentations of such a solution. The relativistic celestial mechanics of light particles (photons) propagating in a time-dependent gravitational field of an N-body system is addressed in Chapter 7. This is a primary subject of relativistic astrometry which became especially important for the analysis of space observations from the Hipparcos satellite in the early 1990s. New astrometric space missions, orders of magnitude more accurate than Hipparcos, for example, Gaia, SIM, JASMINE, and so on, will require even more complete developments. Additionally, relativistic effects play an important role in other areas of modern astronomy, such as, pulsar timing, very long baseline radio interferometry, cosmological gravitational lensing, and so on. High-precision measurements of gravitational light bending in the solar system are among the most crucial experimental tests of the general theory of relativity. Einstein predicted that the amount of light bending by the Sun is twice that given by a Newtonian theory of gravity. This prediction has been confirmed with a relative precision about 0.01%. Measurements of light bending by major planets of the solar system allow us to test the dynamical characteristics of spacetime and draw conclusions about the ultimate speed of gravity as well as to explore the so-called gravitomagnetic phenomena. Chapter 8 deals with the theoretical principles and methods of the high-precision gravimetry and geodesy, based on the framework of general relativity. A gravitational field and the properties of geocentric and topocentric reference frames are described by the metric tensor obtained from the Einstein equations with the help of post-Newtonian iterations. Bymatching the asymptotic, post-Newtonian expansions of the metric tensor in geocentric and topocentric coordinates, we derive the relationship between the reference frames, and relativistic corrections to the Earth's force of gravity and its gradient. Two definitions of a relativistic geoid are discussed, and we prove that these geoids coincide under the condition of a constant rigid-body rotation of the Earth.We consider, as a model of the Earth's matter, the notion of the relativistic level surface of a self-gravitating perfect fluid. We discover that, under conditions of constant rigid rotation of the fluid and hydrostatic behavior of tides, the post-Newtonian equation of the level surface is the same as that of the relativistic geoid. In the conclusion of this chapter, a relativistic generaisation of the Clairaut's equation is obtained. Chapter 9 is a practical guide to the relativistic resolutions of the IAU, with enough background information to place these resolutions into the context of the late twentieth century positional astronomy. These resolutions involve the definitions of reference systems, time scales, and Earth rotationmodels; and some of the resolutions are quite detailed. Although the recommended Earth rotation models have not been developed ab initio within the relativistic framework presented in the other resolutions (in that regard, there still exist some difficult problems to solve), their relativistic terms are accurate enough for all the current and near-future observational techniques. At that level, the Earth rotation models are consistent with the general relativity framework recommended by the IAU and considered in this book. The chapter presents practical algorithms for implementing the recommended models. The appendices to the book contain a list of astronomical constants and the original text of the relevant IAU resolutions adopted by the IAU General Assemblies in 1997, 2000, 2006, and 2009. Numerous colleagues have contributed to this book in one way or or another. It is a pleasure for us to acknowledge the enlightening discussions which one or more of the authors had on different occasions with Victor A. Brumberg of the Institute of Applied Astronomy (St. Petersburg, Russia); Tianyi Huang and Yi Xie of Nanjing University (China); Edward B. Fomalont of the National Radio Astronomical Observatory (USA); Valeri V. Makarov, William J. Tangren, and James L. Hilton of the US Naval Observatory; Gerhard Schäfer of the Institute of Theoretical Physics (Jena, Germany); Clifford M. Will of Washington University (St. Louis, USA); Ignazio Ciufolini of the Università del Salento and INFN Sezione di Lecce (Italy); and Patrick Wallace, retired from Her Majesty's Nautical Almanac Office (UK). We also would like to thank Richard G. French of Wellesley College (Massachusetts, USA); Michael Soffel and Sergei Klioner of the Technical University of Dresden; Bahram Mashhoon of the University of Missouri-Columbia; John D. Anderson, retired from the Jet Propulsion Laboratory (USA); the late Giacomo Giampieri, also of JPL; Michael Kramer, Axel Jessner, and Norbert Wex of the Max-Planck-Institut für Radioastronomie (Bonn, Germany); Alexander F. Zakharov of the Institute of Theoretical and Experimental Physics (Moscow, Russia); the late Yuri P. Ilyasov from Astro Space Center of Russian Academy of Science; Michael V. Sazhin, Vladimir A. Zharov, and Igor Yu. Vlasov of the Sternberg Astronomical Institute (Moscow, Russia); and Vladimir B. Braginsky of Moscow State University (Russia) for their remarks and comments, all of which helped us to properly formulate the theoretical concepts and other material presented in this book. The discussions among themembers of the IAU Worki! ng Group on Relativity in Celestial Mechanics and Astrometry as well as those within the Working Group on Nomenclature for Fundamental Astronomy have also been quite valuable and have contributed to what is presented here. The numerous scientific papers written by Nicole Capitaine of the Paris Observatory and her collaborators have been essential references. Victor Slabinski and Dennis D. McCarthy of the US Naval Observatory, P. Kenneth Seidelmann of the University of Virginia, Catherine Y. Hohenkerk of Her Majesty's Nautical Almanac Office, and E. Myles Standish, retired from the Jet Propulsion Laboratory, reviewed early drafts of the material that became Chapter 9 and made many substantial suggestions for improvement. We were, of course, influenced by many other textbooks available in this field. We would like to pay particular tribute to: C.W. Misner, K. S. Thorne and J. A. Wheeler "Gravitation" V.A. Brumberg "Essential Relativistic Celestial Mechanics" B.F. Schutz "Geometrical Methods of Mathematical Physics" M.H. Soffel "Relativity in Celestial Mechanics, Astrometry and Geodesy" C.M. Will "Theory and Experiment in Gravitational Physics". There are many other books and influential papers that are important as well which are referenced in the relevant parts of the present book. Not one of our aforementioned colleagues is responsible for any remaining errors or omissions in this book, for which, of course, the authors bear full responsibility. Last, but by nomeans least,Michael Efroimsky and George Kaplan wish to thank John A. Bangert of the US Naval Observatory for the administrative support which he so kindly provided to the project during all of its stages. Sergei Kopeikin is sincerely grateful to the Research Council of the University of Missouri-Columbia for the generous financial support (grants RL-08-027, URC-08-062B, SRF-09-012) that was essential for the successful completion of the book.

Binary neutron star mergers and short gamma-ray bursts: Effects of magnetic field orientation, equation of state, and mass ratio

NASA Astrophysics Data System (ADS)

Kawamura, Takumu; Giacomazzo, Bruno; Kastaun, Wolfgang; Ciolfi, Riccardo; Endrizzi, Andrea; Baiotti, Luca; Perna, Rosalba

2016-09-01

We present fully general-relativistic magnetohydrodynamic simulations of the merger of binary neutron star (BNS) systems. We consider BNSs producing a hypermassive neutron star (HMNS) that collapses to a spinning black hole (BH) surrounded by a magnetized accretion disk in a few tens of ms. We investigate whether such systems may launch relativistic jets and hence power short gamma-ray bursts. We study the effects of different equations of state (EOSs), different mass ratios, and different magnetic field orientations. For all cases, we present a detailed investigation of the matter dynamics and of the magnetic field evolution, with particular attention to its global structure and possible emission of relativistic jets. The main result of this work is that we observe the formation of an organized magnetic field structure. This happens independently of EOS, mass ratio, and initial magnetic field orientation. We also show that those models that produce a longer-lived HMNS lead to a stronger magnetic field before collapse to a BH. Such larger fields make it possible, for at least one of our models, to resolve the magnetorotational instability and hence further amplify the magnetic field in the disk. However, by the end of our simulations, we do not (yet) observe a magnetically dominated funnel nor a relativistic outflow. With respect to the recent simulations of Ruiz et al. [Astrophys. J. 824, L6 (2016)], we evolve models with lower and more plausible initial magnetic field strengths and (for computational reasons) we do not evolve the accretion disk for the long time scales that seem to be required in order to see a relativistic outflow. Since all our models produce a similar ordered magnetic field structure aligned with the BH spin axis, we expect that the results found by Ruiz et al. (who only considered an equal-mass system with an ideal fluid EOS) should be general and—at least from a qualitative point of view—independent of the mass ratio, magnetic field orientation, and EOS.

Regionally Implicit Discontinuous Galerkin Methods for Solving the Relativistic Vlasov-Maxwell System Submitted to Iowa State University

NASA Astrophysics Data System (ADS)

Guthrey, Pierson Tyler

The relativistic Vlasov-Maxwell system (RVM) models the behavior of collisionless plasma, where electrons and ions interact via the electromagnetic fields they generate. In the RVM system, electrons could accelerate to significant fractions of the speed of light. An idea that is actively being pursued by several research groups around the globe is to accelerate electrons to relativistic speeds by hitting a plasma with an intense laser beam. As the laser beam passes through the plasma it creates plasma wakes, much like a ship passing through water, which can trap electrons and push them to relativistic speeds. Such setups are known as laser wakefield accelerators, and have the potential to yield particle accelerators that are significantly smaller than those currently in use. Ultimately, the goal of such research is to harness the resulting electron beams to generate electromagnetic waves that can be used in medical imaging applications. High-order accurate numerical discretizations of kinetic Vlasov plasma models are very effective at yielding low-noise plasma simulations, but are computationally expensive to solve because of the high dimensionality. In addition to the general difficulties inherent to numerically simulating Vlasov models, the relativistic Vlasov-Maxwell system has unique challenges not present in the non-relativistic case. One such issue is that operator splitting of the phase gradient leads to potential instabilities, thus we require an alternative to operator splitting of the phase. The goal of the current work is to develop a new class of high-order accurate numerical methods for solving kinetic Vlasov models of plasma. The main discretization in configuration space is handled via a high-order finite element method called the discontinuous Galerkin method (DG). One difficulty is that standard explicit time-stepping methods for DG suffer from time-step restrictions that are significantly worse than what a simple Courant-Friedrichs-Lewy (CFL) argument requires. The maximum stable time-step scales inversely with the highest degree in the DG polynomial approximation space and becomes progressively smaller with each added spatial dimension. In this work, we overcome this difficulty by introducing a novel time-stepping strategy: the regionally-implicit discontinuous Galerkin (RIDG) method. The RIDG is method is based on an extension of the Lax-Wendroff DG (LxW-DG) method, which previously had been shown to be equivalent (for linear constant coefficient problems) to a predictor-corrector approach, where the prediction is computed by a space-time DG method (STDG). The corrector is an explicit method that uses the space-time reconstructed solution from the predictor step. In this work, we modify the predictor to include not just local information, but also neighboring information. With this modification, we show that the stability is greatly enhanced; we show that we can remove the polynomial degree dependence of the maximum time-step and show vastly improved time-steps in multiple spatial dimensions. Upon the development of the general RIDG method, we apply it to the non-relativistic 1D1V Vlasov-Poisson equations and the relativistic 1D2V Vlasov-Maxwell equations. For each we validate the high-order method on several test cases. In the final test case, we demonstrate the ability of the method to simulate the acceleration of electrons to relativistic speeds in a simplified test case.

Nanomodulated electron beams via electron diffraction and emittance exchange for coherent x-ray generation

NASA Astrophysics Data System (ADS)

Nanni, E. A.; Graves, W. S.; Moncton, D. E.

2018-01-01

We present a new method for generation of relativistic electron beams with current modulation on the nanometer scale and below. The current modulation is produced by diffracting relativistic electrons in single crystal Si, accelerating the diffracted beam and imaging the crystal structure, then transferring the image into the temporal dimension via emittance exchange. The modulation period can be tuned by adjusting electron optics after diffraction. This tunable longitudinal modulation can have a period as short as a few angstroms, enabling production of coherent hard x-rays from a source based on inverse Compton scattering with total accelerator length of approximately ten meters. Electron beam simulations from cathode emission through diffraction, acceleration, and image formation with variable magnification are presented along with estimates of the coherent x-ray output properties.

Properties of Blazar Jets Defined by an Economy of Power

NASA Astrophysics Data System (ADS)

Petropoulou, Maria; Dermer, Charles D.

