Axisymmetric toroidal modes of general relativistic magnetized neutron star models
Asai, Hidetaka; Lee, Umin E-mail: lee@astr.tohoku.ac.jp
2014-07-20
We calculate axisymmetric toroidal modes of magnetized neutron stars with a solid crust in the general relativistic Cowling approximation. We assume that the interior of the star is threaded by a poloidal magnetic field, which is continuous at the surface with an outside dipole field. We examine the cases of the field strength B{sub S} ∼ 10{sup 16} G at the surface. Since separation of variables is not possible for the oscillations of magnetized stars, we employ finite series expansions for the perturbations using spherical harmonic functions. We find discrete normal toroidal modes of odd parity, but no toroidal modes of even parity are found. The frequencies of the toroidal modes form distinct mode sequences and the frequency in a given mode sequence gradually decreases as the number of radial nodes of the eigenfunction increases. From the frequency spectra computed for neutron stars of different masses, we find that the frequency is almost exactly proportional to B{sub S} and is well represented by a linear function of R/M for a given B{sub S}, where M and R are the mass and radius of the star. The toroidal mode frequencies for B{sub S} ∼ 10{sup 15} G are in the frequency range of the quasi-periodic oscillations (QPOs) detected in the soft-gamma-ray repeaters, but we find that the toroidal normal modes cannot explain all the detected QPO frequencies.
Axisymmetric general relativistic simulations of the accretion-induced collapse of white dwarfs
Abdikamalov, E. B.; Ott, C. D.; Rezzolla, L.; Dessart, L.; Dimmelmeier, H.; Marek, A.; Janka, H.-T.
2010-02-15
The accretion-induced collapse (AIC) of a white dwarf may lead to the formation of a protoneutron star and a collapse-driven supernova explosion. This process represents a path alternative to thermonuclear disruption of accreting white dwarfs in type Ia supernovae. In the AIC scenario, the supernova explosion energy is expected to be small and the resulting transient short-lived, making it hard to detect by electromagnetic means alone. Neutrino and gravitational-wave (GW) observations may provide crucial information necessary to reveal a potential AIC. Motivated by the need for systematic predictions of the GW signature of AIC, we present results from an extensive set of general-relativistic AIC simulations using a microphysical finite-temperature equation of state and an approximate treatment of deleptonization during collapse. Investigating a set of 114 progenitor models in axisymmetric rotational equilibrium, with a wide range of rotational configurations, temperatures and central densities, and resulting white dwarf masses, we extend previous Newtonian studies and find that the GW signal has a generic shape akin to what is known as a 'type III' signal in the literature. Despite this reduction to a single type of waveform, we show that the emitted GWs carry information that can be used to constrain the progenitor and the postbounce rotation. We discuss the detectability of the emitted GWs, showing that the signal-to-noise ratio for current or next-generation interferometer detectors could be high enough to detect such events in our Galaxy. Furthermore, we contrast the GW signals of AIC and rotating massive star iron core collapse and find that they can be distinguished, but only if the distance to the source is known and a detailed reconstruction of the GW time series from detector data is possible. Some of our AIC models form massive quasi-Keplerian accretion disks after bounce. The disk mass is very sensitive to progenitor mass and angular momentum
A relativistic axisymmetric approach to the galactic rotation curves problem
NASA Astrophysics Data System (ADS)
Herrera-Aguilar, A.; Nucamendi, U.
2014-11-01
It is known that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation curves under a minimal set of assumptions (see [1] and [2] for details): i) that emitted photons come to us from stable timelike circular geodesic orbits of stars in a static spherically symmetric gravitational field, and ii) that these photons propagate to us along null geodesics. This relation can be established without appealing at all to a concrete theory of gravitational interaction. This kinematical spherically symmetric approach to the galactic rotation curves problem can be generalized to the stationary axisymmetric realm, which is precisely the symmetry that spiral galaxies possess [3]. Here we review the relativistic results obtained in the latter work. Namely, by making use of the most general stationary axisymmetric metric, we consider stable circular orbits of stars that emit signals which travel to a distant observer along null geodesics and express the galactic red/blue shifts in terms of three arbitrary metric functions, clarifying the contribution of the rotation as well as the dragging of the gravitational field. This stationary axisymmetric approach distinguishes between red and blue shifts emitted by circularly orbiting receding and approaching stars, respectively, even when they are considered with respect to the center of a spiral galaxy, indicating the need of precise measurements in order to confront predictions with observations. We also point out the difficulties one encounters in the attempt of determining the metric functions from observations and list some potential strategies to overcome them.
Axisymmetric generalized harmonic evolution code
Sorkin, Evgeny
2010-04-15
We describe the first axisymmetric numerical code based on the generalized harmonic formulation of the Einstein equations, which is regular at the axis. We test the code by investigating gravitational collapse of distributions of complex scalar field in a Kaluza-Klein spacetime. One of the key issues of the harmonic formulation is the choice of the gauge source functions, and we conclude that a damped-wave gauge is remarkably robust in this case. Our preliminary study indicates that evolution of regular initial data leads to formation both of black holes with spherical and cylindrical horizon topologies. Intriguingly, we find evidence that near threshold for black hole formation the number of outcomes proliferates. Specifically, the collapsing matter splits into individual pulses, two of which travel in the opposite directions along the compact dimension and one which is ejected radially from the axis. Depending on the initial conditions, a curvature singularity develops inside the pulses.
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.
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.
Relativistic vortex dynamics in axisymmetric stationary perfect fluid configuration
NASA Astrophysics Data System (ADS)
Prasad, G.
2017-06-01
Relativistic formulation of Helmholtz's vorticity transport equation is presented on the basis of Maxwell-like version of Euler's equation of motion. Entangled characteristics associated with vorticity flux conservation in a vortex tube and in a stream tube are displayed on basis of Greenberg's theory of spacelike congruence of vortex lines and 1+1+(2) decomposition of the gradient of fluid's 4-velocity. Vorticity flux surfaces are surfaces of revolution about the rotation axis and are rotating with fluid's angular velocity due to gravitational isorotation in a stationary axisymmetric perfect fluid configuration. Fluid's angular velocity, angular momentum per baryon, injection energy, and invariant rotational potential are constant on such vorticity flux surfaces. Gravitation causes distortion of coaxial cylindrical vorticity flux surfaces in the limit of post-Newtonian approximation. The rotation of the fluid with angular velocity relative to vorticity flux surfaces generates swirl which causes the stretching of material vortex lines being wrapped on vorticity flux surfaces. Fluid helicity which is conserved in the fluid's rest frame does not remain conserved in a locally nonrotating frame because of the existence of swirl. Vortex lines are twist free in the absence of meridional circulations, but the twisting of spacetime due to dragging effect leads to the increase in vorticity flux in a vortex tube.
Exterior axisymmetric solution for a rotating body in the relativistic theory of gravitation
Vlasov, A.A.; Logunov, A.A.
1987-08-01
An exact solution to the complete system of equations of the relativistic theory of gravitation is found in the axisymmetric case for a body with rotation. The existence of gravitational deceleration in the neighborhood of the horizon is shown; as a result test bodies fall toward the horizon for an infinitely long time without being rolled around the horizon.
Fluid-magnetic helicity in axisymmetric stationary relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Prasad, G.
2017-10-01
The present work is intended to gain a fruitful insight into the understanding of the formations of magneto-vortex configurations and their role in the physical processes of mutual exchange of energies associated with fluid's motion and the magnetic fields in an axisymmetric stationary hydromagnetic system subject to strong gravitational field (e.g., neutron star/magnetar). It is found that the vorticity flux vector field associated with vorticity 2-form is a linear combination of fluid's vorticity vector and of magnetic vorticity vector. The vorticity flux vector obeys Helmholtz's flux conservation. The energy equation associated with the vorticity flux vector field is deduced. It is shown that the mechanical rotation of vorticity flux surfaces contributes to the formation of vorticity flux vector field. The dynamo action for the generation of toroidal components of vorticity flux vector field is described in the presence of meridional circulations. It is shown that the stretching of twisting magnetic lines due to differential rotation leads to the breakdown of gravitational isorotation in the absence of meridional circulations. An explicit expression consists of rotation of vorticity flux surface, energy and angular momentum per baryon for the fluid-magnetic helicity current vector is obtained. The conservation of fluid-magnetic helicity is demonstrated. It is found that the fluid-magnetic helicity displays the energy spectrum arising due to the interaction between the mechanical rotation of vorticity flux surfaces and the fluid's motion obeying Euler's equations. The dissipation of a linear combination of modified fluid helicity and magnetic twist is shown to occur due to coupled effect of frame dragging and meridional circulation. It is found that the growing twist of magnetic lines causes the dissipation of modified fluid helicity in the absence of meridional circulations.
Stability of general-relativistic accretion disks
NASA Astrophysics Data System (ADS)
Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard
2011-02-01
Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a Γ-law equation of state with Γ=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric 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. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.
Stability of general-relativistic accretion disks
Korobkin, Oleg; Abdikamalov, Ernazar B.; Schnetter, Erik; Stergioulas, Nikolaos; Zink, Burkhard
2011-02-15
Self-gravitating relativistic disks around black holes can form as transient structures in a number of astrophysical scenarios such as binary neutron star and black hole-neutron star coalescences, as well as the core collapse of massive stars. We explore the stability of such disks against runaway and nonaxisymmetric instabilities using three-dimensional hydrodynamics simulations in full general relativity using the Thor code. We model the disk matter using the ideal fluid approximation with a {Gamma}-law equation of state with {Gamma}=4/3. We explore three disk models around nonrotating black holes with disk-to-black hole mass ratios of 0.24, 0.17, and 0.11. Because of metric blending in our initial data, all of our initial models contain an initial axisymmetric perturbation which induces radial disk oscillations. Despite these oscillations, our models do not develop the runaway instability during the first several orbital periods. Instead, all of the models develop unstable nonaxisymmetric modes on a dynamical time scale. We observe two distinct types of instabilities: the Papaloizou-Pringle and the so-called intermediate type instabilities. The development of the nonaxisymmetric 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. Overall, our simulations show that the properties of the unstable nonaxisymmetric modes in our disk models are qualitatively similar to those in the Newtonian theory.
GRIM: General Relativistic Implicit Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Chandra, Mani; Foucart, Francois; Gammie, Charles F.
2017-02-01
GRIM (General Relativistic Implicit Magnetohydrodynamics) evolves a covariant extended magnetohydrodynamics model derived by treating non-ideal effects as a perturbation of ideal magnetohydrodynamics. Non-ideal effects are modeled through heat conduction along magnetic field lines and a difference between the pressure parallel and perpendicular to the field lines. The model relies on an effective collisionality in the disc from wave-particle scattering and velocity-space (mirror and firehose) instabilities. GRIM, which runs on CPUs as well as on GPUs, combines time evolution and primitive variable inversion needed for conservative schemes into a single step using only the residuals of the governing equations as inputs. This enables the code to be physics agnostic as well as flexible regarding time-stepping schemes.
General relativistic ? orthonormal frame approach
NASA Astrophysics Data System (ADS)
van Elst, Henk; Uggla, Claes
1997-09-01
The dynamical equations of an extended 1 + 3 orthonormal frame approach to the relativistic description of spacetime geometries are explicitly presented and discussed in detail. In particular, the Bianchi identities for the Weyl curvature tensor occur in a fully expanded form, as they are given a central role in the extended formalism. It is shown how one can naturally introduce local coordinates, both in the 1 + 3 threading and the ADM 3 + 1 slicing context. By specializing the general 1 + 3 dynamical equations it is demonstrated how a number of problems of interest can be obtained. In particular, the simplest choices of spatial frames for spatially homogeneous cosmological models, locally rotationally symmetric spacetime geometries, cosmological models with an Abelian isometry group 0264-9381/14/9/021/img6 and `silent' dust cosmological models are discussed.
Numerical computation of gravitational field for general axisymmetric objects
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2016-10-01
We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (i) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (ii) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (i) finite uniform objects covering rhombic spindles and circular toroids, (ii) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (iii) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.
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.
Generalized Ohm's law for relativistic plasmas
NASA Astrophysics Data System (ADS)
Kandus, A.; Tsagas, C. G.
2008-04-01
We generalize the relativistic expression of Ohm's law by studying a multifluid system of charged species using the 1 + 3 covariant formulation of general relativistic electrodynamics. This is done by providing a fully relativistic, fully non-linear propagation equation for the spatial component of the electric 4-current. Our analysis proceeds along the lines of the non-relativistic studies and extends previous relativistic work on cold plasmas. Exploiting the compactness and transparency of the covariant formalism, we provide a direct comparison with the standard Newtonian versions of Ohm's law and identify the relativistic corrections in an unambiguous way. The generalized expression of Ohm's law is initially given relative to an arbitrary observer and for a multicomponent relativistic charged medium. Then, the law is written with respect to the Eckart frame and for a hot two-fluid plasma with zero total charge. Finally, we apply our analysis to a cold proton-electron plasma and recover the well-known magnetohydrodynamic expressions. In every step, we discuss the approximations made and identify familiar effects, like the Biermann battery and the Hall effect.
Generalized Rayleigh criterion for non-axisymmetric centrifugal instabilities
NASA Astrophysics Data System (ADS)
Billant, Paul; Gallaire, François
2005-10-01
The well-known Rayleigh criterion is a necessary and sufficient condition for inviscid centrifugal instability of axisymmetric perturbations. We have generalized this criterion to disturbances of any azimuthal wavenumber m by means of large-axial-wavenumber WKB asymptotics. A sufficient condition for a free axisymmetric vortex with angular velocity Ω(r) to be unstable to a three-dimensional perturbation of azimuthal wavenumber m is that the real part of the growth rate [σ (r) =-imΩ(r)+√{-φ(r)}] is positive at the complex radius r{=}r_0 where ∂ σ (r)/∂ r=0, i.e. [φ'(r_0) =-2{i}mΩ'(r_0)√{-φ(r_0)},] where φ=(1/r^3)∂{r^4Ω^2}/∂ {r} is the Rayleigh discriminant, provided that some a posteriori checks are satisfied. The application of this new criterion to various classes of vortex profiles shows that the growth rate of non-axisymmetric disturbances decreases as m increases until a cutoff is reached. The criterion is in excellent agreement with numerical stability analyses of the Carton & McWilliams (1989) vortices and allows one to analyse the competition between the centrifugal instability and the shear instability. The generalized criterion is also valid for a vertical vortex in a stably stratified and rotating fluid, except that φ becomes φ=(1/r^3)∂{r^4(Ω+Ω_b)^2/∂r, where Ω_b is the background rotation about the vertical axis. The stratification is found to have no effect. For the Taylor Couette flow between two coaxial cylinders, the same criterion applies except that r_0 is real and equal to the inner cylinder radius. In sharp contrast, the maximum growth rate of non-axisymmetric disturbances is then independent of m.
Relativistic Self-similar Equilibria and Non-axisymmetric Neutral Modes
NASA Astrophysics Data System (ADS)
Cai, Mike J.; Shu, F. H.
2002-05-01
We have constructed semi-analytic axisymmetric scale free solutions to Einstein field equations with perfect fluid matter source. These spacetimes are self-similar under the simultaneous transformation r'= ar and t'=a1-nt. We explored the two dimensional solution space parameterized by the rescaling index n and the isothermal sound speed γ 1/2. The isopycnic surfaces are in general toroids. As the equilibrium configuration rotates faster, an ergo region develops in the form of the exterior of a cone centered about the symmetry axis. The sequence of solution terminates when frame dragging becomes infinite and the ergo cone closes onto the axis. In the extreme flattening limit, we have also searched for non-axisymmetric neutral modes in a self-similar disk. Two separate sets of tracks are discovered in the solution space. One corresponds to the bifurcation points to non-axisymmetric equilibria, which is confined in the non-ergo solutions. The other track signals the onset of instability driven by gravitational radiation. These solutions are formally infinite in extent, and thus can not represent realistic astrophysical systems. However, if these properties do not alter qualitatively when the self-similar configurations are truncated, then these solutions may serve as initial data for dynamic collapse in super massive black hole formation.
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 EFFECTS ON NONLINEAR POWER SPECTRA
Jeong, Donghui; Gong, Jinn-Ouk; Noh, Hyerim; Hwang, Jai-chan E-mail: jgong@lorentz.leidenuniv.nl E-mail: jchan@knu.ac.kr
2011-01-20
The nonlinear nature of Einstein's equation introduces genuine relativistic higher order corrections to the usual Newtonian fluid equations describing the evolution of cosmological perturbations. We study the effect of such novel nonlinearities on the next-to-leading order matter and velocity power spectra for the case of a pressureless, irrotational fluid in a flat Friedmann background. We find that pure general relativistic corrections are negligibly small over all scales. Our result guarantees that, in the current paradigm of standard cosmology, one can safely use Newtonian cosmology even in nonlinear regimes.
Generalized energy principle for flute perturbations in axisymmetric mirror machines
Lansky, I.M.; Ryutov, D.D.
1993-01-20
Axial symmetry is a very desirable property of the mirror devices both for fusion and neutron source applications. The main obstacle to be circumvented in the development of such systems, is the flute instability of axisymmetric mirrors. In recent years there appeared a number of proposals, devoted to the stabilization of the flute perturbations in the framework of axisymmetric magnetic configurations, which are based on the combining of the MHD unstable central cell with various types of end-cell stabilizers. In the present paper we concentrate ourselves just on this scheme, including long solenoid with a uniform field, conjugated with the end stabilizing anchor, intended to provide MHD stability of the system as a whole. The attractive feature of such a configuration is that it allows to exploit finite larmor radius (FLR) effects for the stabilization of the flute perturbations. As is well known, FLR effects, being strong, stabilize all flute modes, except the one with azimuthal number m = 1, corresponding to the ``rigid`` displacement of the plasma column (the ``global`` mode). Consequently, in the conditions when FLR effects dominate, the anchor has to stabilize the ``global` mode only. Bearing in mind a favorable influence of FLR effects we, however, don`t restrict our paper by discussion of only ``global`` mode stability and consider a general case of an arbitrary azimuthal mode.
General Relativistic Effects in Atom Interferometry
Dimopoulos, Savas; Graham, Peter W.; Hogan, Jason M.; Kasevich, Mark A.; /Stanford U., Phys. Dept.
2008-03-17
Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom interferometer and deriving its range of validity. From this we develop a method for calculating the phase shift in general relativity. This formalism is then used to find the relativistic effects in an atom interferometer in a weak gravitational field for application to laboratory tests of general relativity. The potentially testable relativistic effects include the non-linear three-graviton coupling, the gravity of kinetic energy, and the falling of light. We propose experiments, one currently under construction, that could provide a test of the principle of equivalence to 1 part in 10{sup 15} (300 times better than the present limit), and general relativity at the 10% level, with many potential future improvements. We also consider applications to other metrics including the Lense-Thirring effect, the expansion of the universe, and preferred frame and location effects.
Spectral Methods in General Relativistic MHD Simulations
NASA Astrophysics Data System (ADS)
Garrison, David
2012-03-01
In this talk I discuss the use of spectral methods in improving the accuracy of a General Relativistic Magnetohydrodynamic (GRMHD) computer code. I introduce SpecCosmo, a GRMHD code developed as a Cactus arrangement at UHCL, and show simulation results using both Fourier spectral methods and finite differencing. This work demonstrates the use of spectral methods with the FFTW 3.3 Fast Fourier Transform package integrated with the Cactus Framework to perform spectral differencing using MPI.
Diffusion processes in general relativistic radiating spheres
Barreto, W.; Herrera, L.; Santos, N.O.; Universidad Central de Venezuela, Caracas; Observatorio Nacional do Brasil, Rio de Janeiro )
1989-09-01
The influence of diffusion processes on the dynamics of general relativistic radiating spheres is systematically studied by means of two examples. Differences between the streaming-out limit and the diffusion limit are exhibited, for both models, through the evolution curves of dynamical variables. In particular it is shown the Bondi mass decreases, for both models, in the diffusion limit as compared with its value at the streaming-out regime. 15 refs.
Relativistic self-similar equilibria and non-axisymmetric neutral modes
NASA Astrophysics Data System (ADS)
Cai, Michael Jun
By semi-analytic means, we examined a class of scale-free solutions to the Einstein equations with perfect fluid matter source. These spacetimes are self-similar under the simultaneous transformation r → ar and t → a1-nt for any constant a. From first principles, the fluid is supported against gravity by rotation and isothermal pressure that are a priori independent of each other. We thus explored the two- dimensional solution space parameterized by the resealing index n and the sound speed γ1/2. As preparatory work toward a more realistic model, we first studied the razor-thin self-similar disks with a two-dimensional scalar pressure. We then relaxed the infinitesimal vertical thickness assumption and considered three-dimensional rotating self-similar solutions. The isopycnic surfaces (surfaces of constant density) are in general toroids, with a certain degree of flattening given by the level of rotation. When the linear rotation velocity is large compared to the sound speed, we recover the disk solution. However, since relativity limits the rotation velocity to be less than that of light, complete flattening is impossible for a sound speed that is not infinitesimal. The last part of this dissertation returns to razor thin- disks and considers the non-axisymmetric neutral modes. By restricting ourselves to self-similar polar perturbations with azimuthal dependence given by eimø , we performed a stability analysis of an axisym-metric disk. We discovered two sets of tracks where the characteristic frequency vanishes in an inertial frame. These solutions are formally infinite in mass and extent, and thus cannot represent realistic astrophysical systems. However, if the properties do not change qualitatively when the self-similar configurations are truncated, then these solutions may serve as initial data for dynamic collapse in the monolithic formation of black holes. (Abstract shortened by UMI.)
General relativistic neutrino transport using spectral methods
NASA Astrophysics Data System (ADS)
Peres, Bruno; Penner, Andrew Jason; Novak, Jérôme; Bonazzola, Silvano
2014-02-01
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, θ, ϕ, ɛ, Θ, Φ), and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (θ, ϕ, Θ, Φ), and is fully energy-dependent. This approach is implemented in a spherical shell, using either Chebyshev polynomials or Fourier series as decomposition bases. It is here restricted to simplified collision terms (isoenergetic scattering) and to the case of a static fluid. We finish this paper by presenting test results using basic configurations, including general relativistic ones in the Schwarzschild metric, in order to demonstrate the convergence properties, the conservation of particle number and correct treatment of some general relativistic effects of our code. The use of spectral methods enables to run our test cases in a six-dimensional setting on a single processor.
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.
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.
Leibnizian relationalism for general relativistic physics
NASA Astrophysics Data System (ADS)
Vassallo, Antonio; Esfeld, Michael
2016-08-01
An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple and being informative.
General-relativistic astrophysics. [gravitational wave astronomy
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1978-01-01
The overall relevance of general relativity to astrophysics is considered, and some of the knowledge about the ways in which general relativity should influence astrophysical systems is reviewed. Attention is focused primarily on finite-sized astrophysical systems, such as stars, globular clusters, galactic nuclei, and primordial black holes. Stages in the evolution of such systems and tools for studying the effects of relativistic gravity in these systems are examined. Gravitational-wave astronomy is discussed in detail, with emphasis placed on estimates of the strongest gravitational waves that bathe earth, present obstacles and future prospects for detection of the predicted waves, the theory of small perturbations of relativistic stars and black holes, and the gravitational waves such objects generate. Characteristics of waves produced by black-hole events in general, pregalactic black-hole events, black-hole events in galactic nuclei and quasars, black-hole events in globular clusters, the collapse of normal stars to form black holes or neutron stars, and corequakes in neutron stars are analyzed. The state of the art in gravitational-wave detection and characteristics of various types of detector are described.
Improving general relativistic astrophysics workflows with ADIOS
NASA Astrophysics Data System (ADS)
Bode, Tanja; Slawinska, Magdalena; Logan, Jeremy; Clark, Michael; Kinsey, Matthew; Wolf, Matthew; Klasky, Scott; Laguna, Pablo
2013-04-01
There are many challenges in analyzing and visualizing data from current cutting-edge general relativistic astrophysics simulations. Many of the associated tasks are time-consuming, with large performance degradation due to the magnitude and complexity of the data. The Adaptable IO System (ADIOS) is a componentization of the IO layer that has demonstrated remarkable IO performance improvements on applications running on leadership class machines while also offering new in-memory ``staging'' operations for transforming data in situ. We have incorporated ADIOS staging technologies into our Maya numerical relativity code based on Cactus infrastructure and Carpet mesh refinement. We present results that demonstrate how ADIOS yields significant gains on IO performance while utilizing leveraged investments in ADIOS plugins for visualization tools such as VisIt.
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.
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.
Time Ephemeris and General Relativistic Scale Factor
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2010-11-01
Time ephemeris is the location-independent part of the transformation formula relating two time coordinates such as TCB and TCG (Fukushima 2009). It is computed from the corresponding (space) ephemerides providing the relative motion of two spatial coordinate origins such as the motion of geocenter relative to the solar system barycenter. The time ephemerides are inevitably needed in conducting precise four dimensional coordinate transformations among various spacetime coordinate systems such as the GCRS and BCRS (Soffel et al. 2003). Also, by means of the time average operation, they are used in determining the information on scale conversion between the pair of coordinate systems, especially the difference of the general relativistic scale factor from unity such as LC. In 1995, we presented the first numerically-integrated time ephemeris, TE245, from JPL's planetary ephemeris DE245 (Fukushima 1995). It gave an estimate of LC as 1.4808268457(10) × 10-8, which was incorrect by around 2 × 10-16. This was caused by taking the wrong sign of the post-Newtonian contribution in the final summation. Four years later, we updated TE245 to TE405 associated with DE405 (Irwin and Fukushima 1999). This time the renewed vale of LC is 1.48082686741(200) × 10-8 Another four years later, by using a precise technique of time average, we improved the estimate of Newtonian part of LC for TE405 as 1.4808268559(6) × 10-8 (Harada and Fukushima 2003). This leads to the value of LC as LC = 1.48082686732(110) × 10-8. If we combine this with the constant defining the mean rate of TCG-TT, LG = 6.969290134 × 10-10 (IAU 2001), we estimate the numerical value of another general relativistic scale factor LB = 1.55051976763(110) × 10-8, which has the meaning of the mean rate of TCB-TT. The main reasons of the uncertainties are the truncation effect in time average and the uncertainty of asteroids' perturbation. As a compact realization of the time ephemeris, we prepared HF2002, a Fortran
Time ephemeris and general relativistic scale factor
NASA Astrophysics Data System (ADS)
Fukushima, Toshio
2010-01-01
Time ephemeris is the location-independent part of the transformation formula relating two time coordinates such as TCB and TCG (Fukushima 1995). It is computed from the corresponding (space) ephemerides providing the relative motion of two spatial coordinate origins such as the motion of geocenter relative to the solar system barycenter. The time ephemerides are inevitably needed in conducting precise four dimensional coordinate transformations among various spacetime coordinate systems such as the GCRS and BCRS (Soffel et al. 2003). Also, by means of the time average operation, they are used in determining the information on scale conversion between the pair of coordinate systems, especially the difference of the general relativistic scale factor from unity such as LC. In 1995, we presented the first numerically-integrated time ephemeris, TE245, from JPL's planetary ephemeris DE245 (Fukushima 1995). It gave an estimate of LC as 1.4808268457(10) × 10-8, which was incorrect by around 2 × 10-16. This was caused by taking the wrong sign of the post-Newtonian contribution in the final summation. Four years later, we updated TE245 to TE405 associated with DE405 (Irwin and Fukushima 1999). This time the renewed vale of LC is 1.48082686741(200) × 10-8 Another four years later, by using a precise technique of time average, we improved the estimate of Newtonian part of LC for TE405 as 1.4808268559(6) × 10-8 (Harada and Fukushima 2003). This leads to the value of LC as LC = 1.48082686732(110) × 10-8. If we combine this with the constant defining the mean rate of TCG-TT, LG = 6.969290134 × 10-10 (IAU 2001), we estimate the numerical value of another general relativistic scale factor LB = 1.55051976763(110) × 10-8, which has the meaning of the mean rate of TCB-TT. The main reasons of the uncertainties are the truncation effect in time average and the uncertainty of asteroids' perturbation. The former is a natural limitation caused by the finite length of numerical
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.; Schultz, Marc R.