2016-07-01

The absolute power of a relativistic black hole jet includes the power in the magnetic field, the leptons, the hadrons, and the radiated photons. A power analysis of a relativistic radio/γ-ray blazar jet leads to bifurcated leptonic synchrotron-Compton (LSC) and leptohadronic synchrotron (LHS) solutions that minimize the total jet power. Higher Doppler factors with increasing peak synchrotron frequency are implied in the LSC model. Strong magnetic fields {B}\\prime ≳ 100 {{G}} are found for the LHS model with variability times ≲ {10}3 {{s}}, in accord with highly magnetized, reconnection-driven jet models. Proton synchrotron models of ≳ 100 {GeV} blazar radiation can have sub-Eddington absolute jet powers, but models of dominant GeV radiation in flat spectrum radio quasars require excessive power.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

NASA Astrophysics Data System (ADS)

Hayata, Tomoya; Hidaka, Yoshimasa; Noumi, Toshifumi; Hongo, Masaru

2015-09-01

We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

Corrections of the finite relativistic contributions to the synodic month period Earth-Moon range oscillations: Agreement between the geocentric and the solar-system barycentric inertial-frame calculations

NASA Astrophysics Data System (ADS)

Nordtvedt, Ken

1993-04-01

We have corrected our calculation of the finite general relativistic contribution to the synodic month period Earth-Moon range oscillation by including previously overlooked terms in the Moon's post-Newtonian equation of motion: the corrected result x(t)~=(3gSr2/c2) cos(ω-Ω)t agrees with the Shahid-Saless calculation which was performed in the geocentric frame. It is also pointed out that at the level of a few millimeters synodic month period amplitude, the Moon's orbit is polarized by the solar radiation pressure force on the Moon.

FAST TRACK COMMUNICATION Initial data for the relativistic gravitational N-body problem

NASA Astrophysics Data System (ADS)

Chruściel, Piotr T.; Corvino, Justin; Isenberg, James

2010-11-01

In general relativity, an initial data set for an isolated gravitational system takes the form of a solution of the Einstein constraint equations which is asymptotically Euclidean on a specified end. Given a collection of N such data sets with a subregion of interest (bounded away from the specified end) chosen in each, we show that there exists a family of new initial data sets, each of which contains exact copies of each of the N chosen subregions, positioned in a chosen array in a single asymptotic end. These composite initial data sets model isolated, relativistic gravitational systems containing N chosen bodies in specified initial configurations.

Analytical attractor and the divergence of the slow-roll expansion in relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Denicol, Gabriel S.; Noronha, Jorge

2018-03-01

We find the general analytical solution of the viscous relativistic hydrodynamic equations (in the absence of bulk viscosity and chemical potential) for a Bjorken expanding fluid with an ideal gas equation of state and a constant shear viscosity relaxation time. We analytically determine the hydrodynamic attractor of this fluid and discuss its properties. We show for the first time that the slow-roll expansion, a commonly used approach to characterize the attractor, diverges. This is shown to hold also in a conformal plasma. The gradient expansion is found to converge in an example where causality and stability are violated.

Numerical Hydrodynamics and Magnetohydrodynamics in General Relativity.

PubMed

Font, José A

2008-01-01

This article presents a comprehensive overview of numerical hydrodynamics and magneto-hydrodynamics (MHD) in general relativity. Some significant additions have been incorporated with respect to the previous two versions of this review (2000, 2003), most notably the coverage of general-relativistic MHD, a field in which remarkable activity and progress has occurred in the last few years. Correspondingly, the discussion of astrophysical simulations in general-relativistic hydrodynamics is enlarged to account for recent relevant advances, while those dealing with general-relativistic MHD are amply covered in this review for the first time. The basic outline of this article is nevertheless similar to its earlier versions, save for the addition of MHD-related issues throughout. Hence, different formulations of both the hydrodynamics and MHD equations are presented, with special mention of conservative and hyperbolic formulations well adapted to advanced numerical methods. A large sample of numerical approaches for solving such hyperbolic systems of equations is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. As previously stated, a comprehensive summary of astrophysical simulations in strong gravitational fields is also presented. These are detailed in three basic sections, namely gravitational collapse, black-hole accretion, and neutron-star evolutions; despite the boundaries, these sections may (and in fact do) overlap throughout the discussion. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances in the formulation of the gravitational field, hydrodynamics and MHD equations and the numerical methodology designed to solve them. To keep the length of this article reasonable, an effort has been made to focus on multidimensional studies, directing the interested reader to earlier versions of the review for discussions on one-dimensional works. Supplementary material is available for this article at 10.12942/lrr-2008-7.

Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

NASA Astrophysics Data System (ADS)

Guercilena, Federico; Radice, David; Rezzolla, Luciano

2017-07-01

We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. (J. Comput. Phys. 230(11):4248-4267, 2011, doi: 10.1016/j.jcp.2010.11.043). Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5 (Suresh and Huynh in J. Comput. Phys. 136(1):83-99, 1997, doi: 10.1006/jcph.1997.5745), one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to {˜}50% speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.

AN OPEN-SOURCE NEUTRINO RADIATION HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE

DOE Office of Scientific and Technical Information (OSTI.GOV)

O’Connor, Evan, E-mail: evanoconnor@ncsu.edu; CITA, Canadian Institute for Theoretical Astrophysics, Toronto, M5S 3H8

2015-08-15

We present an open-source update to the spherically symmetric, general-relativistic hydrodynamics, core-collapse supernova (CCSN) code GR1D. The source code is available at http://www.GR1Dcode.org. We extend its capabilities to include a general-relativistic treatment of neutrino transport based on the moment formalisms of Shibata et al. and Cardall et al. We pay special attention to implementing and testing numerical methods and approximations that lessen the computational demand of the transport scheme by removing the need to invert large matrices. This is especially important for the implementation and development of moment-like transport methods in two and three dimensions. A critical component of neutrinomore » transport calculations is the neutrino–matter interaction coefficients that describe the production, absorption, scattering, and annihilation of neutrinos. In this article we also describe our open-source neutrino interaction library NuLib (available at http://www.nulib.org). We believe that an open-source approach to describing these interactions is one of the major steps needed to progress toward robust models of CCSNe and robust predictions of the neutrino signal. We show, via comparisons to full Boltzmann neutrino-transport simulations of CCSNe, that our neutrino transport code performs remarkably well. Furthermore, we show that the methods and approximations we employ to increase efficiency do not decrease the fidelity of our results. We also test the ability of our general-relativistic transport code to model failed CCSNe by evolving a 40-solar-mass progenitor to the onset of collapse to a black hole.« less

Further studies of particle acceleration in cassiopeia A

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chevalier, R.A.; Oegerle, W.R.; Scott, J.S.

We have further investigated models for statistical particle acceleration in the supernova remnant Cas A. Simple (three-parameter) models involving continuous second order Fermi acceleration and variable relativistic particle injection can reproduce the observed radio properties of Cas A, including the low-frequency flux anomaly first noted by Erickson and Perley. Models dominated by adiabatic expansion losses are preferable to those dominated by particle escape. The gain time determined from these models agrees well with that predicted from the hydrodynamic situation in Cas A. A model predicting the high-frequency nonthermal spectrum of Cas A indicates that the spectrum turns down in themore » optical regime due to synchrotron losses. The maximum relativistic particle energy content of Cas A was probably about several times 10/sup 49/-10/sup 50/ ergs, which can be compared with an estimated initial kinetic energy in the range 0.24 to 1.0 x 10/sup 52/ ergs. If relativistic particles can escape from Cas A, their spectra will have certain characteristics: the electron spectrum will have a turnover due to synchrotron losses and the proton spectrum will have a cutoff due to the particle gyroradii becoming larger than the sizes of the magnetic scattering centers. The observed bend in the galactic cosmic ray spectrum could be due to energy losses within the source remnant itself instead of losses incurred during propagation through the Galaxy. We also comment on other models for the relativistic electron content of Cas A.« less

The Gravity Probe B `Niobium bird' experiment: Verifying the data reduction scheme for estimating the relativistic precession of Earth-orbiting gyroscopes

NASA Technical Reports Server (NTRS)

Uemaatsu, Hirohiko; Parkinson, Bradford W.; Lockhart, James M.; Muhlfelder, Barry

1993-01-01

Gravity Probe B (GP-B) is a relatively gyroscope experiment begun at Stanford University in 1960 and supported by NASA since 1963. This experiment will check, for the first time, the relativistic precession of an Earth-orbiting gyroscope that was predicted by Einstein's General Theory of Relativity, to an accuracy of 1 milliarcsecond per year or better. A drag-free satellite will carry four gyroscopes in a polar orbit to observe their relativistic precession. The primary sensor for measuring the direction of gyroscope spin axis is the SQUID (superconducting quantum interference device) magnetometer. The data reduction scheme designed for the GP-B program processes the signal from the SQUID magnetometer and estimates the relativistic precession rates. We formulated the data reduction scheme and designed the Niobium bird experiment to verify the performance of the data reduction scheme experimentally with an actual SQUID magnetometer within the test loop. This paper reports the results from the first phase of the Niobium bird experiment, which used a commercially available SQUID magnetometer as its primary sensor, and adresses the issues they raised. The first phase resulted in a large, temperature-dependent bias drift in the insensitive design and a temperature regulation scheme.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fujibayashi, Sho; Sekiguchi, Yuichiro; Kiuchi, Kenta

We performed general relativistic, long-term, axisymmetric neutrino radiation hydrodynamics simulations for the remnant formed after a binary neutron star merger, which consists of a massive neutron star and a torus surrounding it. As an initial condition, we employ the result derived in a three-dimensional, numerical relativity simulation for the binary neutron star merger. We investigate the properties of neutrino-driven ejecta. Due to the pair-annihilation heating, the dynamics of the neutrino-driven ejecta are significantly modified. The kinetic energy of the ejecta is about two times larger than that in the absence of pair-annihilation heating. This suggests that the pair-annihilation heating playsmore » an important role in the evolution of merger remnants. The relativistic outflow, which is required for driving gamma-ray bursts, is not observed because the specific heating rate around the rotational axis is not sufficiently high, due to the baryon loading caused by the neutrino-driven ejecta from the massive neutron star. We discuss the condition for launching the relativistic outflow and the nucleosynthesis in the ejecta.« less

A signed particle formulation of non-relativistic quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-09-15

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussedmore » and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.« less

Holographic Tools for Probing the Dynamics of Strongly Coupled Field Theories

NASA Astrophysics Data System (ADS)

Fuini, John F.

Since it was conjectured almost 20 years ago, AdS/CFT duality, or holography, has enabled steady progress in understanding certain gauge theories in the strongly coupled limit. In this thesis we examine various aspects of holography and holographic techniques, as well as particular applications to the dynamics of strongly coupled plasmas. We discuss the energy loss of general probe defects in generic holographic plasmas and the lifetime of quasinormal modes of sufficiently short-wavelength in a strongly coupled N = 4 Super Yang-Mills (SYM) plasma. We then perform a thorough investigation of the far-from-equilibrium dynamics of the SYM plasma, focusing on how the presence of large magnetic fields or chemical potentials affect the timescale of equilibration. Finally we discuss some non-relativistic directions by finding a covariant construction of Lagrangians for spinor fields in generic Newton-Cartan backgrounds via a non-relativistic reduction, which may assist in the construction of non-relativistic versions of holography.

Relativistic wide-angle galaxy bispectrum on the light cone

NASA Astrophysics Data System (ADS)

Bertacca, Daniele; Raccanelli, Alvise; Bartolo, Nicola; Liguori, Michele; Matarrese, Sabino; Verde, Licia

2018-01-01

Given the important role that the galaxy bispectrum has recently acquired in cosmology and the scale and precision of forthcoming galaxy clustering observations, it is timely to derive the full expression of the large-scale bispectrum going beyond approximated treatments which neglect integrated terms or higher-order bias terms or use the Limber approximation. On cosmological scales, relativistic effects that arise from observing the past light cone alter the observed galaxy number counts, therefore leaving their imprints on N-point correlators at all orders. In this paper we compute for the first time the bispectrum including all general relativistic, local and integrated, effects at second order, the tracers' bias at second order, geometric effects as well as the primordial non-Gaussianity contribution. This is timely considering that future surveys will probe scales comparable to the horizon where approximations widely used currently may not hold; neglecting these effects may introduce biases in estimation of cosmological parameters as well as primordial non-Gaussianity.