2012-01-01
A detailed exact solution is presented for laminated-composite circular cylinders with general wall construction and that undergo axisymmetric deformations. The overall solution is formulated in a general, systematic way and is based on the solution of a single fourth-order, nonhomogeneous ordinary differential equation with constant coefficients in which the radial displacement is the dependent variable. Moreover, the effects of general anisotropy are included and positive-definiteness of the strain energy is used to define uniquely the form of the basis functions spanning the solution space of the ordinary differential equation. Loading conditions are considered that include axisymmetric edge loads, surface tractions, and temperature fields. Likewise, all possible axisymmetric boundary conditions are considered. Results are presented for five examples that demonstrate a wide range of behavior for specially orthotropic and fully anisotropic cylinders.
A generalized twistor dynamics of relativistic particles and strings
Soroka, V.A.; Sorokin, D.P.; Tkach, V.I.; Volkov, D.V. )
1992-09-30
In this paper, a generalization of relativistic particle and sting dynamics based on a notion of twistor shift and containing a fundamental length constant is considered, which results in a modification of particle (or string) interactions with background fields.
Relativistic theory of gravitation and criticism of general relativity
Logunov, A.A.; Loskutov, Yu.M.; Mestvirishvili, M.A.
1988-05-01
Two questions are discussed: (1) the invalidity of the general theory of relativity as a physical theory of gravitation and (2) the construction of a relativistic theory of gravitation possessing all attributes of field theories.
User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 1: General ADD code description
NASA Technical Reports Server (NTRS)
Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.
1982-01-01
This User's Manual contains a complete description of the computer codes known as the AXISYMMETRIC DIFFUSER DUCT code or ADD code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.
Cosmological measurements with general relativistic galaxy correlations
NASA Astrophysics Data System (ADS)
Raccanelli, Alvise; Montanari, Francesco; Bertacca, Daniele; Doré, Olivier; Durrer, Ruth
2016-05-01
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 galaxy 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.
Contradictory character of general relativity. The relativistic theory of gravitation
Logunov, A.A.; Loskutov, Y.M.
1986-11-01
It is shown that in its general form general relativity is unsatisfactory. In particular, its predictions for the gravitational time delay of a radio signal and the period of revolution of a satellite are ambiguous. At the same time, it is shown that the relativistic theory of gravitation is free of such shortcomings and agrees with all reliably established experimental facts.
General-relativistic rotation laws in rotating fluid bodies
NASA Astrophysics Data System (ADS)
Mach, Patryk; Malec, Edward
2015-06-01
We formulate new general-relativistic extensions of Newtonian rotation laws for self-gravitating stationary fluids. They have been used to rederive, in the first post-Newtonian approximation, the well-known geometric dragging of frames. We derive two other general-relativistic weak-field effects within rotating tori: the recently discovered dynamic antidragging and a new effect that measures the deviation from the Keplerian motion and/or the contribution of the fluids self-gravity. One can use the rotation laws to study the uniqueness and the convergence of the post-Newtonian approximations as well as the existence of the post-Newtonian limits.
Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves
NASA Astrophysics Data System (ADS)
Chesler, Paul M.; Loeb, Abraham
2017-07-01
In the weak-field limit of general relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of general relativity are supported by the observation of ultrahigh-energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of modified Newtonian dynamics, namely, the generalized Einstein-aether theory and bimetric modified Newtonian dynamics, display fatal inconsistencies with these observations.
Constraining Relativistic Generalizations of Modified Newtonian Dynamics with Gravitational Waves.
Chesler, Paul M; Loeb, Abraham
2017-07-21
In the weak-field limit of general relativity, gravitational waves obey linear equations and propagate at the speed of light. These properties of general relativity are supported by the observation of ultrahigh-energy cosmic rays as well as by LIGO's recent detection of gravitation waves. We argue that two existing relativistic generalizations of modified Newtonian dynamics, namely, the generalized Einstein-aether theory and bimetric modified Newtonian dynamics, display fatal inconsistencies with these observations.
Static axisymmetric rings in general relativity: How diverse they are
NASA Astrophysics Data System (ADS)
Semerák, O.
2016-11-01
Three static and axially symmetric (Weyl-type) ring singularities—the Majumdar-Papapetrou-type (extremally charged) ring, the Bach-Weyl ring, and the Appell ring—are studied in general relativity in order to show how remarkably the geometries in their vicinity differ from each other. This is demonstrated on basic measures of the rings and on invariant characteristics given by the metric and by its first and second derivatives (lapse, gravitational acceleration, and curvature), and also on geodesic motion. The results are also compared against the Kerr space-time which possesses a ring singularity too. The Kerr solution is only stationary, not static, but in spite of the consequent complication by dragging, its ring appears to be simpler than the static rings. We show that this mainly applies to the Bach-Weyl ring, although this straightforward counterpart of the Newtonian homogeneous circular ring is by default being taken as the simplest ring solution, and although the other two static ring sources may seem more "artificial." The weird, directional deformation around the Bach-Weyl ring probably indicates that a more adequate coordinate representation and interpretation of this source should exist.
NASA Astrophysics Data System (ADS)
Damanhuri, Nor Alisa; Ayob, Syafikah
2017-09-01
A general numerical approximation of the stress equilibrium equations and constructing axisymmetric ideal plastic plane deformation of a granular material is considered. The stress components are assumed to satisfy the Coulomb yield criterion and the self-weight of the material is neglected. The standard method of numerical approximation leads to the construction of the small segments of the stress characteristic field. Using the Matlab program, the method is applied to a problem of granular indentation by a smooth flat surface.
Generalized dilatation operator method for non-relativistic holography
NASA Astrophysics Data System (ADS)
Chemissany, Wissam; Papadimitriou, Ioannis
2014-10-01
We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent z and any value of the hyperscaling violation parameter θ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton-Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.
Relativistic Particle in Electromagnetic Fields with a Generalized Uncertainty Principle
NASA Astrophysics Data System (ADS)
Merad, M.; Zeroual, F.; Falek, M.
2012-05-01
In this paper, we propose to solve the relativistic Klein-Gordon and Dirac equations subjected to the action of a uniform electromagnetic field with a generalized uncertainty principle in the momentum space. In both cases, the energy eigenvalues and their corresponding eigenfunctions are obtained. The limit case is then deduced for a small parameter of deformation.
Fuerst, Steven V.; Mizuno, Yosuke; Nishikawa, Ken-Ichi; Wu, Kinwah; /Mullard Space Sci. Lab.
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) observed in black-hole X-ray binaries.
General relativistic magneto-hydrodynamics with the Einstein Toolkit
NASA Astrophysics Data System (ADS)
Moesta, Philipp; Mundim, Bruno; Faber, Joshua; Noble, Scott; Bode, Tanja; Haas, Roland; Loeffler, Frank; Ott, Christian; Reisswig, Christian; Schnetter, Erik
2013-04-01
The Einstein Toolkit Consortium is developing and supporting open software for relativistic astrophysics. Its aim is to provide the core computational tools that can enable new science, broaden our community, facilitate interdisciplinary research and take advantage of petascale computers and advanced cyberinfrastructure. The Einstein Toolkit currently consists of an open set of over 100 modules for the Cactus framework, primarily for computational relativity along with associated tools for simulation management and visualization. The toolkit includes solvers for vacuum spacetimes as well as relativistic magneto-hydrodynamics. This talk will present the current capabilities of the Einstein Toolkit with a particular focus on recent improvements made to the general relativistic magneto-hydrodynamics modeling and will point to information how to leverage it for future research.
NASA Technical Reports Server (NTRS)
Gnoffo, P. A.
1977-01-01
A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.
Causal structure of general relativistic spacetimes
Howard, Ecaterina
2010-06-15
We present some of the recent results and open questions on the causality problem in General Relativity. The concept of singularity is intimately connected with future trapped surface and inner event horizon formation. We offer a brief overview of the Hawking-Penrose singularity theorems and discuss a few open problems concerning the future Cauchy development (domain of dependence), break-down criteria and energy conditions for the horizon stability. A key question is whether causality violating regions, generating a Cauchy horizon are allowed.We raise several questions concerning the invisibility and stability of closed trapped surfaces from future null infinity and derive the imprisonment conditions. We provide an up-to-date perspective of the causal boundaries and spacelike conformal boundary extensions for time oriented Lorentzian manifolds and more exotic settings.
Generalized relativistic harmonic oscillator in minimal length quantum mechanics
NASA Astrophysics Data System (ADS)
Castro, L. B.; E Obispo, A.
2017-07-01
We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions in the presence of a minimal length. Using the momentum space representation, we explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. Furthermore, we also find an isolated solution from the Sturm-Liouville scheme. All cases already analyzed in the literature are obtained as particular cases.
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 Smoothed Particle Hydrodynamics code developments: A progress report
NASA Astrophysics Data System (ADS)
Faber, Joshua; Silberman, Zachary; Rizzo, Monica
2017-01-01
We report on our progress in developing a new general relativistic Smoothed Particle Hydrodynamics (SPH) code, which will be appropriate for studying the properties of accretion disks around black holes as well as compact object binary mergers and their ejecta. We will discuss in turn the relativistic formalisms being used to handle the evolution, our techniques for dealing with conservative and primitive variables, as well as those used to ensure proper conservation of various physical quantities. Code tests and performance metrics will be discussed, as will the prospects for including smoothed particle hydrodynamics codes within other numerical relativity codebases, particularly the publicly available Einstein Toolkit. We acknowledge support from NSF award ACI-1550436 and an internal RIT D-RIG grant.
Weak-field general relativistic dynamics and the Newtonian limit
NASA Astrophysics Data System (ADS)
Cooperstock, F. I.
2016-01-01
We show that the generally held view that the gravity of weak-field nonrelativistic-velocity sources being invariably almost equivalent to Newtonian gravity (NG) (the “Newtonian limit” approach) is in some instances misleading and in other cases incorrect. A particularly transparent example is provided by comparing the Newtonian and general relativistic analyses of a simple variant of van Stockum’s infinite rotating dust cylinder. We show that some very recent criticisms of our work that had been motivated by the Newtonian limit approach were incorrect and note that no specific errors in our work were found in the critique. In the process, we underline some problems that arise from inappropriate coordinate transformations. As further support for our methodology, we note that our weak-field general relativistic treatment of a model galaxy was vindicated recently by the observations of Xu et al. regarding our prediction that the Milky Way was 19-21 kpc in radius as opposed to the commonly held view that the radius was 15 kpc.
Axisymmetric Stagnation-Point Flow with a General Slip Boundary Condition over a Lubricated Surface
NASA Astrophysics Data System (ADS)
Sajid, M.; K., Mahmood; Z., Abbas
2012-02-01
We investigate the axisymmetric stagnation-point flow of a viscous fluid over a lubricated surface by imposing a generalized slip condition at the fluid-fluid interface. The power law non-Newtonian fluid is considered as a lubricant. The lubrication layer is thin and assumed to have a variable thickness. The transformed nonlinear ordinary differential equation governing the flow is linearized using quasilinearization. The method of superposition is adopted to convert the boundary value problem into an initial value problem and the solution is obtained numerically by using the fourth-order Runge—Kutta method. The results are discussed to see the influence of pertinent parameters. The limiting cases of Navier and no-slip boundary conditions are obtained as the special cases and found to be in excellent agreement with the existing results in the literature.
Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Noble, Scott C.; Gammie, Charles F.; McKinney, Jonathan C.; Del Zanna, Luca
2006-04-01
Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between ``conserved'' variables such as momentum and energy density and ``primitive'' variables such as rest-mass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transformation (conserved to primitive) requires the solution of a set of five nonlinear equations. Here we discuss the mathematical properties of the inverse transformation and present six numerical methods for performing the inversion. The first method solves the full set of five nonlinear equations directly using a Newton-Raphson scheme and a guess from the previous time step. The other methods reduce the five nonlinear equations to either one or two nonlinear equations that are solved numerically. Comparisons between the methods are made using a survey over phase space, a two-dimensional explosion problem, and a general relativistic MHD accretion disk simulation. The run time of the methods is also examined. Code implementing the schemes is available with the electronic edition of the article.
General relativistic celestial mechanics. 2. Translational equations of motion
Damour, T.; Soffel, M.; Xu, C.
1991-10-01
The translational laws of motion for gravitationally interacting systems of N, arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses the authors' recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce global equilibrium (relativistic generalization of d'Alembert's principle). Within the post-Newtonian approximation i.e. neglecting terms of order v/c to the 4th power in the equations of motion, the authors' work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. The authors first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of the body to the post-Newtonian tidal moments (recently defined by them) felt by the body. They then give the explicit expression of these tidal moments in terms of the post-Newtonian multiple moments of the other bodies.
General-relativistic celestial mechanics. II. Translational equations of motion
Damour, T. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX ); Soffel, M.; Xu, C. )
1992-02-15
The translational laws of motion for gravitationally interacting systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies are obtained at the first post-Newtonian approximation of general relativity. The derivation uses our recently introduced multi-reference-system method and obtains the translational laws of motion by writing that, in the local center-of-mass frame of each body, relativistic inertial effects combine with post-Newtonian self- and externally generated gravitational forces to produce a global equilibrium (relativistic generalization of d'Alembert's principle). Within the first post-Newtonian approximation (i.e., neglecting terms of order ({ital v}/{ital c}){sup 4} in the equations of motion), our work is the first to obtain complete and explicit results, in the form of infinite series, for the laws of motion of arbitrarily composed and shaped bodies. We first obtain the laws of motion of each body as an infinite series exhibiting the coupling of all the (Blanchet-Damour) post-Newtonian multipole moments of this body to the post-Newtonian tidal moments (recently defined by us) felt by this body. We then give the explicit expression of these tidal moments in terms of post-Newtonian multipole moments of the other bodies.
A General Relativistic Magnetohydrodynamics Simulation of Jet Formation with a State Transition
NASA Technical Reports Server (NTRS)
Nishikawa, K. I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fushman, G. J.
2004-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation of jet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity sim 0.3c) is created as shown by previous two-dimensional axisymmetric simulations with mirror symmetry at the equator. The 3-D simulation ran over one hundred light-crossing time units which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted due in part to magnetic pressure from the twisting the initially uniform magnetic field and from gas pressure associated with shock formation. At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface of the thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outwards with a wider angle than the initial jet. The widening of the jet is consistent with the outward moving shock wave. This evolution of jet-disk coupling suggests that the low/hard state of the jet system may switch to the high/soft state with a wind, as the accretion rate diminishes.