Momentum and charge transport in non-relativistic holographic fluids from Hořava gravity

NASA Astrophysics Data System (ADS)

Davison, Richard A.; Grozdanov, Sašo; Janiszewski, Stefan; Kaminski, Matthias

2016-11-01

We study the linearized transport of transverse momentum and charge in a conjectured field theory dual to a black brane solution of Hořava gravity with Lifshitz exponent z = 1. As expected from general hydrodynamic reasoning, we find that both of these quantities are diffusive over distance and time scales larger than the inverse temperature. We compute the diffusion constants and conductivities of transverse momentum and charge, as well the ratio of shear viscosity to entropy density, and find that they differ from their relativistic counterparts. To derive these results, we propose how the holographic dictionary should be modified to deal with the multiple horizons and differing propagation speeds of bulk excitations in Hořava gravity. When possible, as a check on our methods and results, we use the covariant Einstein-Aether formulation of Hořava gravity, along with field redefinitions, to re-derive our results from a relativistic bulk theory.

Relativistic redshifts in quasar broad lines

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tremaine, Scott; Shen, Yue; Liu, Xin

2014-10-10

The broad emission lines commonly seen in quasar spectra have velocity widths of a few percent of the speed of light, so special- and general-relativistic effects have a significant influence on the line profile. We have determined the redshift of the broad Hβ line in the quasar rest frame (determined from the core component of the [O III] line) for over 20,000 quasars from the Sloan Digital Sky Survey Data Release 7 quasar catalog. The mean redshift as a function of line width is approximately consistent with the relativistic redshift that is expected if the line originates in a randomlymore » oriented Keplerian disk that is obscured when the inclination of the disk to the line of sight exceeds ∼30°-45°, consistent with simple active galactic nucleus unification schemes. This result also implies that the net line-of-sight inflow/outflow velocities in the broad-line region are much less than the Keplerian velocity when averaged over a large sample of quasars with a given line width.« less

Accretion disks around black holes

NASA Technical Reports Server (NTRS)

Abramowicz, M. A.

1994-01-01

The physics of accretion flow very close to a black hole is dominated by several general relativistic effects. It cannot be described by the standard Shakura Sunyaev model or by its relativistic version developed by Novikov and Thome. The most important of these effects is a dynamical mass loss from the inner edge of the disk (Roche lobe overflow). The relativistic Roche lobe overflow induces a strong advective cooling, which is sufficient to stabilize local, axially symmetric thermal and viscous modes. It also stabilizes the non-axially-symmetric global modes discovered by Papaloizou and Pringle. The Roche lobe overflow, however, destabilizes sufficiently self-gravitating accretion disks with respect to a catastrophic runaway of mass due to minute changes of the gravitational field induced by the changes in the mass and angular momentum of the central black hole. One of the two acoustic modes may become trapped near the inner edge of the disk. All these effects, absent in the standard model, have dramatic implications for time-dependent behavior of the accretion disks around black holes.

Group theoretical symmetries and generalized Bäcklund transformations for integrable systems

NASA Astrophysics Data System (ADS)

Haak, Guido

1994-05-01

A notion of symmetry for 1+1-dimensional integrable systems is presented which is consistent with their group theoretic description. It is shown how a group symmetry may be used together with a dynamical reduction to produce new generalizations of the Bäcklund transformation for the Korteweg-de Vries equation to its SL(n,C) generalization. An additional application to the relativistic invariance of the Leznov-Saveliev systems is given.

Matter in general relativity

NASA Technical Reports Server (NTRS)

Ray, J. R.

1982-01-01

Two theories of matter in general relativity, the fluid theory and the kinetic theory, were studied. Results include: (1) a discussion of various methods of completing the fluid equations; (2) a method of constructing charged general relativistic solutions in kinetic theory; and (3) a proof and discussion of the incompatibility of perfect fluid solutions in anisotropic cosmologies. Interpretations of NASA gravitational experiments using the above mentioned results were started. Two papers were prepared for publications based on this work.

The current ability to test theories of gravity with black hole shadows

NASA Astrophysics Data System (ADS)

Mizuno, Yosuke; Younsi, Ziri; Fromm, Christian M.; Porth, Oliver; De Laurentis, Mariafelicia; Olivares, Hector; Falcke, Heino; Kramer, Michael; Rezzolla, Luciano

2018-04-01

Our Galactic Centre, Sagittarius A*, is believed to harbour a supermassive black hole, as suggested by observations tracking individual orbiting stars1,2. Upcoming submillimetre very-long baseline interferometry images of Sagittarius A* carried out by the Event Horizon Telescope collaboration (EHTC)3,4 are expected to provide critical evidence for the existence of this supermassive black hole5,6. We assess our present ability to use EHTC images to determine whether they correspond to a Kerr black hole as predicted by Einstein's theory of general relativity or to a black hole in alternative theories of gravity. To this end, we perform general-relativistic magnetohydrodynamical simulations and use general-relativistic radiative-transfer calculations to generate synthetic shadow images of a magnetized accretion flow onto a Kerr black hole. In addition, we perform these simulations and calculations for a dilaton black hole, which we take as a representative solution of an alternative theory of gravity. Adopting the very-long baseline interferometry configuration from the 2017 EHTC campaign, we find that it could be extremely difficult to distinguish between black holes from different theories of gravity, thus highlighting that great caution is needed when interpreting black hole images as tests of general relativity.

The Conquest of Outer Space--Optional Curriculum Model

ERIC Educational Resources Information Center

Florian, Gabriel; Florian, Aurelia-Daniela; Pufu, Nicolae

2015-01-01

This paper proposes an optional syllabus for the students in the XIIth grade. The proposed theme analyzes the concept of "variable mass" both in terms of classical mechanics and relativistic mechanics. In terms of classical mechanics we refer to the slow motion of a body, whose mass ranges in ascending way (by annealing a mass particle…

The disc-jet symbiosis emerges: modelling the emission of Sagittarius A* with electron thermodynamics

NASA Astrophysics Data System (ADS)

Ressler, S. M.; Tchekhovskoy, A.; Quataert, E.; Gammie, C. F.

2017-05-01

We calculate the radiative properties of Sagittarius A* - spectral energy distribution, variability and radio-infrared images - using the first 3D, physically motivated black hole accretion models that directly evolve the electron thermodynamics in general relativistic MHD simulations. These models reproduce the coupled disc-jet structure for the emission favoured by previous phenomenological analytic and numerical works. More specifically, we find that the low frequency radio emission is dominated by emission from a polar outflow while the emission above 100 GHz is dominated by the inner region of the accretion disc. The latter produces time variable near-infrared (NIR) and X-ray emission, with frequent flaring events (including IR flares without corresponding X-ray flares and IR flares with weak X-ray flares). The photon ring is clearly visible at 230 GHz and 2 μm, which is encouraging for future horizon-scale observations. We also show that anisotropic electron thermal conduction along magnetic field lines has a negligible effect on the radiative properties of our model. We conclude by noting limitations of our current generation of first-principles models, particularly that the outflow is closer to adiabatic than isothermal and thus underpredicts the low frequency radio emission.

Evolution of three-dimensional relativistic current sheets and development of self-generated turbulence

NASA Astrophysics Data System (ADS)

Takamoto, M.

2018-05-01

In this paper, the temporal evolution of three-dimensional relativistic current sheets in Poynting-dominated plasma is studied for the first time. Over the past few decades, a lot of efforts have been conducted on studying the evolution of current sheets in two-dimensional space, and concluded that sufficiently long current sheets always evolve into the so-called plasmoid chain, which provides a fast reconnection rate independent of its resistivity. However, it is suspected that plasmoid chain can exist only in the case of two-dimensional approximation, and would show transition to turbulence in three-dimensional space. We performed three-dimensional numerical simulation of relativistic current sheet using resistive relativistic magnetohydrodynamic approximation. The results showed that the three-dimensional current sheets evolve not into plasmoid chain but turbulence. The resulting reconnection rate is 0.004, which is much smaller than that of plasmoid chain. The energy conversion from magnetic field to kinetic energy of turbulence is just 0.01 per cent, which is much smaller than typical non-relativistic cases. Using the energy principle, we also showed that the plasmoid is always unstable for a displacement in the opposite direction to its acceleration, probably interchange-type instability, and this always results in seeds of turbulence behind the plasmoids. Finally, the temperature distribution along the sheet is discussed, and it is found that the sheet is less active than plasmoid chain. Our finding can be applied for many high-energy astrophysical phenomena, and can provide a basic model of the general current sheet in Poynting-dominated plasma.

Optical drift effects in general relativity

NASA Astrophysics Data System (ADS)

Korzyński, Mikołaj; Kopiński, Jarosław

2018-03-01

We consider the question of determining the optical drift effects in general relativity, i.e. the rate of change of the apparent position, redshift, Jacobi matrix, angular distance and luminosity distance of a distant object as registered by an observer in an arbitrary spacetime. We present a fully relativistic and covariant approach, in which the problem is reduced to a hierarchy of ODE's solved along the line of sight. The 4-velocities and 4-accelerations of the observer and the emitter and the geometry of the spacetime along the line of sight constitute the input data. We build on the standard relativistic geometric optics formalism and extend it to include the time derivatives of the observables. In the process we obtain two general, non-perturbative relations: the first one between the gravitational lensing, represented by the Jacobi matrix, and the apparent position drift, also called the cosmic parallax, and the second one between the apparent position drift and the redshift drift. The applications of the results include the theoretical study of the drift effects of cosmological origin (so-called real-time cosmology) in numerical or exact Universe models.

Comparing fully general relativistic and Newtonian calculations of structure formation

NASA Astrophysics Data System (ADS)

East, William E.; Wojtak, Radosław; Abel, Tom

2018-02-01

In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. They only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.

Numerical Hydrodynamics in General Relativity.

PubMed

Font, José A

2003-01-01

The current status of numerical solutions for the equations of ideal general relativistic hydrodynamics is reviewed. With respect to an earlier version of the article, the present update provides additional information on numerical schemes, and extends the discussion of astrophysical simulations in general relativistic hydrodynamics. Different formulations of the equations are presented, with special mention of conservative and hyperbolic formulations well-adapted to advanced numerical methods. A large sample of available numerical schemes is discussed, paying particular attention to solution procedures based on schemes exploiting the characteristic structure of the equations through linearized Riemann solvers. A comprehensive summary of astrophysical simulations in strong gravitational fields is presented. These include gravitational collapse, accretion onto black holes, and hydrodynamical evolutions of neutron stars. The material contained in these sections highlights the numerical challenges of various representative simulations. It also follows, to some extent, the chronological development of the field, concerning advances on the formulation of the gravitational field and hydrodynamic equations and the numerical methodology designed to solve them. Supplementary material is available for this article at 10.12942/lrr-2003-4.

A new approach for modeling gravitational radiation from the inspiral of two neutron stars

NASA Astrophysics Data System (ADS)

Luke, Stephen A.

In this dissertation, a new method of applying the ADM formalism of general relativity to model the gravitational radiation emitted from the realistic inspiral of a neutron star binary is described. A description of the conformally flat condition (CFC) is summarized, and the ADM equations are solved by use of the CFC approach for a neutron star binary. The advantages and limitations of this approach are discussed, and the need for a more accurate improvement to this approach is described. To address this need, a linearized perturbation of the CFC spatial three metric is then introduced. The general relativistic hydrodynamic equations are then allowed to evolve against this basis under the assumption that the first-order corrections to the hydrodynamic variables are negligible compared to their CFC values. As a first approximation, the linear corrections to the conformal factor, lapse function, and shift vector are also assumed to be small compared to the extrinsic curvature and the three metric. A boundary matching method is then introduced as a way of computing the gravitational radiation of this relativistic system without use of the multipole expansion as employed by earlier applications of the CFC approach. It is assumed that at a location far from the source, the three metric is accurately described by a linear correction to Minkowski spacetime. The two polarizations of gravitational radiation can then be computed at that point in terms of the linearized correction to the metric. The evolution equations obtained from the linearized perturbative correction to the CFC approach and the method for recovery of the gravity wave signal are then tested by use of a three-dimensional numerical simulation. This code is used to compute the gravity wave signal emitted a pair of equal mass neutron stars in quasi-stable circular orbits at a point early in their inspiral phase. From this simple numerical analysis, the correct general trend of gravitational radiation is recovered. Comparisons with (5/2) post-Newtonian solutions show a similar gravitational waveform, although inaccuracies are still found to exist from this computation. Finally, several areas for improvement and potential future applications of this technique are discussed.