McKinney, Jonathan C.; Tchekhovskoy, Alexander; Blandford, Roger D.
2012-04-26
Black hole (BH) accretion flows and jets are qualitatively affected by the presence of ordered magnetic fields. We study fully three-dimensional global general relativistic magnetohydrodynamic (MHD) simulations of radially extended and thick (height H to cylindrical radius R ratio of |H/R| {approx} 0.2-1) accretion flows around BHs with various dimensionless spins (a/M, with BH mass M) and with initially toroidally-dominated ({phi}-directed) and poloidally-dominated (R-z directed) magnetic fields. Firstly, for toroidal field models and BHs with high enough |a/M|, coherent large-scale (i.e. >> H) dipolar poloidal magnetic flux patches emerge, thread the BH, and generate transient relativistic jets. Secondly, for poloidal field models, poloidal magnetic flux readily accretes through the disk from large radii and builds-up to a natural saturation point near the BH. While models with |H/R| {approx} 1 and |a/M| {le} 0.5 do not launch jets due to quenching by mass infall, for sufficiently high |a/M| or low |H/R| the polar magnetic field compresses the inflow into a geometrically thin highly non-axisymmetric 'magnetically choked accretion flow' (MCAF) within which the standard linear magneto-rotational instability is suppressed. The condition of a highly-magnetized state over most of the horizon is optimal for the Blandford-Znajek mechanism that generates persistent relativistic jets with and 100% efficiency for |a/M| {approx}> 0.9. A magnetic Rayleigh-Taylor and Kelvin-Helmholtz unstable magnetospheric interface forms between the compressed inflow and bulging jet magnetosphere, which drives a new jet-disk oscillation (JDO) type of quasi-periodic oscillation (QPO) mechanism. The high-frequency QPO has spherical harmonic |m| = 1 mode period of {tau} {approx} 70GM/c{sup 3} for a/M {approx} 0.9 with coherence quality factors Q {approx}> 10. Overall, our models are qualitatively distinct from most prior MHD simulations (typically, |H/R| << 1 and poloidal flux is limited by
bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport
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
bhlight: General Relativistic Radiation Magnetohydrodynamics with Monte Carlo Transport
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 to a slowly accreting Kerr black hole in axisymmetry.
bhlight: GENERAL RELATIVISTIC RADIATION MAGNETOHYDRODYNAMICS WITH MONTE CARLO TRANSPORT
Ryan, B. R.; Gammie, C. F.; Dolence, J. C.
2015-07-01
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 to a slowly accreting Kerr black hole in axisymmetry.
Koide, Shinji
2010-01-10
To study phenomena of plasmas around rotating black holes, we have derived a set of 3+1 formalism of generalized general relativistic magnetohydrodynamic (GRMHD) equations. In particular, we investigated general relativistic phenomena with respect to the Ohm's law. We confirmed the electromotive force due to the gravitation, centrifugal force, and frame-dragging effect in plasmas near the black holes. These effects are significant only in the local small-scale phenomena compared to the scale of astrophysical objects. We discuss the possibility of magnetic reconnection, which is triggered by one of these effects in a small-scale region and influences the plasmas globally. We clarify the conditions of applicability of the generalized GRMHD, standard resistive GRMHD, and ideal GRMHD for plasmas in black hole magnetospheres.
General criteria for determining rotation or oscillation in a two-dimensional axisymmetric system
NASA Astrophysics Data System (ADS)
Koyano, Yuki; Yoshinaga, Natsuhiko; Kitahata, Hiroyuki
2015-07-01
A self-propelled particle in a two-dimensional axisymmetric system, such as a particle in a central force field or confined in a circular region, may show rotational or oscillatory motion. These motions do not require asymmetry of the particle or the boundary, but arise through spontaneous symmetry breaking. We propose a generic model for a self-propelled particle in a two-dimensional axisymmetric system. A weakly nonlinear analysis establishes criteria for determining rotational or oscillatory motion.
Generalized charge-screening in relativistic Thomas–Fermi model
Akbari-Moghanjoughi, M.
2014-10-15
In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, (N{sub s}∝r{sub TF}{sup 3}/r{sub d}{sup 3} where r{sub TF} and r{sub d} are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar
General relativistic effects in quantum interference of photons
NASA Astrophysics Data System (ADS)
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Ralph, Timothy C.; Brukner, Časlav
2012-11-01
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon’s coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
Comments on "Two exact solutions to the general relativistic Binet's equation"
NASA Astrophysics Data System (ADS)
Navickas, Zenonas; Ragulskis, Minvydas
2013-04-01
In their recent manuscript He and Zeng claim that they have solved the general relativistic Binet's orbit equation using the exp-function method and have obtained two exact solutions useful for theoretical analysis. We argue that the obtained solutions do not satisfy the original differential equation. Moreover, we present the alternative framework for the solution of the general relativistic Binet's orbit equation.
Relativistic many-body perturbation theory for general open-shell multiplet states of atoms
NASA Astrophysics Data System (ADS)
Ishikawa, Yasuyuki; Koc, Konrad
1996-06-01
A relativistic many-body perturbation theory, which accounts for relativistic and electron-correlation effects for general open-shell multiplet states of atoms and molecules, is developed and implemented with analytic basis sets of Gaussian spinors. The theory retains the essential aspects of Mo/ller-Plesset perturbation theory by employing the relativistic single-Fock-operator method of Koc and Ishikawa [Phys. Rev. A 49, 794 (1994)] for general open-shell systems. Open-shell Dirac-Fock and relativistic many-body perturbation calculations are reported for the ground and low-lying excited states of Li, B2+, Ne7+, and Ca11+.
NASA Astrophysics Data System (ADS)
Sekiguchi, Yuichiro
2010-06-01
Performing fully general relativistic simulations taking account of microphysical processes (e.g. weak interactions and neutrino cooling) is one of the long-standing problems in numerical relativity. One of main difficulties in implementation of weak interactions in the general relativistic framework lies in the fact that the characteristic timescale of weak interaction processes (the WP timescale, t_wp \\sim \\vert Y_{e}/\\dot{Y}_{e} \\vert) in hot dense matters is much shorter than the dynamical timescale (tdyn). Numerically this means that stiff source terms appear in the equations so that an implicit scheme is in general necessary to stably solve the relevant equations. Otherwise a very short timestep (Δt < twp Lt tdyn) will be required to solve them explicitly, which is unrealistic in the present computational resources. Furthermore, in the relativistic framework, the Lorentz factor is coupled with the rest mass density and the energy density. The specific enthalpy is also coupled with the momentum. Due to these couplings, it is very complicated to recover the primitive variables and the Lorentz factor from conserved quantities. Consequently, it is very difficult to solve the equations implicitly in the fully general relativistic framework. At the current status, no implicit procedure has been proposed except for the case of the spherical symmetry. Therefore, an approximate explicit procedure is developed in the fully general relativistic framework in this paper as a first implementation of the microphysics toward a more realistic sophisticated model. The procedure is based on the so-called neutrino leakage schemes which are based on the property that the characteristic timescale in which neutrinos leak out of the system (the leakage timescale, tleak) is much longer than the WP timescale. In the previous leakage schemes, however, the problems of the stiff source terms are avoided in an artificial manner. In this paper, I present a detailed neutrino leakage
NASA Astrophysics Data System (ADS)
Chu, M. S.; Guo, Wenfeng
2016-06-01
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the "electrostatic continua." Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
Chu, M. S.; Guo, Wenfeng
2016-06-15
The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the “electrostatic continua.” Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solved analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic
Magnetohydrodynamics in stationary and axisymmetric spacetimes: A fully covariant approach
Gourgoulhon, Eric; Markakis, Charalampos; Uryu, Koji; Eriguchi, Yoshiharu
2011-05-15
A fully geometrical treatment of general relativistic magnetohydrodynamics is developed under the hypotheses of perfect conductivity, stationarity, and axisymmetry. The spacetime is not assumed to be circular, which allows for greater generality than the Kerr-type spacetimes usually considered in general relativistic magnetohydrodynamics. Expressing the electromagnetic field tensor solely in terms of three scalar fields related to the spacetime symmetries, we generalize previously obtained results in various directions. In particular, we present the first relativistic version of the Soloviev transfield equation, subcases of which lead to fully covariant versions of the Grad-Shafranov equation and of the Stokes equation in the hydrodynamical limit. We have also derived, as another subcase of the relativistic Soloviev equation, the equation governing magnetohydrodynamical equilibria with purely toroidal magnetic fields in stationary and axisymmetric spacetimes.
General-relativistic force-free pulsar magnetospheres
NASA Astrophysics Data System (ADS)
Pétri, J.
2016-02-01
Pulsar magnetospheres are shaped by ultrarelativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been less discussed to quantify its influence on the neutron star electrodynamics. It is the purpose of this paper to compute general-relativistic force-free pulsar magnetospheres for realistic magnetic field configurations such as the inclined dipole. We performed time-dependent simulations of Maxwell equations in the 3+1 formalism of a stationary background metric in the slow-rotation approximation. We computed the resulting Poynting flux depending on the ratio R/rL and on frame-dragging through the spin parameter as, R is the neutron star radius and rL the light-cylinder radius. Both effects act together to increase the total Poynting flux seen by a distant observer by a factor up to 2 depending on the rotation rate. Moreover we retrieve the sin 2χ dependence of this luminosity, χ being the obliquity of the pulsar, as well as a braking index close to n = 3. We also show that the angular dependence of the Poynting flux scales like sin 2ϑ for the aligned rotator but like sin 4ϑ for the orthogonal rotator, ϑ being the colatitude.
A General Relativistic Magnetohydrodynamic Simulation of Jet Formation
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Richardson, G.; Koide, S.; Shibata, K.; Kudoh, T.; Hardee, P.; Fishman, G. J.
2005-01-01
We have performed a fully three-dimensional general relativistic magnetohydrodynamic (GRMHD) simulation ofjet formation from a thin accretion disk around a Schwarzschild black hole with a free-falling corona. The initial simulation results show that a bipolar jet (velocity approx.0.3c) is created, as shown by previous two-dimensional axi- symmetric simulations with mirror symmetry at the equator. The three-dimensional simulation ran over 100 light crossing time units (T(sub s) = r(sub s)/c, where r(sub s = 2GM/c(sup 2), which is considerably longer than the previous simulations. We show that the jet is initially formed as predicted owing in part to magnetic pressure from the twisting of the initially uniform magnetic field and from gas pressure associated with shock formation in the region around r = 3r(sub s). At later times, the accretion disk becomes thick and the jet fades resulting in a wind that is ejected from the surface ofthe thickened (torus-like) disk. It should be noted that no streaming matter from a donor is included at the outer boundary in the simulation (an isolated black hole not binary black hole). The wind flows outward with a wider angle than the initial jet. The widening of the jet is consistent with the outward-moving torsional Alfven waves. This evolution of disk-jet coupling suggests that the jet fades with a thickened accretion disk because of the iack of streaming materiai from an accompanying star.
Mass of Newtonian stars in the relativistic theory of gravitation and in general relativity
Vlasov, A.A.
1988-04-01
We consider the problem of determining the mass of a Newtonian star in the relativistic theory of gravitation and in general relativity and we note the difference between these theories. In contrast to the relativistic theory of gravitation, the mass of a Newtonian star is not determined unambiguously by the equations of general relativity and depends on the arbitrariness in the choice of the coordinate conditions.
NASA Astrophysics Data System (ADS)
Umeh, Obinna; Jolicoeur, Sheean; Maartens, Roy; Clarkson, Chris
2017-03-01
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 complex 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 gtrsim 10% when the short modes are k lesssim (50 Mpc)‑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.
General relativistic polytropes with a repulsive cosmological constant
NASA Astrophysics Data System (ADS)
Stuchlík, Zdeněk; Hledík, Stanislav; Novotný, Jan
2016-11-01
Spherically symmetric equilibrium configurations of perfect fluid obeying a polytropic equation of state are studied in spacetimes with a repulsive cosmological constant. The configurations are specified in terms of three parameters—the polytropic index n , the ratio of central pressure and central energy density of matter σ , and the ratio of energy density of vacuum and central density of matter λ . The static equilibrium configurations are determined by two coupled first-order nonlinear differential equations that are solved by numerical methods with the exception of polytropes with n =0 corresponding to the configurations with a uniform distribution of energy density, when the solution is given in terms of elementary functions. The geometry of the polytropes is conveniently represented by embedding diagrams of both the ordinary space geometry and the optical reference geometry reflecting some dynamical properties of the geodesic motion. The polytropes are represented by radial profiles of energy density, pressure, mass, and metric coefficients. For all tested values of n >0 , the static equilibrium configurations with fixed parameters n , σ , are allowed only up to a critical value of the cosmological parameter λc=λc(n ,σ ). In the case of n >3 , the critical value λc tends to zero for special values of σ . The gravitational potential energy and the binding energy of the polytropes are determined and studied by numerical methods. We discuss in detail the polytropes with an extension comparable to those of the dark matter halos related to galaxies, i.e., with extension ℓ>100 kpc and mass M >1 012 M⊙ . For such largely extended polytropes, the cosmological parameter relating the vacuum energy to the central density has to be larger than λ =ρvac/ρc˜10-9. We demonstrate that the extension of the static general relativistic polytropic configurations cannot exceed the so-called static radius related to their external spacetime, supporting the idea
AXISYMMETRIC, NONSTATIONARY BLACK HOLE MAGNETOSPHERES: REVISITED
Song, Yoo Geun; Park, Seok Jae E-mail: sjpark@kasi.re.kr
2015-10-10
An axisymmetric, stationary, general-relativistic, electrodynamic engine model of an active galactic nucleus was formulated by Macdonald and Thorne that consisted of a supermassive black hole surrounded by a plasma magnetosphere and a magnetized accretion disk. Based on this initial formulation, a nonstationary, force-free version of their model was constructed by Park and Vishniac (PV), with the simplifying assumption that the poloidal component of the magnetic field line velocity be confined along the radial direction in cylindrical polar coordinates. In this paper, we derive the new, nonstationary “Transfield Equation,” which was not specified in PV. If we can solve this “Transfield Equation” numerically, then we will understand the axisymmetric, nonstationary black hole magnetosphere in more rigorous ways.
3-D General Relativistic MHD Simulations of Generating Jets
NASA Astrophysics Data System (ADS)
Nishikawa, K.-I.; Koide, S.; Shibata, K.; Kudoh, T.; Frank, J.; Sol, H.
1999-12-01
We have investigated the dynamics of an accretion disk around Schwarzschild black holes initially threaded by a uniform poloidal magnetic field in a non-rotating corona (either in a steady-state infalling state or in hydrostatic equilibrium) around a non-rotating black hole using a 3-D GRMHD with the ``axisymmetry'' along the z-direction. Magnetic field is tightly twisted by the rotation of the disk, and plasmas in the shocked region of the disk are accelerated by J x B force to form bipolar relativistic jets. In order to investigate variabilities of generated relativistic jets and magnetic field structure inside jets, we have performed calculations using the 3-D GRMHD code with a full 3-dimensional system. We will investigate how the third dimension affects the global disk dynamics and jet generation.
3-D General Relativistic MHD Simulations of Generating Jets
NASA Astrophysics Data System (ADS)
Nishikawa, K.-I.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Hughes, J. P.
2001-12-01
We have investigated the dynamics of an accretion disk around Schwarzschild black holes initially threaded by a uniform poloidal magnetic field in a non-rotating corona (either in a steady-state infalling state) around a non-rotating black hole using a 3-D GRMHD with the ``axisymmetry'' along the z-direction. Magnetic field is tightly twisted by the rotation of the disk, and plasmas in the shocked region of the disk are accelerated by J x B force to form bipolar relativistic jets. In order to investigate variabilities of generated relativistic jets and magnetic field structure inside jets, we have performed calculations using the 3-D GRMHD code with a full 3-dimensional system without the axisymmetry. We have investigated how the third dimension affects the global disk dynamics and jet generation. We will perform simulations with various incoming flows from an accompanying star.
3-D General Relativistic MHD Simulations of Generating Jets
NASA Astrophysics Data System (ADS)
Nishikawa, K.-I.; Koide, S.; Shibata, K.; Kudoh, T.; Frank, J.; Sol, H.
1999-05-01
Koide et al have investigated the dynamics of an accretion disk initially threaded by a uniform poloidal magnetic field in a non-rotating corona (either in a steady-state infalling state or in hydrostatic equilibrium) around a non-rotating black hole using a 3-D GRMHD with the ``axisymmetry'' along the z-direction. Magnetic field is tightly twisted by the rotation of the disk, and plasmas in the shocked region of the disk are accelerated by J x B force to form bipolar relativistic jets. In order to investigate variabilities of generated relativistic jets and magnetic field structure inside jets, we have performed calculations using the 3-D GRMHD code on a full 3-dimensional system. We will investigate how the third dimension affects the global disk dynamics. 3-D RMHD simulations wil be also performed to investigate the dynamics of a jet with a helical mangetic field in it.
3-D General Relativistic MHD Simulations of Generating Jets
NASA Astrophysics Data System (ADS)
Nishikawa, K.-I.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Hughes, J. P.
2000-12-01
We have investigated the dynamics of an accretion disk around Schwarzschild black holes initially threaded by a uniform poloidal magnetic field in a non-rotating corona (either in a steady-state infalling state) around a non-rotating black hole using a 3-D GRMHD with the ``axisymmetry'' along the z-direction. Magnetic field is tightly twisted by the rotation of the disk, and plasmas in the shocked region of the disk are accelerated by J x B force to form bipolar relativistic jets. In order to investigate variabilities of generated relativistic jets and magnetic field structure inside jets, we have performed calculations using the 3-D GRMHD code with a full 3-dimensional system. We will investigate how the third dimension affects the global disk dynamics and jet generation.
Jet Formation with 3-D General Relativistic MHD Simulations
NASA Astrophysics Data System (ADS)
Richardson, G. A.; Nishikawa, K.-I.; Preece, R.; Hardee, P.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Hughes, J. P.; Fishman, J.
2002-12-01
We have investigated the dynamics of an accretion disk around Schwarzschild black holes initially threaded by a uniform poloidal magnetic field in a non-rotating corona (in a steady-state infalling state) around a non-rotating black hole using 3-D GRMHD with the ``axisymmetry'' along the z-direction. The magnetic field is tightly twisted by the rotation of the accretion disk, and plasmas in the shocked region of the disk are accelerated by the J x B force to form bipolar relativistic jets. In order to investigate variabilities of generated relativistic jets and the magnetic field structure inside jets, we have performed calculations using the 3-D GRMHD code with a full 3-dimensional system without the axisymmetry. We have investigated how the third dimension affects the global disk dynamics and jet generation. We will perform simulations with various incoming flows from an accompanying star.
3-D General Relativistic MHD Simulations of Generating Jets
NASA Astrophysics Data System (ADS)
Nishikawa, Ken-Ichi; Koide, Shinji; Shibata, Kazunari; Kudoh, Takashiro; Sol, Helene; Hughes, John
2002-04-01
We have investigated the dynamics of an accretion disk around Schwarzschild black holes initially threaded by a uniform poloidal magnetic field in a non-rotating corona (either in a steady-state infalling state) around a non-rotating black hole using a 3-D GRMHD with the ``axisymmetry'' along the z-direction. Magnetic field is tightly twisted by the rotation of the disk, and plasmas in the shocked region of the disk are accelerated by J × B force to form bipolar relativistic jets. In order to investigate variabilities of generated relativistic jets and magnetic field structure inside jets, we have performed calculations using the 3-D GRMHD code with a full 3-dimensional system without the axisymmetry. We have investigated how the third dimension affects the global disk dynamics and jet generation. We will perform simulations with various incoming flows from an accompanying star.
Generalized quantum similarity in atomic systems: A quantifier of relativistic effects
NASA Astrophysics Data System (ADS)
Martín, A. L.; Angulo, J. C.; Antolín, J.; López-Rosa, S.
2017-02-01
Quantum similarity between Hartree-Fock and Dirac-Fock electron densities reveals the depth of relativistic effects on the core and valence regions in atomic systems. The results emphasize the relevance of differences in the outermost subshells, as pointed out in recent studies by means of Shannon-like functionals. In this work, a generalized similarity functional allows us to go far beyond the Shannon-based analyses. The numerical results for systems throughout the Periodic Table show that discrepancies between the relativistic and non-relativistic descriptions are patently governed by shell-filling patterns.
Choreographic solution to the general-relativistic three-body problem.
Imai, Tatsunori; Chiba, Takamasa; Asada, Hideki
2007-05-18
We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.
Choreographic Solution to the General-Relativistic Three-Body Problem
NASA Astrophysics Data System (ADS)
Imai, Tatsunori; Chiba, Takamasa; Asada, Hideki
2007-05-01
We reexamine the three-body problem in the framework of general relativity. The Newtonian N-body problem admits choreographic solutions, where a solution is called choreographic if every massive particle moves periodically in a single closed orbit. One is a stable figure-eight orbit for a three-body system, which was found first by Moore (1993) and rediscovered with its existence proof by Chenciner and Montgomery (2000). In general relativity, however, the periastron shift prohibits a binary system from orbiting in a single closed curve. Therefore, it is unclear whether general-relativistic effects admit choreography such as the figure eight. We examine general-relativistic corrections to initial conditions so that an orbit for a three-body system can be choreographic and a figure eight. This illustration suggests that the general-relativistic N-body problem also may admit a certain class of choreographic solutions.
NASA Astrophysics Data System (ADS)
Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh
2016-09-01
A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.
General relativistic magnetohydrodynamical simulations of the jet in M 87
NASA Astrophysics Data System (ADS)
Mościbrodzka, Monika; Falcke, Heino; Shiokawa, Hotaka
2016-02-01
Context. The connection between black hole, accretion disk, and radio jet can be constrained best by fitting models to observations of nearby low-luminosity galactic nuclei, in particular the well-studied sources Sgr A* and M 87. There has been considerable progress in modeling the central engine of active galactic nuclei by an accreting supermassive black hole coupled to a relativistic plasma jet. However, can a single model be applied to a range of black hole masses and accretion rates? Aims: Here we want to compare the latest three-dimensional numerical model, originally developed for Sgr A* in the center of the Milky Way, to radio observations of the much more powerful and more massive black hole in M 87. Methods: We postprocess three-dimensional GRMHD models of a jet-producing radiatively inefficient accretion flow around a spinning black hole using relativistic radiative transfer and ray-tracing to produce model spectra and images. As a key new ingredient in these models, we allow the proton-electron coupling in these simulations depend on the magnetic properties of the plasma. Results: We find that the radio emission in M 87 is described well by a combination of a two-temperature accretion flow and a hot single-temperature jet. Most of the radio emission in our simulations comes from the jet sheath. The model fits the basic observed characteristics of the M 87 radio core: it is "edge-brightened", starts subluminally, has a flat spectrum, and increases in size with wavelength. The best fit model has a mass-accretion rate of Ṁ ~ 9 × 10-3M⊙ yr-1 and a total jet power of Pj ~ 1043 erg s-1. Emission at λ = 1.3 mm is produced by the counter-jet close to the event horizon. Its characteristic crescent shape surrounding the black hole shadow could be resolved by future millimeter-wave VLBI experiments. Conclusions: The model was successfully derived from one for the supermassive black hole in the center of the Milky Way by appropriately scaling mass and
General relativistic study of astrophysical jets with internal shocks
NASA Astrophysics Data System (ADS)
Vyas, Mukesh K.; Chattopadhyay, Indranil
2017-08-01
We explore the possibility of the formation of steady internal shocks in jets around black holes. We consider a fluid described by a relativistic equation of state, flowing about the axis of symmetry (θ = 0) in a Schwarzschild metric. We use two models for the jet geometry: (i) a conical geometry and (ii) a geometry with non-conical cross-section. A jet with conical geometry has a smooth flow, while the jet with non-conical cross-section undergoes multiple sonic points and even standing shock. The jet shock becomes stronger, as the shock location is situated farther from the central black hole. Jets with very high energy and very low energy do not harbour shocks, but jets with intermediate energies do harbour shocks. One advantage of these shocks, as opposed to shocks mediated by external medium, is that these shocks have no effect on the jet terminal speed, but may act as possible sites for particle acceleration. Typically, a jet with specific energy 1.8c2 will achieve a terminal speed of v∞ = 0.813c for jet with any geometry, where, c is the speed of light in vacuum. But for a jet of non-conical cross-section for which the length scale of the inner torus of the accretion disc is 40rg, then, in addition, a steady shock will form at rsh ∼ 7.5rg and compression ratio of R ∼ 2.7. Moreover, electron-proton jet seems to harbour the strongest shock. We will discuss possible consequences of such a scenario.
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.
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.
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.
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.
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.
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.
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.
Gravity Control Propulsion - Towards a General Relativistic Approach
NASA Astrophysics Data System (ADS)
Bertolami, O.; Pedro, F. G.
Evaluation of gravity control concepts should be examined with respect to currently known physical theories. In this work we study the hypothetical conversion of gravitational potential energy into kinetic energy using the formalism of general relativity. We show that the energy involved in the process greatly exceeds the Newtonian estimate, given the nature of general relativity. We conclude that the impact of any gravity manipulation for propulsion greatly depends fundamentally on its exact definition.
On the foundations of general relativistic celestial mechanics
NASA Astrophysics Data System (ADS)
Battista, Emmanuele; Esposito, Giampiero; Dell’Agnello, Simone
2017-09-01
Towards the end of nineteenth century, Celestial Mechanics provided the most powerful tools to test Newtonian gravity in the solar system and also led to the discovery of chaos in modern science. Nowadays, in light of general relativity, Celestial Mechanics leads to a new perspective on the motion of satellites and planets. The reader is here introduced to the modern formulation of the problem of motion, following what the leaders in the field have been teaching since the nineties, in particular, the use of a global chart for the overall dynamics of N bodies and N local charts describing the internal dynamics of each body. The next logical step studies in detail how to split the N-body problem into two sub-problems concerning the internal and external dynamics, how to achieve the effacement properties that would allow a decoupling of the two sub-problems, how to define external-potential-effacing coordinates and how to generalize the Newtonian multipole and tidal moments. The review paper ends with an assessment of the nonlocal equations of motion obtained within such a framework, a description of the modifications induced by general relativity on the theoretical analysis of the Newtonian three-body problem, and a mention of the potentialities of the analysis of solar-system metric data carried out with the Planetary Ephemeris Program.
RAISHIN: A High-Resolution Three-Dimensional General Relativistic Magnetohydrodynamics Code
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Fishman, Gerald J.
2006-01-01
We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code, RAISHIN, using a conservative, high resolution shock-capturing scheme. The numerical fluxes are calculated using the Harten, Lax, & van Leer (HLL) approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. In order to examine the numerical accuracy and the numerical efficiency, the code uses four different reconstruction methods: piecewise linear methods with Minmod and MC slope-limiter function, convex essentially non-oscillatory (CENO) method, and piecewise parabolic method (PPM) using multistep TVD Runge-Kutta time advance methods with second and third-order time accuracy. We describe code performance on an extensive set of test problems in both special and general relativity. Our new GRMHD code has proven to be accurate in second order and has successfully passed with all tests performed, including highly relativistic and magnetized cases in both special and general relativity.
General relativistic effects in quantum interference of “clocks”
NASA Astrophysics Data System (ADS)
Zych, M.; Pikovski, I.; Costa, F.; Brukner, Č.
2016-06-01
Quantum mechanics and general relativity have been each successfully tested in numerous experiments. However, the regime where both theories are jointly required to explain physical phenomena remains untested by laboratory experiments, and is also not fully understood by theory. This contribution reviews recent ideas for a new type of experiments: quantum interference of “clocks”, which aim to test novel quantum effects that arise from time dilation. “Clock” interference experiments could be realised with atoms or photons in near future laboratory experiments.
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.
Vlasov, A.A.; Logunov, A.A.