Relativistic MHD simulations of collision-induced magnetic dissipation in poynting-flux-dominated jets/outflows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deng, Wei; Li, Hui; Zhang, Bing

We perform 3D relativistic ideal MHD simulations to study the collisions between high-σ (Poynting- ux-dominated) blobs which contain both poloidal and toroidal magnetic field components. This is meant to mimic the interactions inside a highly variable Poynting- ux-dominated jet. We discover a significant electromagnetic field (EMF) energy dissipation with an Alfvenic rate with the efficiency around 35%. Detailed analyses show that this dissipation is mostly facilitated by the collision-induced magnetic reconnection. Additional resolution and parameter studies show a robust result that the relative EMF energy dissipation efficiency is nearly independent of the numerical resolution or most physical parameters in themore » relevant parameter range. The reconnection outflows in our simulation can potentially form the multi-orientation relativistic mini-jets as needed for several analytical models. We also find a linear relationship between the σ values before and after the major EMF energy dissipation process. In conclusion, our results give support to the proposed astrophysical models that invoke signi cant magnetic energy dissipation in Poynting- ux-dominated jets, such as the internal collision-induced magnetic reconnection and turbulence (ICMART) model for GRBs, and reconnection triggered mini-jets model for AGNs.« less

Relativistic MHD simulations of collision-induced magnetic dissipation in poynting-flux-dominated jets/outflows

DOE PAGES

Deng, Wei; Li, Hui; Zhang, Bing; ...

2015-05-29

We perform 3D relativistic ideal MHD simulations to study the collisions between high-σ (Poynting- ux-dominated) blobs which contain both poloidal and toroidal magnetic field components. This is meant to mimic the interactions inside a highly variable Poynting- ux-dominated jet. We discover a significant electromagnetic field (EMF) energy dissipation with an Alfvenic rate with the efficiency around 35%. Detailed analyses show that this dissipation is mostly facilitated by the collision-induced magnetic reconnection. Additional resolution and parameter studies show a robust result that the relative EMF energy dissipation efficiency is nearly independent of the numerical resolution or most physical parameters in themore » relevant parameter range. The reconnection outflows in our simulation can potentially form the multi-orientation relativistic mini-jets as needed for several analytical models. We also find a linear relationship between the σ values before and after the major EMF energy dissipation process. In conclusion, our results give support to the proposed astrophysical models that invoke signi cant magnetic energy dissipation in Poynting- ux-dominated jets, such as the internal collision-induced magnetic reconnection and turbulence (ICMART) model for GRBs, and reconnection triggered mini-jets model for AGNs.« less

Correlation Analysis of Prompt Emission from Gamma Ray Bursts

NASA Astrophysics Data System (ADS)

Pothapragada, Sriharsha

Prompt emission from gamma-ray bursts (GRBs) exhibits very rapid, complicated temporal and spectral evolution. This diverse variability in the light-curves reflects the complicated nature of the underlying physics, in which inter-penetrating relativistic shells in the outflow are believed to generate strong magnetic fields that vary over very small scales. We use the theory of jitter radiation to model the emission from such regions and the resulting overall prompt gamma ray emission from a series of relativistic collisionless shocks. We present simulated GRB light-curves developed as a series of "pulses" corresponding to instantaneously illuminated "thin-shell" regions emitting via the jitter radiation mechanism. The effects of various geometries, viewing angles, and bulk Lorentz factor profiles of the radiating outflow jets on the spectral features and evolution of these light-curves are explored. Our results demonstrate how an anisotropic jitter radiation pattern, in conjunction with relativistic shock kinematics, can produce certain features observed in the GRB prompt emission spectra, such as the occurrence of hard, synchrotron violating spectra, the "tracking" of observed flux with spectral parameters, and spectral softening below peak energy within individual episodes of the light curve. We highlight predictions in the light of recent advances in the observational sphere of GRBs.

Extreme enhancements and depletions of relativistic electrons in Earth's radiation belts

NASA Astrophysics Data System (ADS)

Turner, D. L.; Claudepierre, S. G.; O'Brien, T. P., III; Fennell, J. F.; Blake, J. B.; Baker, D. N.; Jaynes, A. N.; Morley, S.; Geoffrey, R.

2015-12-01

Earth's electron radiation belts consist of toroidal zones in near-Earth space characterized by intense levels of relativistic electrons with distinct energy-dependent boundaries. It has been known for decades that the outer electron radiation belt is highly variable, with electron intensities varying by orders of magnitude on timescales ranging from minutes to years. Now, we are gaining much insight into the nature of this extreme variability thanks to the unprecedented number of observatories capable of measuring radiation belt electrons, the most recent of which is NASA's Van Allen Probes mission. In this presentation, we analyze and review several of the most extreme events observed in Earth's outer radiation belt. We begin with very sudden and strong enhancements of the outer radiation belt that can result in several orders of magnitude enhancements of electron intensities up to several MeV that sometimes occur in less than one day. We compare and contrast two of the most extreme cases of sudden and strong enhancements from the Van Allen Probes era, 08-09 October 2012 and 17-18 March 2015, and review evidence of the dominant acceleration mechanism in each event. Sudden enhancements of the radiation belts can also occur from injections by interplanetary shocks impacting the magnetosphere, such as occurred on 24 March 1991. We compare shock characteristics from previous injection events to those from the Van Allen Probes era to investigate why none of the interplanetary shocks since September 2012 have caused MeV electron injections into the slot region and inner radiation belt, which has surprisingly been devoid of measurable quantities of >~1 MeV electrons throughout the Van Allen Probes era. Our last topic concerns loss processes. We discuss drastic loss events, known as "flux dropouts", and present evidence that these loss events can eliminate the vast majority of relativistic electrons in the outer radiation belt on time scales of only a few hours. We finish with cases of prolonged outer belt depletions, such as occurred throughout most of 2009 and in September 2014, and discuss how these can result from flux dropout events combined with a subsequent lack of any source of new relativistic electrons.

FE K EMISSION AND ABSORPTION FEATURES IN THE XMM-EPIC SPECTRUM OF THE SEYFERT GALAXY IC 4329A

NASA Technical Reports Server (NTRS)

Markowitz, A.; Reeves, J. N.; Braito, V.

2001-01-01

We present a re-analysis of the XMM-Newton long-look of the X-ray bright Seyfert galaxy IC 4329a. The Fe K bandpass is dominated by two peaks, consistent with emission from neutral or near-neutral Fe Ka and KP. A relativistic diskline model whereby both peaks are the result of one doubly-peaked diskline profile is found to be a poor description of the data. Models using two relativistic disklines are found to describe the emission profile well. A low-inclination, moderately-relativistic dual-diskline model is possible if the contribution from narrow components, due to distant material, is small or absent. A high-inclination, moderately relativistic profile for each peak is possible if there are roughly equal contributions from both the broad and narrow components. Upper limits on Fe XXV and Fe XXVI emission and absorption at the systemic velocity of IC 4329a are obtained. We also present the results of RXTE monitoring of this source obtained so far; the combined XMM-Newton and RXTE data sets allow us to explore the time-resolved spectral behavior of this source on time scales ranging from hours to 2 years. We find no strong evidence for variability of the Fe Ka emission line on any time scale probed, likely due to the minimal level of continuum variability. We detect a narrow absorption line, at a energy of 7.68 keV in the rest frame of the source; its significance has been confirmed using Monte Carlo simulations. This feature is most likely due to absorption from Fe XXVI blueshifted to approximately 0.1c relative to the systemic velocity, making IC 4329a the lowest-redshift AGN known with a high-velocity, highly-ionized outflow component. As is often the case with similar outflows seen in high-luminosity quasars, the estimated mass outflow rate is larger than the inflow accretion rate, signaling that the outflow represents a substantial portion of the total energy budget of the AGN. The outflow could arise from a radiatively-driven disk wind, or it may be in the form of a discrete, transient blob of ejected material.

Gravity, black holes, and the universe

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nicolson, I.

1981-01-01

The book treats current understandings of the nature and properties of gravity, with particular emphasis on its role in the physics of black holes and the structure and evolution of the universe as a whole. The development of modern ideas on force, motion and gravity is traced from the systems of Aristotle and Ptolemy through the work of Copernicus, Galileo and Kepler to Newton's law of universal gravitation and Einstein's general theory of relativity. Particular attention is then given to the role of gravity in stellar motions and to the phenomena determined by the immense gravitational forces associated with bodiesmore » of such great density, including relativistic effects, tidal forces, space-time effects, event horizons, rotation, mass and electrical charge, the existence of naked singularities and white holes, and black-hole thermodynamics. The existence of actual black holes in the universe is considered, and various black-hole candidates in the Galaxy, quasars and galactic nuclei are indicated. The role of gravity in cosmology is then examined, with attention given to the implications of general relativity, the Hubble law, the age of the universe, the density of the universe and its eventual fate. Possible alternative to general relativity as a theory of gravitation are considered, including theories of variable gravitational constant, grand unified theories, and quantum gravity.« less

Gravity, black holes and the universe

NASA Astrophysics Data System (ADS)

Nicolson, I.

The book treats current understandings of the nature and properties of gravity, with particular emphasis on its role in the physics of black holes and the structure and evolution of the universe as a whole. The development of modern ideas on force, motion and gravity is traced from the systems of Aristotle and Ptolemy through the work of Copernicus, Galileo and Kepler to Newton's law of universal gravitation and Einstein's general theory of relativity. Particular attention is then given to the role of gravity in stellar motions and to the phenomena determined by the immense gravitational forces associated with bodies of such great density, including relativistic effects, tidal forces, space-time effects, event horizons, rotation, mass and electrical charge, the existence of naked singularities and white holes, and black-hole thermodynamics. The existence of actual black holes in the universe is considered, and various black-hole candidates in the Galaxy, quasars and galactic nuclei are indicated. The role of gravity in cosmology is then examined, with attention given to the implications of general relativity, the Hubble law, the age of the universe, the density of the universe and its eventual fate. Possible alternative to general relativity as a theory of gravitation are considered, including theories of variable gravitational constant, grand unified theories, and quantum gravity.

ON THE EVOLUTION OF THE INNER DISK RADIUS WITH FLUX IN THE NEUTRON STAR LOW-MASS X-RAY BINARY SERPENS X-1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chiang, Chia-Ying; Morgan, Robert A.; Cackett, Edward M.

We analyze the latest Suzaku observation of the bright neutron star (NS) low-mass X-ray binary Serpens X-1 taken in 2013 October and 2014 April. The observation was taken using the burst mode and only suffered mild pile-up effects. A broad iron line is clearly detected in the X-ray spectrum. We test different models and find that the iron line is asymmetric and best interpreted by relativistic reflection. The relativistically broadened iron line is generally believed to originate from the innermost regions of the accretion disk, where strong gravity causes a series of special and general relativistic effects. The iron linemore » profile indicates an inner radius of ∼8 R {sub G}, which gives an upper limit on the size of the NS. The asymmetric iron line has been observed in a number of previous observations, which gives several inner radius measurements at different flux states. We find that the inner radius of Serpens X-1 does not evolve significantly over the range of L / L {sub Edd} ∼ 0.4–0.6, and the lack of flux dependence of the inner radius implies that the accretion disk may be truncated outside of the innermost stable circular orbit by the boundary layer, rather than the stellar magnetic field.« less

On the Evolution of the Inner Disk Radius with Flux in the Neutron Star Low-mass X-Ray Binary Serpens X-1

NASA Technical Reports Server (NTRS)

Chiang, Chia - Ying; Morgan, Robert A.; Cackett, Edward M.; Miller, Jon M.; Bhattacharyya, Sudip; Strohmayer, Tod E.