1987-12-01
The fundamental difference between the predictions of the relativistic theory of gravitation and the general theory of relativity is demonstrated for the example of gravitational collapse. In accordance with the relativistic theory of gravitation, neither static nor nonstatic spherically symmetric bodies with radius less than or equal to mG can exist in nature.
General Relativistic Non-radial Oscillations of Compact Stars
NASA Astrophysics Data System (ADS)
Hall, Zack, II; Jaikumar, Prashanth
2017-01-01
Currently, we lack a means of identifying the type of matter at the core of compact stars, but in the future, we may be able to use gravitational wave signals produced by fluid oscillations inside compact stars to discover new phases of dense matter. To this end, we study the fluid perturbations inside compact stars such as Neutron Stars and Strange Quark Stars, focusing on modes that couple to gravitational waves. Using a modern equation of state for quark matter that incorporates interactions at moderately high densities, we implement an efficient computational scheme to solve the oscillation equations in the framework of General Relativity, and determine the complex eigenfrequencies that describe the oscillation and damping of the non-radial fluid modes. We discuss the significance of our results for future detection of these modes through gravitational waves. This work is supported in part by the CSULB Graduate Research Fellowship and by the National Science Foundation NSF PHY-1608959.
Quantum interferometric visibility as a witness of general relativistic proper time
Zych, Magdalena; Costa, Fabio; Pikovski, Igor; Brukner, Časlav
2011-01-01
Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. PMID:22009037
Critical rotation of general-relativistic polytropic models revisited
NASA Astrophysics Data System (ADS)
Geroyannis, V.; Karageorgopoulos, V.
2013-09-01
We develop a perturbation method for computing the critical rotational parameter as a function of the equatorial radius of a rigidly rotating polytropic model in the "post-Newtonia approximation" (PNA). We treat our models as "initial value problems" (IVP) of ordinary differential equations in the complex plane. The computations are carried out by the code dcrkf54.f95 (Geroyannis and Valvi 2012 [P1]; modified Runge-Kutta-Fehlberg code of fourth and fifth order for solving initial value problems in the complex plane). Such a complex-plane treatment removes the syndromes appearing in this particular family of IVPs (see e.g. P1, Sec. 3) and allows continuation of the numerical integrations beyond the surface of the star. Thus all the required values of the Lane-Emden function(s) in the post-Newtonian approximation are calculated by interpolation (so avoiding any extrapolation). An interesting point is that, in our computations, we take into account the complete correction due to the gravitational term, and this issue is a remarkable difference compared to the classical PNA. We solve the generalized density as a function of the equatorial radius and find the critical rotational parameter. Our computations are extended to certain other physical characteristics (like mass, angular momentum, rotational kinetic energy, etc). We find that our method yields results comparable with those of other reliable methods. REFERENCE: V.S. Geroyannis and F.N. Valvi 2012, International Journal of Modern Physics C, 23, No 5, 1250038:1-15.
Malec, Edward; Rembiasz, Tomasz
2010-12-15
We compare Newtonian and general relativistic descriptions of the stationary accretion of self-gravitating fluids onto compact bodies. Spherical symmetry and thin gas approximation are assumed. Luminosity depends, among other factors, on the temperature and the contribution of gas to the total mass, in both--general relativistic (L{sub GR}) and Newtonian (L{sub N})--models. We discover a remarkable universal behavior for transonic flows: the ratio of respective luminosities L{sub GR}/L{sub N} is independent of the fractional mass of the gas and depends on asymptotic temperature. It is close to 1 in the regime of low asymptotic temperatures and can grow several times at high temperatures. These conclusions are valid for a wide range of polytropic equations of state.
The structure and interpretation of cosmology: Part I-general relativistic cosmology
NASA Astrophysics Data System (ADS)
McCabe, Gordon
The purpose of this work is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon mathematical objects and structures, rather than numerical computations. This paper concentrates on general relativistic cosmology. The opening section reviews and clarifies the Friedmann-Robertson-Walker models of general relativistic cosmology, while Section 2 deals with the spatially homogeneous models. Particular attention is paid in these opening sections to the topological and geometrical aspects of cosmological models. Section 3 explains how the mathematical formalism can be linked with astronomical observation. In particular, the informal, observational notion of the celestial sphere is given a rigorous mathematical implementation. Part II of this work will concentrate on inflationary cosmology and quantum cosmology.
Near-critical spherical accretion by neutron stars - General relativistic treatment
NASA Technical Reports Server (NTRS)
Park, Myeong-Gu; Miller, Guy S.
1991-01-01
Time-independent spherical accretion by a neutron star is studied using general relativistic radiation hydrodynamics. Numerical integrations of the flow equations are presented. These show that when the luminosity is sufficiently close to (but below) the Eddington limit, the flow velocity increases with decreasing radius far from the neutron star, reaches a maximum at an intermediate radius, and decreases at small radii. A large fraction of the binding energy of the flow is transferred to the radiation through scattering before the flow strikes the surface of the neutron star. Following Miller's treatment of accretion at luminosites near the Eddington limit (which neglected general relativistic effects), analytic approximations for the decelerating phase of the flow's velocity profile are derived. The dependence of the solutions on the variable Eddington factor prescription chosen to close the radiation moment equations is also examined.
General Relativistic Simulations of Magnetized Plasmas around Merging Supermassive Black Holes
NASA Astrophysics Data System (ADS)
Giacomazzo, Bruno; Baker, John G.; Miller, M. Coleman; Reynolds, Christopher S.; van Meter, James R.
2012-06-01
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 Letter, 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 a total amplification of the magnetic field of ~2 orders of magnitude, which is driven by the accretion onto the binary and that leads to much stronger electromagnetic signals, more than a factor of 104 larger than comparable calculations done in the force-free regime where such amplifications are not possible.
Predictions of axisymmetric free turbulent shear flows using a generalized eddy-viscosity approach
NASA Technical Reports Server (NTRS)
Morgenthaler, J. H.
1973-01-01
The generalized eddy viscosity approach is described and results are presented of test cases which show that predictions obtained by this approach are adequate for most engineering applications. Because of the importance of starting computations from the injection station where experimentally determined mean and turbulence parameters are rarely available, a very simple core model applicable to simple step-type (slug) profiles was developed. Agreement between predicted and experimental mean profiles was generally almost as good for calculations made by using this model throughout the core region and the transition model for all subsequent regions as predictions made by starting from experimental profiles in the transition region. The generalized eddy-viscosity model, which was developed in part through correlation of turbulence parameters, successfully predicted turbulent shear stress, turbulent intensity, and mean velocity profiles for a 0.040-inch-diameter microjet. Therefore, successful scaling by the model was demonstrated since data used in its development was for jet areas up to 90,000 times as large as the microjet and velocities only 1/20th as high.
General Relativistic Precession in Small Solar System Bodies
NASA Astrophysics Data System (ADS)
Sekhar, Aswin; Werner, Stephanie; Hoffmann, Volker; Asher, David; Vaubaillon, Jeremie; Hajdukova, Maria; Li, Gongjie
2016-10-01
Introduction: One of the greatest successes of the Einstein's General Theory of Relativity (GR) was the correct prediction of the precession of perihelion of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre (ω) can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Analytical Approach and Numerical Integrations: Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of ω. Numerical integrations were done with package MERCURY incorporating the GR code to test the same effects. Numerical approach showed the same interesting relationship (as shown by analytical theory) between values of ω and the peaks/dips in MOID values. Previous works have shown that GR precession suppresses Kozai oscillations and this aspect was verified using our integrations. There is an overall agreement between both analytical and numerical methods.Summary and Discussion: We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements). Previous works have looked into impact probabilities and collision scenarios on
General method to evaluate two-body integrals for relativistic atomic calculations
NASA Astrophysics Data System (ADS)
Ley-Koo, E.; Jáuregui, R.; Góngora-T., A.; Bunge, C. F.
1993-03-01
The method of Ley-Koo and Bunge [Phys. Rev. A 40, 1215 (1989)] to evaluate nonrelativistic atomic two-body integrals without a series expansion of the interaction function is extended to the relativistic case. Explicit and general formulas are obtained for the efficient evaluation or handling of atomic electron-electron integrals over bispinorial one-electron functions, including the electromagnetic interaction with retardation effects and the parity-nonconserving weak interaction in both the Yukawa and contact forms.
Generalized Ohm's law for a background plasma in the presence of relativistic charged particles.
Sherlock, M
2010-05-21
A generalized Ohm's law is derived for a system composed of a background magnetohydrodynamic plasma and a lower density relativistic charged-particle distribution. The interpretation of Ohmic electric fields occurring due to force balance breaks down for such a system and instead an approach based on Maxwell's equations along with the particle flux equations is necessary. Three additional terms arise in Ohm's law and each is verified numerically.
Generalized Ohm's Law for a Background Plasma in the Presence of Relativistic Charged Particles
Sherlock, M.
2010-05-21
A generalized Ohm's law is derived for a system composed of a background magnetohydrodynamic plasma and a lower density relativistic charged-particle distribution. The interpretation of Ohmic electric fields occurring due to force balance breaks down for such a system and instead an approach based on Maxwell's equations along with the particle flux equations is necessary. Three additional terms arise in Ohm's law and each is verified numerically.
A generalized Jaynes-Cummings model: The relativistic parametric amplifier and a single trapped ion
Ojeda-Guillén, D.; 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.
NASA Astrophysics Data System (ADS)
Pétri, J.
2015-03-01
The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1 formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multidomain decomposition of the simulation box belongs to the discontinuous Galerkin finite element methods. We performed several sets of simulations to look for the general relativistic force-free monopole and split monopole solutions. Results show that our code is extremely powerful in handling extended domains of hundredth of light cylinder radii rL. The code has been validated against known exact analytical monopole solutions in flat space-time. We also present semi-analytical calculations for the general relativistic vacuum monopole.
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.
Exact relativistic expressions for wave refraction in a generally moving fluid.
Cavalleri, G; Tonni, E; Barbero, F
2013-04-01
The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins' linearized theory of gravitation.
NASA Astrophysics Data System (ADS)
Farafonov, V. G.; Ustimov, V. I.
2017-02-01
In the problem of light scattering by small axisymmetric particles, we have constructed the Rayleigh approximation in which the polarizability of particles is determined by the generalized separation of variables method (GSVM). In this case, electric-field strengths are gradients of scalar potentials, which are represented as expansions in term of eigenfunctions of the Laplace operator in the spherical coordinate system. By virtue of the fact that the separation of variables in the boundary conditions is incomplete, the initial problem is reduced to infinite systems of linear algebraic equations (ISLAEs) with respect to unknown expansion coefficients. We have examined the asymptotic behavior of ISLAE elements at large values of indices. It has been shown that the necessary condition of the solvability of the ISLAE coincides with the condition of correct application of the extended boundary conditions method (EBCM). We have performed numerical calculations for Chebyshev particles with one maximum (also known as Pascal's snails or limaçons of Pascal). The obtained numerical results for the asymptotics of ISLAE elements and for the matrix support theoretical inferences. We have shown that the scattering and absorption cross sections of examined particles can be calculated in a wide range of variation of parameters with an error of about 1-2% using the spheroidal model. This model is also applicable in the case in which the solvability condition of the ISLAE for nonconvex particles is violated; in this case, the SVM should be considered as an approximate method, which frequently ensures obtaining results with an error less than 0.1-0.5%.
NASA Astrophysics Data System (ADS)
Sądowski, Aleksander; Narayan, Ramesh; Tchekhovskoy, Alexander; Abarca, David; Zhu, Yucong; McKinney, Jonathan C.
2015-02-01
We present a mean-field model that emulates the magnetic dynamo operating in magnetized accretion discs. We have implemented this model in the general relativisic radiation magnetohydrodynamic (GRRMHD) code KORAL, using results from local shearing sheet simulations of the magnetorotational instability to fix the parameters of the dynamo. With the inclusion of this dynamo, we are able to run 2D axisymmetric GRRMHD simulations of accretion discs for arbitrarily long times. The simulated discs exhibit sustained turbulence, with the poloidal and toroidal magnetic field components driven towards a state similar to that seen in 3D studies. Using this dynamo code, we present a set of long-duration global simulations of super-Eddington, optically thick discs around non-spinning and spinning black holes. Super-Eddington discs around non-rotating black holes exhibit a surprisingly large efficiency, η ≈ 0.04, independent of the accretion rate, where we measure efficiency in terms of the total energy output, both radiation and mechanical, flowing out to infinity. This value significantly exceeds the efficiency predicted by slim disc models for these accretion rates. Super-Eddington discs around spinning black holes are even more efficient, and appear to extract black hole rotational energy through a process similar to the Blandford-Znajek mechanism. All the simulated models are characterized by highly super-Eddington radiative fluxes collimated along the rotation axis. We also present a set of simulations that were designed to have Eddington or slightly sub-Eddington accretion rates (dot{M} ≲ 2dot{M}_Edd). None of these models reached a steady state. Instead, the discs collapsed as a result of runaway cooling, presumably because of a thermal instability.
Logunov, A.A.; Loskutov, Y.M.
1987-05-01
It is shown that whereas the predictions of the relativistic theory of gravitation for gravitational effects are unambiguous and agree with the known experimental data, the corresponding predictions of the general theory of relativity are ambiguous. In some effects, the ambiguity appears in the first order in the gravitational coupling constant; in others, in the second. The absence in the general theory of relativity of conservation laws for energy, momentum, and angular momentum of the matter and gravitational field taken together, and also its inability to give unique predictions for gravitational phenomena, make it necessary to abandon the theory of relativity as a physical theory.
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.
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.
Towards Robust Discontinuous Galerkin Methods for General Relativistic Neutrino Radiation Transport
NASA Astrophysics Data System (ADS)
Endeve, E.; Hauck, C. D.; Xing, Y.; Mezzacappa, A.
2015-10-01
With an eye towards simulating neutrino transport in core-collapse supernovae, we have developed a conservative, robust, and high-order numerical method for solving the general relativistic phase space advection problem in stationary spacetimes. The method achieves high-order accuracy using Discontinuous Galerkin discretization and Runge-Kutta time integration. For robustness, care is taken to ensure that the physical bounds on the phase space distribution function are preserved; i.e., f ∈ [0,1]. We briefly describe the bound-preserving scheme, and present results from numerical experiments in spherical symmetry adopting the Schwarzschild metric, which demonstrate that the method preserves the bounds on the distribution function.
NASA Astrophysics Data System (ADS)
Paschalidis, Vasileios; Etienne, Zachariah B.; Shapiro, Stuart L.
2013-07-01
We perform the first general relativistic force-free simulations of neutron star magnetospheres in orbit about spinning and nonspinning black holes. We find promising precursor electromagnetic emission: typical Poynting luminosities at, e.g., an orbital separation of r=6.6RNS are LEM˜6×1042(BNS,p/1013G)2(MNS/1.4M⊙)2erg/s. The Poynting flux peaks within a broad beam of ˜40° in the azimuthal direction and within ˜60° from the orbital plane, establishing a possible lighthouse effect. Our calculations, though preliminary, preview more detailed simulations of these systems that we plan to perform in the future.
Caballero, O. L.; McLaughlin, G. C.; Surman, R. E-mail: olcaball@ncsu.edu E-mail: surmanr@union.edu
2012-02-01
Black hole (BH) accretion disks have been proposed as good candidates for a range of interesting nucleosynthesis, including the r-process. The presence of the BH influences the neutrino fluxes and affects the nucleosynthesis resulting from the interaction of the emitted neutrinos and hot outflowing material ejected from the disk. We study the impact of general relativistic effects on the neutrinos emitted from BH accretion disks. We present abundances obtained by considering null geodesics and energy shifts for two different disk models. We find that both the bending of the neutrino trajectories and the energy shifts have important consequences for the nucleosynthetic outcome.
Cosmological Relativity: A General-Relativistic Theory for the Accelerating Expanding Universe
NASA Astrophysics Data System (ADS)
Carmeli, M.; Behar, S.
Recent observations of distant supernovae imply, in defiance of expectations, that the universe growth is accelerating, contrary to what has always been assumed that the expansion is slowing down due to gravity. In this paper a general-relativistic cosmological theory that gives a direct relationship between distances and redshifts in an expanding universe is presented. The theory is actually a generalization of Hubble's law taking gravity into account by means of Einstein's theory of general relativity. The theory predicts that the universe can have three phases of expansion, decelerating, constant and accelerating, but it is shown that at present the first two cases are excluded, although in the past it had experienced them. Our theory shows that the universe now is definitely in the stage of accelerating expansion, confirming the recent experimental results.
General relativistic x ray (UV) polarization rotations as a quantitative test for black holes
NASA Technical Reports Server (NTRS)
Stark, Richard F.
1989-01-01
It is now 11 years since a potentially easily observable and quantitative test for black holes using general relativistic polarization rotations was proposed (Stark and Connors 1977, and Connors and Stark 1977). General relativistic rotations of the x ray polarization plane of 10 to 100 degrees with x ray energy (between 1 and 100 keV) are predicted for black hole x ray binaries. (Classically, by symmetry, there is no rotation.) Unfortunately, x ray polarimetry has not been taken sufficiently seriously during this period, and this test has not yet been performed. A similar (though probably less clean) effect is expected in the UV for supermassive black holes in some quasars active galactic nuclei. Summarizing: (1) a quantitative test (proposed in 1977) for black holes exists; (2) x ray polarimetry of galactic x ray binaries sensitive to at least 1/2 percent between 1 keV and 100 keV is needed (polarimetry in the UV of quasars and AGN will also be of interest); and (3) proportional counters using timerise discrimination were shown in laboratory experiments able to perform x ray polarimetry and this and other methods need to be developed.
GENERAL RELATIVISTIC SIMULATIONS OF MAGNETIZED PLASMAS AROUND MERGING SUPERMASSIVE BLACK HOLES
Giacomazzo, Bruno; Baker, John G.; Van Meter, James R.; Coleman Miller, M.; Reynolds, Christopher S.
2012-06-10
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 Letter, 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 a 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 much stronger electromagnetic signals, more than a factor of 10{sup 4} larger than comparable calculations done in the force-free regime where such amplifications are not possible.
THE GENERAL RELATIVISTIC EQUATIONS OF RADIATION HYDRODYNAMICS IN THE VISCOUS LIMIT
Coughlin, Eric R.; Begelman, Mitchell C. E-mail: mitch@jila.colorado.edu
2014-12-20
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.
NASA Astrophysics Data System (ADS)
Silenko, Alexander J.
2015-02-01
A general method of the Foldy-Wouthuysen transformation is developed. This method is applicable to relativistic particles with any spin in arbitrarily strong external fields. It can be used when the de Broglie wavelength is much smaller than the characteristic distance. Contrary to previously developed relativistic methods, the present method satisfies the condition of the exact Foldy-Wouthuysen transformation and is well substantiated. The derived relativistic Foldy-Wouthuysen Hamiltonian is expanded in powers of the Planck constant. In this expansion, terms proportional to the zero and first powers are determined exactly in accordance with the above condition, and terms proportional to higher powers are not specified. The obtained result agrees with the corresponding formula for the Foldy-Wouthuysen Hamiltonian previously deduced by an iterative relativistic method and proves the validity of results obtained with this formula.
NASA Astrophysics Data System (ADS)
Shiokawa, Hotaka; Dolence, Joshua C.; Gammie, Charles F.; Noble, Scott C.
2012-01-01
Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 × 96 × 64 to 384 × 384 × 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma β (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma β decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model ("shearing box") calculations and with the recent non-relativistic global convergence studies of Hawley et al.
General-relativistic celestial mechanics. I. Method and definition of reference systems
Damour, T. Departement d'Astrophysique Relativiste et de Cosmologie, Observatoire de Paris, Centre National de la Recherche Scientifique, 92195 Meudon CEDEX, France ); Soffel, M.; Xu, C. )
1991-05-15
We present a new formalism for treating the general-relativistic celestial mechanics of systems of {ital N} arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies. This formalism is aimed at yielding a complete description, at the first post-Newtonian approximation level, of (i) the global dynamics of such {ital N}-body systems ( external problem''), (ii) the local gravitational structure of each body ( internal problem''), and, (iii) the way the external and the internal problems fit together ( theory of reference systems''). This formalism uses in a complementary manner {ital N}+1 coordinate charts (or reference systems''): one global'' chart for describing the overall dynamics of the {ital N} bodies, and {ital N} local'' charts adapted to the separate description of the structure and environment of each body. The main tool which allows us to develop, in an elegant manner, a constructive theory of these {ital N}+1 reference systems is a systematic use of a particular exponential'' parametrization of the metric tensor which has the effect of linearizing both the field equations, and the transformation laws under a change of reference system. This linearity allows a treatment of the first post-Newtonian relativistic celestial mechanics which is, from a structural point of view, nearly as simple and transparent as its Newtonian analogue.
General relativistic simulations of black-hole-neutron-star mergers: Effects of magnetic fields
NASA Astrophysics Data System (ADS)
Etienne, Zachariah B.; Liu, Yuk Tung; Paschalidis, Vasileios; Shapiro, Stuart L.
2012-03-01
As a neutron star (NS) is tidally disrupted by a black hole (BH) companion at the end of a black-hole-neutron-star (BHNS) binary inspiral, its magnetic fields will be stretched and amplified. If sufficiently strong, these magnetic fields may impact the gravitational waveforms, merger evolution and mass of the remnant disk. Formation of highly-collimated magnetic field lines in the disk+spinning BH remnant may launch relativistic jets, providing the engine for a short-hard GRB. We analyze this scenario through fully general relativistic, magnetohydrodynamic BHNS simulations from inspiral through merger and disk formation. Different initial magnetic field configurations and strengths are chosen for the NS interior for both nonspinning and moderately spinning (aBH/MBH=0.75) BHs aligned with the orbital angular momentum. Only strong interior (Bmax˜1017G) initial magnetic fields in the NS significantly influence merger dynamics, enhancing the remnant disk mass by 100% and 40% in the nonspinning and spinning BH cases, respectively. However, detecting the imprint of even a strong magnetic field may be challenging for Advanced LIGO. Though there is no evidence of mass outflows or magnetic field collimation during the preliminary simulations we have performed, higher resolution, coupled with longer disk evolutions and different initial magnetic field configurations, may be required to definitively assess the possibility of BHNS binaries as short-hard gamma-ray burst progenitors.
Shiokawa, Hotaka; Dolence, Joshua C.; Gammie, Charles F.; Noble, Scott C.
2012-01-10
Global, general relativistic magnetohydrodynamic (GRMHD) simulations of non-radiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of four in linear resolution, from 96 Multiplication-Sign 96 Multiplication-Sign 64 to 384 Multiplication-Sign 384 Multiplication-Sign 256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma {beta}; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma {beta} decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of two in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model ({sup s}hearing box{sup )} calculations and with the recent non-relativistic global convergence studies of Hawley et al.
NASA Astrophysics Data System (ADS)
Del Zanna, L.; Zanotti, O.; Bucciantini, N.; Londrillo, P.
2007-10-01
Aims:We present a new numerical code, ECHO, based on a Eulerian conservative high-order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework based on the 3+1 Eulerian formalism, allowing for different sets of equations and different algorithms and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein's equations. Methods: Our finite-difference conservative scheme previously developed for special relativistic hydrodynamics and MHD is extended here to the general relativistic case. Various high-order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the upwind constrained transport (UCT) procedures, appropriate to preserving the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the contribution of matter to the stress tensor. Results: ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, like magnetized accretion onto black holes and constant angular momentum thick disks threaded by toroidal fields. A novel test of the propagation of large-amplitude, circularly polarized Alfvén waves is proposed, and this allows us to prove the spatial and temporal high-order properties of ECHO very accurately. In particular, we show that reconstruction based on a monotonicity-preserving (MP) filter applied to a
The 2D surfaces that generate Newtonian and general relativistic orbits with small eccentricities
NASA Astrophysics Data System (ADS)
Middleton, Chad A.
2015-07-01
Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript, we present a different 2D construct that also serves as a useful conceptual tool for gaining insight into gravitation: orbital dynamics—namely, the cylindrically symmetric surfaces that generate Newtonian and general relativistic orbits with small eccentricities. Although we first show that no such surface exists that can exactly reproduce the arbitrary bound orbits of Newtonian gravitation or of general relativity (or, more generally, of any spherically symmetric potential), surfaces do exist that closely approximate the resulting orbital motion for small eccentricities (exactly the regime that describes the motion of the solar system planets). These surfaces help to illustrate the similarities and differences between the two theories of gravitation (i.e., stationary elliptical orbits in Newtonian gravitation and precessing elliptical-like orbits in general relativity) and offer, in this age of 3D printing, an opportunity for students and instructors to experimentally explore the predictions made by each.
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.
General relativistic models for rotating magnetized neutron stars in conformally flat space-time
NASA Astrophysics Data System (ADS)
Pili, A. G.; Bucciantini, N.; Del Zanna, L.
2017-09-01
The extraordinary energetic activity of magnetars is usually explained in terms of dissipation of a huge internal magnetic field of the order of 1015-16 G. How such a strong magnetic field can originate during the formation of a neutron star (NS) is still subject of active research. An important role can be played by fast rotation: if magnetars are born as millisecond rotators dynamo mechanisms may efficiently amplify the magnetic field inherited from the progenitor star during the collapse. In this case, the combination of rapid rotation and strong magnetic field determine the right physical condition not only for the development of a powerful jet-driven explosion, manifesting as a gamma-ray burst, but also for a copious gravitational waves emission. Strong magnetic fields are indeed able to induce substantial quadrupolar deformations in the star. In this paper, we analyse the joint effect of rotation and magnetization on the structure of a polytropic and axisymmetric NS, within the ideal magneto-hydrodynamic regime. We will consider either purely toroidal or purely poloidal magnetic field geometries. Through the sampling of a large parameter space, we generalize previous results in literature, inferring new quantitative relations that allow for a parametrization of the induced deformation, that takes into account also the effects due to the stellar compactness and the current distribution. Finally, in the case of purely poloidal field, we also discuss how different prescription on the surface charge distribution (a gauge freedom) modify the properties of the surrounding electrosphere and its physical implications.
GENERAL-RELATIVISTIC SIMULATIONS OF THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE
Ott, Christian D.; Abdikamalov, Ernazar; Moesta, Philipp; Haas, Roland; Drasco, Steve; O'Connor, Evan P.; Reisswig, Christian; Meakin, Casey A.; Schnetter, Erik
2013-05-10
We study the three-dimensional (3D) hydrodynamics of the post-core-bounce phase of the collapse of a 27 M{sub Sun} star and pay special attention to the development of the standing accretion shock instability (SASI) and neutrino-driven convection. To this end, we perform 3D general-relativistic simulations with a three-species neutrino leakage scheme. The leakage scheme captures the essential aspects of neutrino cooling, heating, and lepton number exchange as predicted by radiation-hydrodynamics simulations. The 27 M{sub Sun} progenitor was studied in 2D by Mueller et al., who observed strong growth of the SASI while neutrino-driven convection was suppressed. In our 3D simulations, neutrino-driven convection grows from numerical perturbations imposed by our Cartesian grid. It becomes the dominant instability and leads to large-scale non-oscillatory deformations of the shock front. These will result in strongly aspherical explosions without the need for large-scale SASI shock oscillations. Low-l-mode SASI oscillations are present in our models, but saturate at small amplitudes that decrease with increasing neutrino heating and vigor of convection. Our results, in agreement with simpler 3D Newtonian simulations, suggest that once neutrino-driven convection is started, it is likely to become the dominant instability in 3D. Whether it is the primary instability after bounce will ultimately depend on the physical seed perturbations present in the cores of massive stars. The gravitational wave signal, which we extract and analyze for the first time from 3D general-relativistic models, will serve as an observational probe of the postbounce dynamics and, in combination with neutrinos, may allow us to determine the primary hydrodynamic instability.
Cosmology and stellar equilibrium using Newtonian hydrodynamics with general relativistic pressure
NASA Astrophysics Data System (ADS)
Baqui, P. O.; Fabris, J. C.; Piattella, O. F.