2016-01-01

We analyze the latest Suzaku observation of the bright neutron star (NS) low-mass X-ray binary Serpens X-1 taken in 2013 October and 2014 April. The observation was taken using the burst mode and only suffered mild pile-up effects. A broad iron line is clearly detected in the X-ray spectrum. We test different models and find that the iron line is asymmetric and best interpreted by relativistic reflection. The relativistically broadened iron line is generally believed to originate from the innermost regions of the accretion disk, where strong gravity causes a series of special and general relativistic effects. The iron line profile indicates an inner radius of approx. 8 R(sub G), which gives an upper limit on the size of the NS. The asymmetric iron line has been observed in a number of previous observations, which gives several inner radius measurements at different flux states. We find that the inner radius of Serpens X-1 does not evolve significantly over the range of L/L(sub Edd) approx. 0.4-0.6, and the lack of flux dependence of the inner radius implies that the accretion disk may be truncated outside of the innermost stable circular orbit by the boundary layer, rather than the stellar magnetic field.

The Discovery of Gravitational Repulsion by Johannes Droste

NASA Astrophysics Data System (ADS)

McGruder, Charles Hosewell; VanDerMeer, B. Wieb

2018-01-01

In 1687 Newton published his universal law of gravitation, which states that the gravitational force is always attractive. This law is based on our terrestrial experience with slowly moving bodies (v << c). In 1915 Einstein completed his theory of general relativity (also referred to as Einstein’s Theory of Gravitation), which is valid not just for slowly moving bodies but also for those with relativistic velocities. In 1916 Johannes Droste submitted a PhD thesis on general relativity to his advisor, H.A. Lorentz. In it he calculated the motion of a particle in what he called a “single center” and today we call the Schwarzschild field and found that highly relativistic particles experience gravitational repulsion. Thus, his thesis written in Dutch and never before translated contains the discovery of gravitational repulsion. Because of its historical importance we translate the entire section of his thesis containing the discovery of gravitational repulsion. We also translate his thesis in the hope of clearing up a major historical misconception. Namely, that David Hilbert in 1917 discovered gravitational repulsion. In fact, Hilbert rediscovered it, apparently completely independent of Droste’s work. Finally we note that one of the biggest mysteries of astrophysics is the question of how highly energetic particles in relativistic jets and cosmic rays are accelerated. It has been suggested that gravitational repulsion is the mechanism responsible for these phenomena. An historical understanding of gravitational repulsion is therefore pertinent.

Observational Signatures of Mass-loading in Jets Launched by Rotating Black Holes

NASA Astrophysics Data System (ADS)

O’ Riordan, Michael; Pe’er, Asaf; McKinney, Jonathan C.

2018-01-01

It is widely believed that relativistic jets in X-ray binaries (XRBs) and active-galactic nuclei are powered by the rotational energy of black holes. This idea is supported by general-relativistic magnetohydrodynamic (GRMHD) simulations of accreting black holes, which demonstrate efficient energy extraction via the Blandford–Znajek mechanism. However, due to uncertainties in the physics of mass loading, and the failure of GRMHD numerical schemes in the highly magnetized funnel region, the matter content of the jet remains poorly constrained. We investigate the observational signatures of mass loading in the funnel by performing general-relativistic radiative transfer calculations on a range of 3D GRMHD simulations of accreting black holes. We find significant observational differences between cases in which the funnel is empty and cases where the funnel is filled with plasma, particularly in the optical and X-ray bands. In the context of Sgr A*, current spectral data constrains the jet filling only if the black hole is rapidly rotating with a ≳ 0.9. In this case, the limits on the infrared flux disfavor a strong contribution from material in the funnel. We comment on the implications of our models for interpreting future Event Horizon Telescope observations. We also scale our models to stellar-mass black holes, and discuss their applicability to the low-luminosity state in XRBs.

Electronic structure and dissociation curves for the ground states of Tl/sub 2/ and Tl/sub 2//sup +/ from relativistic effective potential calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christiansen, P.A.; Pitzer, K.S.

The dissociation curves for the ground states of Tl/sub 2/ and Tl/sub 2//sup +/ were computed using a generalization of the molecular relativistic ..omega..--..omega.. coupling formalism of Lee, Ermler, and Pitzer. Relativistic effects, as represented by the Dirac equation, were introduced using effective potentials generated from atomic Dirac--nFock wave functions using a generalization of the improved effective potential formulation of Christiansen, Lee, and Pitzer. Our calculations show that the ground state of Tl/sub 2//sup +/ is 1/2/sub g/ with computed D/sub e/ and R/sub e/ values of 0.58 eV and 3.84 A. For Tl/sub 2/ we find that the groundmore » state is 0/sub u//sup -/ but the 0/sub g//sup +/ and the 1/sub u/ states are only slightly higher in energy; the potential curves for these states are repulsive to about 3.5 A and then essentially flat beyond that radius. While corrections for correlation will increase D/sub e/ somewhat, Tl/sub 2/ is only weakly bound in any of these states which dissociate to normal atoms. The cause is undoubtedly related to the large spin-orbit splitting between the 6p/sub 1/2/ and 6p/sub 3/2/ thallium spinors.« less

Radiative, two-temperature simulations of low-luminosity black hole accretion flows in general relativity

NASA Astrophysics Data System (ADS)

Sądowski, Aleksander; Wielgus, Maciek; Narayan, Ramesh; Abarca, David; McKinney, Jonathan C.; Chael, Andrew

2017-04-01

We present a numerical method that evolves a two-temperature, magnetized, radiative, accretion flow around a black hole, within the framework of general relativistic radiation magnetohydrodynamics. As implemented in the code KORAL, the gas consists of two sub-components - ions and electrons - which share the same dynamics but experience independent, relativistically consistent, thermodynamical evolution. The electrons and ions are heated independently according to a prescription from the literature for magnetohydrodynamical turbulent dissipation. Energy exchange between the particle species via Coulomb collisions is included. In addition, electrons gain and lose energy and momentum by absorbing and emitting synchrotron and bremsstrahlung radiation and through Compton scattering. All evolution equations are handled within a fully covariant framework in the relativistic fixed-metric space-time of the black hole. Numerical results are presented for five models of low-luminosity black hole accretion. In the case of a model with a mass accretion rate dot{M}˜ 4× 10^{-8} dot{M}_Edd, we find that radiation has a negligible effect on either the dynamics or the thermodynamics of the accreting gas. In contrast, a model with a larger dot{M}˜ 4× 10^{-4} dot{M}_Edd behaves very differently. The accreting gas is much cooler and the flow is geometrically less thick, though it is not quite a thin accretion disc.

The Expanding Universe and the Large-Scale Geometry of Spacetime.

ERIC Educational Resources Information Center

Shu, Frank

1983-01-01

Presents a condensed version of textbook account of cosmological theory and principles. Topics discussed include quasars, general and special relativity, relativistic cosmology, and the curvature of spacetime. Some philosophical assumptions necessary to the theory are also discussed. (JM)

Synchro-Curvature Radiation of Charged Particles in the Strong Curved Magnetic Fields

NASA Astrophysics Data System (ADS)

Kelner, S. R.; Prosekin, A. Yu.; Aharonian, F. A.

2015-01-01

It is generally believed that the radiation of relativistic particles in a curved magnetic field proceeds in either the synchrotron or the curvature radiation modes. In this paper we show that in strong curved magnetic fields a significant fraction of the energy of relativistic electrons can be radiated away in the intermediate, the so-called synchro-curvature regime. Because of the persistent change of the trajectory curvature, the radiation varies with the frequency of particle gyration. While this effect can be ignored in the synchrotron and curvature regimes, the variability plays a key role in the formation of the synchro-curvature radiation. Using the Hamiltonian formalism, we find that the particle trajectory has the form of a helix wound around the drift trajectory. This allows us to calculate analytically the intensity and energy distribution of prompt radiation in the general case of magnetic bremsstrahlung in the curved magnetic field. We show that the transition to the limit of the synchrotron and curvature radiation regimes is determined by the relation between the drift velocity and the component of the particle velocity perpendicular to the drift trajectory. The detailed numerical calculations, which take into account the energy losses of particles, confirm the principal conclusions based on the simplified analytical treatment of the problem, and allow us to analyze quantitatively the transition between different radiation regimes for a broad range of initial pitch angles. These calculations demonstrate that even very small pitch angles may lead to significant deviations from the spectrum of the standard curvature radiation when it is formally assumed that a charged particle moves strictly along the magnetic line. We argue that in the case of realization of specific configurations of the electric and magnetic fields, the gamma-ray emission of the pulsar magnetospheres can be dominated by the component radiated in the synchro-curvature regime.

Synchro-curvature radiation of charged particles in the strong curved magnetic fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kelner, S. R.; Prosekin, A. Yu.; Aharonian, F. A., E-mail: Stanislav.Kelner@mpi-hd.mpg.de, E-mail: Anton.Prosekin@mpi-hd.mpg.de, E-mail: Felix.Aharonian@mpi-hd.mpg.de

It is generally believed that the radiation of relativistic particles in a curved magnetic field proceeds in either the synchrotron or the curvature radiation modes. In this paper we show that in strong curved magnetic fields a significant fraction of the energy of relativistic electrons can be radiated away in the intermediate, the so-called synchro-curvature regime. Because of the persistent change of the trajectory curvature, the radiation varies with the frequency of particle gyration. While this effect can be ignored in the synchrotron and curvature regimes, the variability plays a key role in the formation of the synchro-curvature radiation. Usingmore » the Hamiltonian formalism, we find that the particle trajectory has the form of a helix wound around the drift trajectory. This allows us to calculate analytically the intensity and energy distribution of prompt radiation in the general case of magnetic bremsstrahlung in the curved magnetic field. We show that the transition to the limit of the synchrotron and curvature radiation regimes is determined by the relation between the drift velocity and the component of the particle velocity perpendicular to the drift trajectory. The detailed numerical calculations, which take into account the energy losses of particles, confirm the principal conclusions based on the simplified analytical treatment of the problem, and allow us to analyze quantitatively the transition between different radiation regimes for a broad range of initial pitch angles. These calculations demonstrate that even very small pitch angles may lead to significant deviations from the spectrum of the standard curvature radiation when it is formally assumed that a charged particle moves strictly along the magnetic line. We argue that in the case of realization of specific configurations of the electric and magnetic fields, the gamma-ray emission of the pulsar magnetospheres can be dominated by the component radiated in the synchro-curvature regime.« less

Fast and Slow Precession of Gaseous Debris Disks around Planet-accreting White Dwarfs

NASA Astrophysics Data System (ADS)

Miranda, Ryan; Rafikov, Roman R.

2018-04-01

Spectroscopic observations of some metal-rich white dwarfs (WDs), believed to be polluted by planetary material, reveal the presence of compact gaseous metallic disks orbiting them. The observed variability of asymmetric, double-peaked emission-line profiles in about half of such systems could be interpreted as the signature of precession of an eccentric gaseous debris disk. The variability timescales—from decades down to 1.4 year (recently inferred for the debris disk around HE 1349–2305)—are in rough agreement with the rate of general relativistic (GR) precession in the test-particle limit. However, it has not been demonstrated that this mechanism can drive such a fast, coherent precession of a radially extended (out to 1 {R}ȯ ) gaseous disk mediated by internal stresses (pressure). Here, we use the linear theory of eccentricity evolution in hydrodynamic disks to determine several key properties of eccentric modes in gaseous debris disks around WDs. We find a critical dependence of both the precession period and radial eccentricity distribution of the modes on the inner disk radius, r in. For small inner radii, {r}in}≲ (0.2{--}0.4) {R}ȯ , the modes are GR-driven, with periods of ≈1–10 year. For {r}in}≳ (0.2{--}0.4) {R}ȯ , the modes are pressure dominated, with periods of ≈3–20 year. Correspondence between the variability periods and inferred inner radii of the observed disks is in general agreement with this trend. In particular, the short period of HE 1349–2305 is consistent with its small r in. Circum-WD debris disks may thus serve as natural laboratories for studying the evolution of eccentric gaseous disks.

Imaging an Event Horizon: Mitigation of Source Variability of Sagittarius A*

NASA Astrophysics Data System (ADS)

Lu, Ru-Sen; Roelofs, Freek; Fish, Vincent L.; Shiokawa, Hotaka; Doeleman, Sheperd S.; Gammie, Charles F.; Falcke, Heino; Krichbaum, Thomas P.; Zensus, J. Anton

2016-02-01

The black hole in the center of the Galaxy, associated with the compact source Sagittarius A* (Sgr A*), is predicted to cast a shadow upon the emission of the surrounding plasma flow, which encodes the influence of general relativity (GR) in the strong-field regime. The Event Horizon Telescope (EHT) is a Very Long Baseline Interferometry (VLBI) network with a goal of imaging nearby supermassive black holes (in particular Sgr A* and M87) with angular resolution sufficient to observe strong gravity effects near the event horizon. General relativistic magnetohydrodynamic (GRMHD) simulations show that radio emission from Sgr A* exhibits variability on timescales of minutes, much shorter than the duration of a typical VLBI imaging experiment, which usually takes several hours. A changing source structure during the observations, however, violates one of the basic assumptions needed for aperture synthesis in radio interferometry imaging to work. By simulating realistic EHT observations of a model movie of Sgr A*, we demonstrate that an image of the average quiescent emission, featuring the characteristic black hole shadow and photon ring predicted by GR, can nonetheless be obtained by observing over multiple days and subsequent processing of the visibilities (scaling, averaging, and smoothing) before imaging. Moreover, it is shown that this procedure can be combined with an existing method to mitigate the effects of interstellar scattering. Taken together, these techniques allow the black hole shadow in the Galactic center to be recovered on the reconstructed image.

The Soft State of Cygnus X-1 Observed with NuSTAR: A Variable Corona and a Stable Inner Disk

NASA Technical Reports Server (NTRS)

Walton, D. J.; Tomsick, J. A.; Madsen, K. K.; Grinberg, V.; Barret, D.; Boggs, S. E.; Christensen, F. E.; Clavel, M.; Craig, W. W.; Fabian, A. C.;

The Soft State of Cygnus X-1 Observed with NuSTAR: A Variable Corona and a Stable Inner Disk

NASA Astrophysics Data System (ADS)

Walton, D. J.; Tomsick, J. A.; Madsen, K. K.; Grinberg, V.; Barret, D.; Boggs, S. E.; Christensen, F. E.; Clavel, M.; Craig, W. W.; Fabian, A. C.; Fuerst, F.; Hailey, C. J.; Harrison, F. A.; Miller, J. M.; Parker, M. L.; Rahoui, F.; Stern, D.; Tao, L.; Wilms, J.; Zhang, W.

2016-07-01

We present a multi-epoch hard X-ray analysis of Cygnus X-1 in its soft state based on four observations with the Nuclear Spectroscopic Telescope Array (NuSTAR). Despite the basic similarity of the observed spectra, there is clear spectral variability between epochs. To investigate this variability, we construct a model incorporating both the standard disk-corona continuum and relativistic reflection from the accretion disk, based on prior work on Cygnus X-1, and apply this model to each epoch independently. We find excellent consistency for the black hole spin and the iron abundance of the accretion disk, which are expected to remain constant on observational timescales. In particular, we confirm that Cygnus X-1 hosts a rapidly rotating black hole, 0.93≲ {a}* ≲ 0.96, in broad agreement with the majority of prior studies of the relativistic disk reflection and constraints on the spin obtained through studies of the thermal accretion disk continuum. Our work also confirms the apparent misalignment between the inner disk and the orbital plane of the binary system reported previously, finding the magnitude of this warp to be ˜10°-15°. This level of misalignment does not significantly change (and may even improve) the agreement between our reflection results and the thermal continuum results regarding the black hole spin. The spectral variability observed by NuSTAR is dominated by the primary continuum, implying variability in the temperature of the scattering electron plasma. Finally, we consistently observe absorption from ionized iron at ˜6.7 keV, which varies in strength as a function of orbital phase in a manner consistent with the absorbing material being an ionized phase of the focused stellar wind from the supergiant companion star.

Quasi-radial modes of rotating stars in general relativity

NASA Astrophysics Data System (ADS)

Yoshida, Shin'ichirou; Eriguchi, Yoshiharu

2001-04-01

By using the Cowling approximation, quasi-radial modes of rotating general relativistic stars are computed along equilibrium sequences from non-rotating to maximally rotating models. The eigenfrequencies of these modes are decreasing functions of the rotational frequency. The eigenfrequency curve of each mode as a function of the rotational frequency has discontinuities, which arise from the avoided crossing with other curves of axisymmetric modes.

Moments of inertia of relativistic magnetized stars

NASA Astrophysics Data System (ADS)

Konno, K.

2001-06-01

We consider principal moments of inertia of axisymmetric, magnetically deformed stars in the context of general relativity. The general expression for the moment of inertia with respect to the symmetric axis is obtained. The numerical estimates are derived for several polytropic stellar models. We find that the values of the principal moments of inertia are modified by a factor of 2 at most from Newtonian estimates.

Blazars: The accelerating inner jet model.

NASA Astrophysics Data System (ADS)

Georganopoulos, M.; Marscher, A. P.

1996-05-01

The standard interpretation of the nonthermal continuum radiation of blazars from radio to gamma -rays is thought to be synchrotron and inverse Compton radiation from a relativistic jet. The inner jet of a blazar is the section of the jet that connects the central engine with the VLBI core of the radio jet. This is a small (la 1 pc) region where the jet is formed, collimated and accelerated to speeds close to that of light. In the accelerating inner jet model ultrarelativistic plasma is generated continuously near the central engine of the AGN and is accelerated hydrodynamically. An external hydrostatic and/or magnetohydrodynamic pressure collimates the flow. In this work a simple relativistic hydrodynamic scheme that produces a simultaneously accelerating and converging flow is coupled with a detailed calculation of the evolution of the electron energy distribution and synchrotron emissivity due to relativistic electrons radiating in a mostly random magnetic field. Higher frequency radiation emanates from smaller distances from the central engine, implying shorter flux variation timescales at higher frequencies, as observed. The velocity of the jet increases with distance; this implies larger Doppler boosting for greater distances down the jet up to the point where the Lorentz factor Gamma la theta (-1) , where theta is the angle between the velocity vector and the line of sight, and therefore at lower frequencies. This can explain some of the differences between RBLs and XBLs as a line-of-sight orientation effect. A square density wave is propagated with the jet velocity and the variability thus induced is studied, taking into account time delay effects. The model is found to agree qualitatively with the observed steady state spectra as well as with the observed variability properties of BL Lac objects.

Nanomodulated electron beams via electron diffraction and emittance exchange for coherent x-ray generation

DOE PAGES

Nanni, E. A.; Graves, W. S.; Moncton, D. E.

2018-01-19

We present a new method for generation of relativistic electron beams with current modulation on the nanometer scale and below. The current modulation is produced by diffracting relativistic electrons in single crystal Si, accelerating the diffracted beam and imaging the crystal structure, then transferring the image into the temporal dimension via emittance exchange. The modulation period can be tuned by adjusting electron optics after diffraction. This tunable longitudinal modulation can have a period as short as a few angstroms, enabling production of coherent hard x-rays from a source based on inverse Compton scattering with total accelerator length of approximately tenmore » meters. Electron beam simulations from cathode emission through diffraction, acceleration, and image formation with variable magnification are presented along with estimates of the coherent x-ray output properties.« less

BRST technique for the cosmological density matrix

NASA Astrophysics Data System (ADS)

Barvinsky, A. O.

2013-10-01

The microcanonical density matrix in closed cosmology has a natural definition as a projector on the space of solutions of Wheeler-DeWitt equations, which is motivated by the absence of global non-vanishing charges and energy in spatially closed gravitational systems. Using the BRST/BFV formalism in relativistic phase space of gauge and ghost variables we derive the path integral representation for this projector and the relevant statistical sum. This derivation circumvents the difficulties associated with the open algebra of noncommutative quantum Dirac constraints and the construction/regularization of the physical inner product in the subspace of BRS singlets. This inner product is achieved via the Batalin-Marnelius gauge fixing in the space of BRS-invariant states, which in its turn is shown to be a result of truncation of the BRST/BFV formalism to the "matter" sector of relativistic phase space.

Nanomodulated electron beams via electron diffraction and emittance exchange for coherent x-ray generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nanni, E. A.; Graves, W. S.; Moncton, D. E.

We present a new method for generation of relativistic electron beams with current modulation on the nanometer scale and below. The current modulation is produced by diffracting relativistic electrons in single crystal Si, accelerating the diffracted beam and imaging the crystal structure, then transferring the image into the temporal dimension via emittance exchange. The modulation period can be tuned by adjusting electron optics after diffraction. This tunable longitudinal modulation can have a period as short as a few angstroms, enabling production of coherent hard x-rays from a source based on inverse Compton scattering with total accelerator length of approximately tenmore » meters. Electron beam simulations from cathode emission through diffraction, acceleration, and image formation with variable magnification are presented along with estimates of the coherent x-ray output properties.« less

Dispersion characteristics of anisotropic unmagnetized ultra-relativistic transverse plasma wave with arbitrary electron degeneracy

NASA Astrophysics Data System (ADS)

Sarfraz, M.; Farooq, H.; Abbas, G.; Noureen, S.; Iqbal, Z.; Rasheed, A.

2018-03-01

Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (T/e TF e ≈1 ) comprising arbitrary electron degeneracy, where Te and TF e, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-07-01

The study of the electrodynamics of static, axisymmetric, and force-free Kerr magnetospheres relies vastly on solutions of the so-called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give a detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established set-ups (split-monopole, paraboloidal, BH disc, uniform).

Efficiencies for production of atomic nitrogen and oxygen by relativistic proton impact in air

NASA Technical Reports Server (NTRS)

Porter, H. S.; Jackman, C. H.; Green, A. E. S.

1976-01-01

Relativistic electron and proton impact cross sections are obtained and represented by analytic forms which span the energy range from threshold to 1 GeV. For ionization processes, the Massey-Mohr continuum generalized oscillator strength surface is parameterized. Parameters are determined by simultaneous fitting to (1) empirical data, (2) the Bethe sum rule, and (3) doubly differential cross sections for ionization. Branching ratios for dissociation and predissociation from important states of N2 and O2 are determined. The efficiency for the production of atomic nitrogen and oxygen by protons with kinetic energy less than 1 GeV is determined using these branching ratio and cross section assignments.

New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

NASA Astrophysics Data System (ADS)

Csörgő, Tamás; Kasza, Gábor; Csanád, Máté; Jiang, Zefang

2018-06-01

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables like the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton-proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa-Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

Numerically solving the relativistic Grad-Shafranov equation in Kerr spacetimes: Numerical techniques

NASA Astrophysics Data System (ADS)

Mahlmann, J. F.; Cerdá-Durán, P.; Aloy, M. A.

2018-04-01

The study of the electrodynamics of static, axisymmetric and force-free Kerr magnetospheres relies vastly on solutions of the so called relativistic Grad-Shafranov equation (GSE). Different numerical approaches to the solution of the GSE have been introduced in the literature, but none of them has been fully assessed from the numerical point of view in terms of efficiency and quality of the solutions found. We present a generalization of these algorithms and give detailed background on the algorithmic implementation. We assess the numerical stability of the implemented algorithms and quantify the convergence of the presented methodology for the most established setups (split-monopole, paraboloidal, BH-disk, uniform).

The PLUTO code for astrophysical gasdynamics .

NASA Astrophysics Data System (ADS)

Mignone, A.

Present numerical codes appeal to a consolidated theory based on finite difference and Godunov-type schemes. In this context we have developed a versatile numerical code, PLUTO, suitable for the solution of high-mach number flow in 1, 2 and 3 spatial dimensions and different systems of coordinates. Different hydrodynamic modules and algorithms may be independently selected to properly describe Newtonian, relativistic, MHD, or relativistic MHD fluids. The modular structure exploits a general framework for integrating a system of conservation laws, built on modern Godunov-type shock-capturing schemes. The code is freely distributed under the GNU public license and it is available for download to the astrophysical community at the URL http://plutocode.to.astro.it.

On the relativistic large-angle electron collision operator for runaway avalanches in plasmas

NASA Astrophysics Data System (ADS)

Embréus, O.; Stahl, A.; Fülöp, T.

2018-02-01

Large-angle Coulomb collisions lead to an avalanching generation of runaway electrons in a plasma. We present the first fully conservative large-angle collision operator, derived from the relativistic Boltzmann operator. The relation to previous models for large-angle collisions is investigated, and their validity assessed. We present a form of the generalized collision operator which is suitable for implementation in a numerical kinetic equation solver, and demonstrate the effect on the runaway-electron growth rate. Finally we consider the reverse avalanche effect, where runaways are slowed down by large-angle collisions, and show that the choice of operator is important if the electric field is close to the avalanche threshold.

The influence of orbit selection on the accuracy of the Stanford Relativity gyroscope experiment

NASA Technical Reports Server (NTRS)

Vassar, R.; Everitt, C. W. F.; Vanpatten, R. A.; Breakwell, J. V.

1980-01-01

This paper discusses an error analysis for the Stanford Relativity experiment, designed to measure the precession of a gyroscope's spin-axis predicted by general relativity. Measurements will be made of the spin-axis orientations of 4 superconducting spherical gyroscopes carried by an earth-satellite. Two relativistic precessions are predicted: a 'geodetic' precession associated with the satellite's orbital motion and a 'motional' precession due to the earth's rotation. Using a Kalman filter covariance analysis with a realistic error model we have computed the error in determining the relativistic precession rates. Studies show that a slightly off-polar orbit is better than a polar orbit for determining the 'motional' drift.

Pulsar Emission: Is It All Relative?

NASA Technical Reports Server (NTRS)

Harding, Alice K.

2004-01-01

Thirty-five years after the discovery of pulsars, we still do not understand the fundamentals of their pulsed emission at any wavelength. The fact that even detailed pulse profiles cannot identlfy the origin of the emission in a magnetosphere that extends fiom the neutron star surface to plasma moving at relativistic speeds near the light cylinder compounds the problem. I will discuss the role of special and general relativistic effects on pulsar emission, fiom inertial frame-dragging near the stellar surface to aberration, time-of-flight and retardation of the magnetic field near the light cylinder. Understanding how these effects determine what we observe at different wavelengths is critical to unraveling the emission physics.

Binary collision rates of relativistic thermal plasmas. I Theoretical framework

NASA Technical Reports Server (NTRS)

Dermer, C. D.

1985-01-01

Binary collision rates for arbitrary scattering cross sections are derived in the case of a beam of particles interacting with a Maxwell-Boltzmann (MB) plasma, or in the case of two MB plasmas interacting at generally different temperatures. The expressions are valid for all beam energies and plasma temperatures, from the nonrelativistic to the extreme relativistic limits. The calculated quantities include the reaction rate, the energy exchange rate, and the average rate of change of the squared transverse momentum component of a monoenergetic particle beam as a result of scatterings with particles of a MB plasma. Results are specialized to elastic scattering processes, two-temperature reaction rates, or the cold plasma limit, reproducing previous work.

Radio and X-ray variability of the nucleus of Centaurus A /NGC 5128/

NASA Technical Reports Server (NTRS)

Beall, J. H.; Rose, W. K.; Graf, W.; Price, K. M.; Dent, W. A.; Hobbs, R. W.; Dennis, B. R.; Crannell, C. J.; Conklin, E. K.; Ulich, B. L.

1978-01-01

Centaurus A (NGC 5128) has been observed at radio frequencies of 10.7, 31.4, 85.2, and 89 GHz and at X-ray energies greater than 20 keV. These observations, together with results reported by other workers, are interpreted in terms of models of the nucleus of this radio galaxy. The radio observations cover the period from 1973 through early 1977. The X-ray observations cover two 10-day intervals, one in July and August (1975) and the other in July and August 1976. The source exhibits significant variability in all the observed radio frequencies. The observed radio and X-ray intensities show some concurrent variations but do not track one another throughout the observations. A model of the source in which X-rays are produced by inverse Compton scattering of blackbody photons by relativistic electrons is proposed to explain these observations. The observed variations in the electromagnetic spectrum are shown to be consistent with adiabatic expansion of a trapped plasma in conjunction with turbulent accelerations of the relativistic electrons. Upper limits obtained with the model indicate that there may be sufficient energy available in the nucleus to form radio lobes with the same total energy as those already present.

A Long Look at MCG-5-23-16 with NuSTAR . I. Relativistic Reflection and Coronal Properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zoghbi, Abderahmen; Miller, J. M.; Matt, G.

MCG-5-23-16 was targeted in early 2015 with a half mega-second observing campaign using NuSTAR . Here we present the spectral analysis of these data sets along with an earlier observation and study the relativistic reflection and the primary coronal source. The data show strong reflection features in the form of both narrow and broad iron lines plus a Compton reflection hump. A cutoff energy is significantly detected in all exposures. The shape of the reflection spectrum does not change in the two years spanned by the observations, suggesting a stable geometry. A strong positive correlation is found between the cutoffmore » energy and both the hard X-ray flux and spectral index. The measurements imply that the coronal plasma is not at the runaway electron–positron pair limit, and instead contains mostly electrons. The observed variability in the coronal properties is driven by a variable optical depth. A constant heating-to-cooling ratio is measured, implying that there is a feedback mechanism in which a significant fraction of the photons cooling the corona are due to reprocessed hard X-rays.« less

A Long Look at MCG-5-23-16 with NuSTAR. I. Relativistic Reflection and Coronal Properties

NASA Technical Reports Server (NTRS)

Zoghbi, Abderahmen; Matt, G.; Miller, J. M.; Lohfink, A. M.; Walton, D. J.; Ballantyne, D. R.; Garcia, J. A.; Stern, D.; Koss, M. J.; Farrah, D.;

ON THE ORIGIN OF THE {gamma}-RAY/OPTICAL LAGS IN LUMINOUS BLAZARS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Janiak, Mateusz; Sikora, Marek; Moderski, Rafal

2012-12-01

Blazars are strongly variable sources that occasionally show spectacular flares visible in various energy bands. These flares are often, but not always, correlated. In a number of cases, the peaks of optical flares are found to be somewhat delayed with respect to the {gamma}-ray peaks. One notable example of such a delay was found in 3C 279 by Hayashida et al. and interpreted as a result of steeper drop with a distance of the energy density of an external radiation field than of the magnetic energy density. In this paper, we demonstrate that, in general, depending on the respective energymore » density profile along the jet, such lags can have both signs and that they can take place for any ratio of these energy densities. We study the dependence of such lags on the ratio of these energy densities at a distance of a maximal energy dissipation in a jet, on their gradients, as well as on the time profile of the relativistic electron injection within the moving source. We show how prominent such lags can be, and their expected timescales. We suggest that studies of such lags can provide a powerful tool to resolve the structure of relativistic jets and their radiative environment. As an example we model the lag observed in 3C 279, showing that in this object the flare is produced at a distance of a few parsecs from the central black hole, consistent with our previous inferences based on the spectra and optical polarization properties.« less

On the relativistic micro-canonical ensemble and relativistic kinetic theory for N relativistic particles in inertial and non-inertial rest frames

NASA Astrophysics Data System (ADS)

Alba, David; Crater, Horace W.; Lusanna, Luca

2015-03-01

A new formulation of relativistic classical mechanics allows a reconsideration of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincaré generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonical ensemble in terms of the Galilei generators.

Empirical predictive models of daily relativistic electron flux at geostationary orbit: Multiple regression analysis

DOE PAGES

Simms, Laura E.; Engebretson, Mark J.; Pilipenko, Viacheslav; ...

2016-04-07

The daily maximum relativistic electron flux at geostationary orbit can be predicted well with a set of daily averaged predictor variables including previous day's flux, seed electron flux, solar wind velocity and number density, AE index, IMF Bz, Dst, and ULF and VLF wave power. As predictor variables are intercorrelated, we used multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Empirical models produced from regressions of flux on measured predictors from 1 day previous were reasonably effective at predicting novel observations. Adding previous flux to the parameter set improves the predictionmore » of the peak of the increases but delays its anticipation of an event. Previous day's solar wind number density and velocity, AE index, and ULF wave activity are the most significant explanatory variables; however, the AE index, measuring substorm processes, shows a negative correlation with flux when other parameters are controlled. This may be due to the triggering of electromagnetic ion cyclotron waves by substorms that cause electron precipitation. VLF waves show lower, but significant, influence. The combined effect of ULF and VLF waves shows a synergistic interaction, where each increases the influence of the other on flux enhancement. Correlations between observations and predictions for this 1 day lag model ranged from 0.71 to 0.89 (average: 0.78). Furthermore, a path analysis of correlations between predictors suggests that solar wind and IMF parameters affect flux through intermediate processes such as ring current ( Dst), AE, and wave activity.« less

Empirical predictive models of daily relativistic electron flux at geostationary orbit: Multiple regression analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Simms, Laura E.; Engebretson, Mark J.; Pilipenko, Viacheslav

The daily maximum relativistic electron flux at geostationary orbit can be predicted well with a set of daily averaged predictor variables including previous day's flux, seed electron flux, solar wind velocity and number density, AE index, IMF Bz, Dst, and ULF and VLF wave power. As predictor variables are intercorrelated, we used multiple regression analyses to determine which are the most predictive of flux when other variables are controlled. Empirical models produced from regressions of flux on measured predictors from 1 day previous were reasonably effective at predicting novel observations. Adding previous flux to the parameter set improves the predictionmore » of the peak of the increases but delays its anticipation of an event. Previous day's solar wind number density and velocity, AE index, and ULF wave activity are the most significant explanatory variables; however, the AE index, measuring substorm processes, shows a negative correlation with flux when other parameters are controlled. This may be due to the triggering of electromagnetic ion cyclotron waves by substorms that cause electron precipitation. VLF waves show lower, but significant, influence. The combined effect of ULF and VLF waves shows a synergistic interaction, where each increases the influence of the other on flux enhancement. Correlations between observations and predictions for this 1 day lag model ranged from 0.71 to 0.89 (average: 0.78). Furthermore, a path analysis of correlations between predictors suggests that solar wind and IMF parameters affect flux through intermediate processes such as ring current ( Dst), AE, and wave activity.« less

Eclipsing binary stars as tests of gravity theories - The apsidal motion of AS Camelopardalis

NASA Technical Reports Server (NTRS)

Maloney, Frank P.; Guinan, Edward F.; Boyd, Patricia T.

1989-01-01

AS Camelopardalis is an 8th-magnitude eclipsing binary that consists of two main-sequence (B8 V and a B9.5 V) components in an eccentric orbit (e = 0.17) with an orbital period of 3.43 days. Like the eccentric eclipsing system DI Herculis, and a few other systems, AS Cam is an important test case for studying relativistic apsidal motion. In these systems, the theoretical general relativistic apsidal motion is comparable to that expected from classical effects arising from tidal and rotational deformation of the stellar components. Accurate determinations of the orbital and stellar properties of AS Cam have been made by Hilditch (1972) and Khalliulin and Kozyreva (1983) that permit the theoretical relativistic and classical contributions to the apsidal motion to be determined reasonably well. All the published timings of primary and secondary minima have been gathered and supplemented with eclipse timings from 1899 to 1920 obtained from the Harvard plate collection. Least-squares solutions of the eclipse timings extending over an 80 yr interval yield a smaller than expected apsidal motion, in agreement with that found by Khalliulin and Kozyreva from a smaller set of data. The observed apsidal motion for AS Cam is about one-third that expected from the combined relativistic and classical effects. Thus, AS Cam joins DI Her in having an observed apsidal motion significantly less than that predicted from theory.

The 'Supercritical Pile' GRB Model: Afterglows and GRB, XRR, XRF Unification

NASA Technical Reports Server (NTRS)

Kazanas, D.

2007-01-01

We present the general notions and observational consequences of the "Supercritical Pile" GRB model; the fundamental feature of this model is a detailed process for the conversion of the energy stored in relativistic protons in the GRB Relativistic Blast Waves (RBW) into relativistic electrons and then into radiation. The conversion is effected through the $p \\, \\gamma \\rightarrow p \\, e circumflex + e circumflex -$ reaction, whose kinematic threshold is imprinted on the GRB spectra to provide a peak of their emitted luminosity at energy \\Ep $\\sim 1$ MeV in the lab frame. We extend this model to include, in addition to the (quasi--)thermal relativistic post-shock protons an accelerated component of power law form. This component guarantees the production of $e circumflex +e circumflex- - $pairs even after the RBW has slowed down to the point that its (quasi-) thermal protons cannot fulfill the threshold of the above reaction. We suggest that this last condition marks the transition from the prompt to the afterglow GRB phase. We also discuss conditions under which this transition is accompanied by a significant drop in the flux and could thus account for several puzzling, recent observations. Finally, we indicate that the same mechanism applied to the late stages of the GRB evolution leads to a decrease in \\Ep $\\propto \\Gamma circumflex 2(t)\\propto t circumflex {-3/4}$, a feature amenable to future observational tests.

General post-Minkowskian expansion and application of the phase function

NASA Astrophysics Data System (ADS)

Qin, Cheng-Gang; Shao, Cheng-Gang

2017-07-01

The phase function is a useful tool to study all observations of space missions, since it can give all the information about light propagation in a gravitational field. For the extreme accuracy of the modern space missions, a precise relativistic modeling of observations is required. So, we develop a recursive procedure enabling us to expand the phase function into a perturbative series of ascending powers of the Newtonian gravitational constant. Any n th-order perturbation of the phase function can be determined by the integral along the straight line connecting two point events. To illustrate the result, we carry out the calculation of the phase function outside a static, spherically symmetric body up to the order of G2. Then, we develop a precise relativistic model that is able to calculate the phase function and the derivatives of the phase function in the gravitational field of rotating and uniformly moving bodies. This model allows the computing of the Doppler, radio science, and astrometric observables of the space missions in the Solar System. With the development of space technology, the relativistic corrections due to the motion of a planet's spin must be considered in the high-precision space missions in the near future. As an example, we give the estimates of the relativistic corrections on the observables about the space missions TianQin and BEACON.

Relativistic chaos is coordinate invariant.

PubMed

Motter, Adilson E

2003-12-05

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

NASA Astrophysics Data System (ADS)

Na, D.-Y.; Moon, H.; Omelchenko, Y. A.; Teixeira, F. L.

2018-01-01

Accurate modeling of relativistic particle motion is essential for physical predictions in many problems involving vacuum electronic devices, particle accelerators, and relativistic plasmas. A local, explicit, and charge-conserving finite-element time-domain (FETD) particle-in-cell (PIC) algorithm for time-dependent (non-relativistic) Maxwell-Vlasov equations on irregular (unstructured) meshes was recently developed by Moon et al. [Comput. Phys. Commun. 194, 43 (2015); IEEE Trans. Plasma Sci. 44, 1353 (2016)]. Here, we extend this FETD-PIC algorithm to the relativistic regime by implementing and comparing three relativistic particle-pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

2D Relativistic MHD simulations of the Kruskal-Schwarzschild instability in a relativistic striped wind

NASA Astrophysics Data System (ADS)

Gill, Ramandeep; Granot, Jonathan; Lyubarsky, Yuri

2018-03-01

We study the linear and non-linear development of the Kruskal-Schwarzchild instability in a relativisitically expanding striped wind. This instability is the generalization of Rayleigh-Taylor instability in the presence of a magnetic field. It has been suggested to produce a self-sustained acceleration mechanism in strongly magnetized outflows found in active galactic nuclei, gamma-ray bursts, and micro-quasars. The instability leads to magnetic reconnection, but in contrast with steady-state Sweet-Parker reconnection, the dissipation rate is not limited by the current layer's small aspect ratio. We performed two-dimensional (2D) relativistic magnetohydrodynamic (RMHD) simulations featuring two cold and highly magnetized (1 ≤ σ ≤ 103) plasma layers with an anti-parallel magnetic field separated by a thin layer of relativistically hot plasma with a local effective gravity induced by the outflow's acceleration. Our simulations show how the heavier relativistically hot plasma in the reconnecting layer drips out and allows oppositely oriented magnetic field lines to reconnect. The instability's growth rate in the linear regime matches the predictions of linear stability analysis. We find turbulence rather than an ordered bulk flow near the reconnection region, with turbulent velocities up to ˜0.1c, largely independent of model parameters. However, the magnetic energy dissipation rate is found to be much slower, corresponding to an effective ordered bulk velocity inflow into the reconnection region vin = βinc of 10-3 ≲ βin ≲ 5 × 10-3. This occurs due to the slow evacuation of hot plasma from the current layer, largely because of the Kelvin-Helmholtz instability experienced by the dripping plasma. 3D RMHD simulations are needed to further investigate the non-linear regime.

Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Garbaczewski, Piotr; Klauder, John R.; Olkiewicz, Robert

1995-05-01

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for the temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schrödinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feynman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard ``free'' case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schrödinger problem, the ``free noise'' can also be extended to any infinitely divisible probability law, as covered by the Lévy-Khintchine formula. Since the relativistic Hamiltonians ||∇|| and √-Δ+m2 -m are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schrödinger evolution is analyzed in detail. The relativistic covariance of related wave equations is exploited to demonstrate how the associated stochastic jump processes comply with the principles of special relativity.

Particle acceleration and plasma dynamics during magnetic reconnection in the magnetically dominated regime

DOE PAGES

Guo, Fan; Liu, Yi -Hsin; Daughton, William; ...

2015-06-17

Magnetic reconnection is thought to be the driver for many explosive phenomena in the universe. The energy release and particle acceleration during reconnection have been proposed as a mechanism for producing high-energy emissions and cosmic rays. We carry out two- and three-dimensional (3D) kinetic simulations to investigate relativistic magnetic reconnection and the associated particle acceleration. The simulations focus on electron–positron plasmas starting with a magnetically dominated, force-free current sheet (σ ≡ B 2 / (4πn em ec 2) >> 1). For this limit, we demonstrate that relativistic reconnection is highly efficient at accelerating particles through a first-order Fermi process accomplishedmore » by the curvature drift of particles along the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra f α (γ - 1) -p and approaches p = 1 for sufficiently large σ and system size. Eventually most of the available magnetic free energy is converted into nonthermal particle kinetic energy. An analytic model is presented to explain the key results and predict a general condition for the formation of power-law distributions. The development of reconnection in these regimes leads to relativistic inflow and outflow speeds and enhanced reconnection rates relative to nonrelativistic regimes. In the 3D simulation, the interplay between secondary kink and tearing instabilities leads to strong magnetic turbulence, but does not significantly change the energy conversion, reconnection rate, or particle acceleration. This paper suggests that relativistic reconnection sites are strong sources of nonthermal particles, which may have important implications for a variety of high-energy astrophysical problems.« less

Testing the equivalence principle on cosmological scales

NASA Astrophysics Data System (ADS)

Bonvin, Camille; Fleury, Pierre

2018-05-01

The equivalence principle, that is one of the main pillars of general relativity, is very well tested in the Solar system; however, its validity is more uncertain on cosmological scales, or when dark matter is concerned. This article shows that relativistic effects in the large-scale structure can be used to directly test whether dark matter satisfies Euler's equation, i.e. whether its free fall is characterised by geodesic motion, just like baryons and light. After having proposed a general parametrisation for deviations from Euler's equation, we perform Fisher-matrix forecasts for future surveys like DESI and the SKA, and show that such deviations can be constrained with a precision of order 10%. Deviations from Euler's equation cannot be tested directly with standard methods like redshift-space distortions and gravitational lensing, since these observables are not sensitive to the time component of the metric. Our analysis shows therefore that relativistic effects bring new and complementary constraints to alternative theories of gravity.

The Outcome of Neutron Star Mergers

NASA Astrophysics Data System (ADS)

Foucart, Francois

2014-10-01

Black hole-neutron star and neutron star-neutron star mergers are among the main sources of gravitational waves which will be detected in the coming years by the Advanced LIGO/VIRGO/KAGRA observatories. In some cases, these mergers can also power bright electromagnetic emissions: they are the most likely progenitors of short gamma-ray bursts, and the radioactive decay of neutron-rich material ejected by the merger can power optical/infrared transients days after the merger. Finally, they may provide important constraints on the equation of state of cold dense matter, and on the source of heavy elements in the universe. I will discuss the general relativistic simulations which are required to properly model these events, and what they have told us so far about the outcome of neutron star mergers. I will also discuss efforts to improve the physical realism of the simulations by improving the treatment of the most important effects beyond general relativistic hydrodynamics: magnetic fields, neutrinos, and the properties of nuclear matter.

Spin-up of a rapidly rotating star by angular momentum loss - Effects of general relativity

NASA Technical Reports Server (NTRS)

Cook, Gregory B.; Shapiro, Stuart L.; Teukolsky, Saul A.

1992-01-01

It has recently been shown that a rapidly rotating Newtonian star can spin up by radiating angular momentum. Extremely fast pulsars losing energy and angular momentum by magnetic dipole radiation or gravitational radiation may exhibit this behavior. Here, we show that this phenomenon is more widespread for rapidly rotating stars in general relativity. We construct and tabulate polytropic sequences of fully relativistic rotating stars of constant rest mass and entropy. We find that the range of adiabatic indices allowing spin-up extends somewhat above 4/3 because of the nonlinear effects of relativistic gravity. In addition, there is a new class of 'supramassive' stars which will inevitably spin up by losing angular momentum regardless of their equation of state. A supramassive star, spinning up via angular momentum loss, will ultimately evolve until it becomes unstable to catastrophic collapse to a black hole. Spin-up in a rapidly rotating star may thus be an observational precursor to such collapse.

Modeling the Physics of Sliding Objects on Rotating Space Elevators and Other Non-relativistic Strings

NASA Astrophysics Data System (ADS)

Golubovic, Leonardo; Knudsen, Steven

2017-01-01

We consider general problem of modeling the dynamics of objects sliding on moving strings. We introduce a powerful computational algorithm that can be used to investigate the dynamics of objects sliding along non-relativistic strings. We use the algorithm to numerically explore fundamental physics of sliding climbers on a unique class of dynamical systems, Rotating Space Elevators (RSE). Objects sliding along RSE strings do not require internal engines or propulsion to be transported from the Earth's surface into outer space. By extensive numerical simulations, we find that sliding climbers may display interesting non-linear dynamics exhibiting both quasi-periodic and chaotic states of motion. While our main interest in this study is in the climber dynamics on RSEs, our results for the dynamics of sliding object are of more general interest. In particular, we designed tools capable of dealing with strongly nonlinear phenomena involving moving strings of any kind, such as the chaotic dynamics of sliding climbers observed in our simulations.

Electron Cyclotron Current Drive Efficiency in General Tokamak Geometry and Its Application to Advanced Tokamak Plasmas

NASA Astrophysics Data System (ADS)

Lin-Liu, Y. R.; Chan, V. S.; Luce, T. C.; Prater, R.

1998-11-01

Owing to relativistic mass shift in the cyclotron resonance condition, a simple and accurate interpolation formula for estimating the current drive efficiency, such as those(S.C. Chiu et al.), Nucl. Fusion 29, 2175 (1989).^,(D.A. Ehst and C.F.F. Karney, Nucl. Fusion 31), 1933 (1991). commonly used in FWCD, is not available in the case of ECCD. In this work, we model ECCD using the adjoint techniques. A semi-analytic adjoint function appropriate for general tokamak geometry is obtained using Fisch's relativistic collision model. Predictions of off-axis ECCD qualitatively and semi-quantitatively agrees with those of Cohen,(R.H. Cohen, Phys. Fluids 30), 2442 (1987). currently implemented in the raytracing code TORAY. The dependences of the current drive efficiency on the wave launch configuration and the plasma parameters will be presented. Strong absorption of the wave away from the resonance layer is shown to be an important factor in optimizing the off-axis ECCD for application to advanced tokamak operations.