2016-04-01
We revisit the analysis made by Hwang and Noh [JCAP 1310 (2013)] aiming the construction of a Newtonian set of equations incorporating pressure effects typical of the General Relativity theory. We explicitly derive the Hwang-Noh equations, comparing them with similar computations found in the literature. Then, we investigate i) the cosmological expansion, ii) linear cosmological perturbations theory and iii) stellar equilibrium by using the new set of equations and comparing the results with those coming from the usual Newtonian theory, from the Neo-Newtonian theory and from the General Relativity theory. We show that the predictions for the background evolution of the Universe are deeply changed with respect to the General Relativity theory: the acceleration of the Universe is achieved with positive pressure. On the other hand, the behaviour of small cosmological perturbations reproduces the one found in the relativistic context, even if only at small scales. We argue that this last result may open new possibilities for numerical simulations for structure formation in the Universe. Finally, the properties of neutron stars are qualitatively reproduced by Hwang-Noh equations, but the upper mass limit is at least one order of magnitude higher than the one obtained in General Relativity.
General relativistic corrections to N -body simulations and the Zel'dovich approximation
NASA Astrophysics Data System (ADS)
Fidler, Christian; Rampf, Cornelius; Tram, Thomas; Crittenden, Robert; Koyama, Kazuya; Wands, David
2015-12-01
The initial conditions for Newtonian N -body simulations are usually generated by applying the Zel'dovich approximation to the initial displacements of the particles using an initial power spectrum of density fluctuations generated by an Einstein-Boltzmann solver. We show that in most gauges the initial displacements generated in this way receive a first-order relativistic correction. We define a new gauge, the N -body gauge, in which this relativistic correction vanishes and show that a conventional Newtonian N -body simulation includes all first-order relativistic contributions (in the absence of radiation) if we identify the coordinates in Newtonian simulations with those in the relativistic N -body gauge.
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
A GENERAL RELATIVISTIC MODEL OF ACCRETION DISKS WITH CORONAE SURROUNDING KERR BLACK HOLES
You Bei; Cao Xinwu; Yuan Yefei E-mail: cxw@shao.ac.cn
2012-12-20
We calculate the structure of a standard accretion disk with a corona surrounding a massive Kerr black hole in the general relativistic frame, in which the corona is assumed to be heated by the reconnection of the strongly buoyant magnetic fields generated in the cold accretion disk. The emergent spectra of accretion disk-corona systems are calculated by using the relativistic ray-tracing method. We propose a new method to calculate the emergent Comptonized spectra from the coronae. The spectra of disk-corona systems with a modified {alpha}-magnetic stress show that both the hard X-ray spectral index and the hard X-ray bolometric correction factor L{sub bol}/L{sub X,2-10keV} increase with the dimensionless mass accretion rate, which is qualitatively consistent with the observations of active galactic nuclei. The fraction of the power dissipated in the corona decreases with increasing black hole spin parameter a, which leads to lower electron temperatures of the coronae for rapidly spinning black holes. The X-ray emission from the coronae surrounding rapidly spinning black holes becomes weak and soft. The ratio of the X-ray luminosity to the optical/UV luminosity increases with the viewing angle, while the spectral shape in the X-ray band is insensitive to the viewing angle. We find that the spectral index in the infrared waveband depends on the mass accretion rate and the black hole spin a, which deviates from the f{sub {nu}}{proportional_to}{nu}{sup 1/3} relation expected by the standard thin disk model.
Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics
NASA Astrophysics Data System (ADS)
Wu, Kailiang
2017-05-01
The paper develops high-order physical-constraint-preserving (PCP) methods for general relativistic hydrodynamic (GRHD) equations, equipped with a general equation of state. Here the physical constraints, describing the admissible states of GRHD, are referred to the subluminal constraint on the fluid velocity and the positivity of the density, pressure and specific internal energy. Preserving these constraints is very important for robust computations, otherwise violating one of them will lead to the ill-posed problem and numerical instability. To overcome the difficulties arising from the inherent strong nonlinearity contained in the constraints, we derive an equivalent definition of the admissible states. Using this definition, we prove the convexity, scaling invariance and Lax-Friedrichs (LxF) splitting property of the admissible state set G , and discover the dependence of G on the spacetime metric. Unfortunately, such dependence yields the nonequivalence of G at different points in curved spacetime, and invalidates the convexity of G in analyzing PCP schemes. This obstacle is effectively overcame by introducing a new formulation of the GRHD equations. Based on this formulation and the above theories, a first-order LxF scheme is designed on general unstructured mesh and rigorously proved to be PCP under a Courant-Friedrichs-Lewy (CFL) condition. With two types of PCP limiting procedures, we design high-order, provably (not probably) PCP methods under discretization on the proposed new formulation. These high-order methods include the PCP finite difference, finite volume and discontinuous Galerkin methods.
Zhang Yongpeng; Liu Guozhi; Yang Zhanfeng; Shao Hao; Xiao Renzhen; Xing Qingzi; Zhong Huaqiang; Lin Yuzheng
2009-04-15
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.
NASA Astrophysics Data System (ADS)
Shiokawa, Hotaka
The goal of the series of studies in this thesis is to understand the black hole accretion process and predict its observational properties. The highly non-linear process involves a turbulent magnetized plasma in a general relativistic regime, thus making it hard to study analytically. We use numerical simulations, specifically general relativistic magnetohydrodynamics (GRMHD), to construct a realistic dynamical and radiation model of accretion disks. Our simulations are for black holes in low luminous regimes that probably possesses a hot and thick accretion disk. Flows in this regime are called radiatively inefficient accretion flows (RIAF). The most plausible mechanism for transporting angular momentum is turbulence induced by magnetorotational instability (MRI). The RIAF model has been used to model the supermassive black hole at the center of our Milky Way galaxy, Sagittarius A* (Sgr A*). Owing to its proximity, rich observational data of Sgr A* is available to compare with the simulation results. We focus mainly on four topics. First, we analyse numerical convergence of 3D GRMHD global disk simulations. Convergence is one of the essential factors in deciding quantitative outcomes of the simulations. We analyzed dimensionless shell-averaged quantities such as plasma beta, the azimuthal correlation length (angle) of fluid variables, and spectra of the source for four different resolutions. We found that all the variables converged with the highest resolution (384x384x256 in radial, poloidal, and azimuthal directions) except the magnetic field correlation length. It probably requires another factor of 2 in resolution to achieve convergence. Second, we studied the effect of equation of state on dynamics of GRMHD simulation and radiative transfer. Temperature of RIAF gas is high, and all the electrons are relativistic, but not the ions. In addition, the dynamical time scale of the accretion disk is shorter than the collisional time scale of electrons and ions
Relativistic thermodynamics, a Lagrangian field theory for general flows including rotation
NASA Astrophysics Data System (ADS)
Frønsdal, Christian
Any theory that is based on an action principle has a much greater predictive power than one that does not have such a formulation. The formulation of a dynamical theory of General Relativity, including matter, is here viewed as a problem of coupling Einstein’s theory of pure gravity to an independently chosen and well-defined field theory of matter. It is well known that this is accomplished in a most natural way when both theories are formulated as relativistic, Lagrangian field theories, as is the case with Einstein-Maxwell theory. Special matter models of this type have been available; here a more general thermodynamical model that allows for vortex flows is presented. In a wider context, the problem of subjecting hydrodynamics and thermodynamics to an action principle is one that has been pursued for at least 150 years. A solution to this problem has been known for some time, but only under the strong restriction to potential flows. A variational principle for general flows has become available. It represents a development of the Navier-Stokes-Fourier approach to fluid dynamics. The principal innovation is the recognition that two kinds of flow velocity fields are needed, one the gradient of a scalar field and the other the time derivative of a vector field, the latter closely associated with vorticity. In the relativistic theory that is presented here, the latter is the Hodge dual of an exact 3-form, well known as the notoph field of Ogievetskij and Palubarinov, the B-field of Kalb and Ramond and the vorticity field of Lund and Regge. The total number of degrees of freedom of a unary system, including the density and the two velocity fields is 4, as expected — as in classical hydrodynamics. In this paper, we do not reduce Einstein’s dynamical equation for the metric to phenomenology, which would have denied the relevance of any intrinsic dynamics for the matter sector, nor do we abandon the equation of continuity - the very soul of hydrodynamics.
Generalizing spin and pseudospin symmetries for relativistic spin 1/2 fermions
NASA Astrophysics Data System (ADS)
Alberto, P.; Malheiro, M.; Frederico, T.; de Castro, A.
2016-08-01
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70’s by Smith and Tassie, and Bell and Ruegg. As relativistic symmetries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrödinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2- and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
NASA Astrophysics Data System (ADS)
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Newtonian analogue of static general relativistic spacetimes: An extension to naked singularities
NASA Astrophysics Data System (ADS)
Ghosh, Shubhrangshu; Sarkar, Tamal; Bhadra, Arunava
2015-10-01
We formulate a generic Newtonian-like analogous potential for static spherically symmetric general relativistic (GR) spacetime and subsequently derived proper Newtonian-like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials were found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries show altogether different behaviors with distinctive traits as compared to the nature of particle dynamics in Schwarzschild geometry. Exploiting the Newtonian-like analogous potentials, we found that the radiative efficiency of a geometrically thin and optically thick Keplerian accretion disk around naked singularities corresponding to both JNW and RN geometries, in general, is always higher than that for Schwarzschild geometry. The derived potentials would thus be useful to study astrophysical processes, especially to investigate more complex accretion phenomena in active galactic nuclei (AGNs) or in x-ray binaries (XRBs) in the presence of naked singularities and thereby to explore any noticeable differences in their observational features from those in the presence of black holes (BHs) to ascertain outstanding debatable issues relating to gravity—whether the end state of gravitational collapse in our physical Universe renders BH or naked singularity.
Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: thj@mpa-garching.mpg.de
2012-09-01
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M{sub Sun} progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas; Marek, Andreas
2012-09-01
We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the COCONUT hydrodynamics code in combination with the VERTEX solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the space-time metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15 M ⊙ progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the PROMETHEUS hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared with Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models, the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50%-100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions.
NASA Astrophysics Data System (ADS)
Varjú, Katalin; Ryder, Lewis H.
2000-05-01
In the Colella-Overhauser-Werner (COW) experiment a gravity-induced phase shift of spin 1/2 particles was detected. The experimental results were explained by using the Newtonian theory of gravity. The explanation can be easily given using general relativistic arguments and the highest order term reproduces the result of Colella, Overhauser, and Werner together with additional, lower order corrections. The derivation can be considered as an interesting exercise for students with basic knowledge of the field of general relativity.
Non-axisymmetric annular curtain stability
NASA Astrophysics Data System (ADS)
Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian
2013-08-01
A stability analysis of non-axisymmetric annular curtain is carried out for an axially moving viscous jet subject in surrounding viscous gas media. The effect of inertia, surface tension, gas-to-liquid density ratio, inner-to-outer radius ratio, and gas-to-liquid viscosity ratio on the stability of the jet is studied. In general, the axisymmetric disturbance is found to be the dominant mode. However, for small wavenumber, the non-axisymmetric mode is the most unstable mode and the one likely observed in reality. Inertia and the viscosity ratio for non-axisymmetric disturbances show a similar stability influence as observed for axisymmetric disturbances. The maximum growth rate in non-axisymmetric flow, interestingly, appears at very small wavenumber for all inertia levels. The dominant wavenumber increases (decreases) with inertia for non-axisymmetric (axisymmetric) flow. Gas-to-liquid density ratio, curvature effect, and surface tension, however, exhibit an opposite influence on growth rate compared to axisymmetric disturbances. Surface tension tends to stabilize the flow with reductions of the unstable wavenumber range and the maximum growth rate as well as the dominant wavenumber. The dominant wavenumber remains independent of viscosity ratio indicating the viscosity ratio increases the breakup length of the sheet with very little influence on the size of the drops. The range of unstable wavenumbers is affected only by curvature in axisymmetric flow, whereas all the stability parameters control the range of unstable wavenumbers in non-axisymmetric flow. Inertia and gas density increase the unstable wavenumber range, whereas the radius ratio, surface tension, and the viscosity ratio decrease the unstable wavenumber range. Neutral curves are plotted to separate the stable and unstable domains. Critical radius ratio decreases linearly and nonlinearly with the wavenumber for axisymmetric and non-axisymmetric disturbances, respectively. At smaller Weber numbers, a
The general relativistic instability supernova of a supermassive population III star
Chen, Ke-Jung; Woosley, Stan; Heger, Alexander; Almgren, Ann; Whalen, Daniel J.; Johnson, Jarrett L.
2014-08-01
The formation of supermassive Population III stars with masses ≳10,000 M{sub ☉} in primeval galaxies in strong ultraviolet backgrounds at z ∼ 15 may be the most viable pathway to the formation of supermassive black holes by z ∼ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M{sub ☉} can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 10{sup 55} erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z ≲ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.
NASA Astrophysics Data System (ADS)
Endrizzi, Andrea; Ciolfi, Riccardo; Giacomazzo, Bruno; Kastaun, Wolfgang; Kawamura, Takumu
2016-03-01
We present new results of fully general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state (EOS) for cold matter, together with a ''hybrid'' part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole (BH) is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant properties, disk mass). Our new simulations provide a further important step in the understanding of these GW sources and their possible connection with the engine of short gamma-ray bursts (both in the ``standard'' and in the ``time-reversal'' scenarios) and with other electromagnetic counterparts.
NASA Astrophysics Data System (ADS)
Endrizzi, A.; Ciolfi, R.; Giacomazzo, B.; Kastaun, W.; Kawamura, T.
2016-08-01
We present new results of fully general relativistic magnetohydrodynamic simulations of binary neutron star (BNS) mergers performed with the Whisky code. All the models use a piecewise polytropic approximation of the APR4 equation of state for cold matter, together with a ‘hybrid’ part to incorporate thermal effects during the evolution. We consider both equal and unequal-mass models, with total masses such that either a supramassive NS or a black hole is formed after merger. Each model is evolved with and without a magnetic field initially confined to the stellar interior. We present the different gravitational wave (GW) signals as well as a detailed description of the matter dynamics (magnetic field evolution, ejected mass, post-merger remnant/disk properties). Our simulations provide new insights into BNS mergers, the associated GW emission and the possible connection with the engine of short gamma-ray bursts (both in the ‘standard’ and in the ‘time-reversal’ scenarios) and other electromagnetic counterparts.
The General Relativistic Instability Supernova of a Supermassive Population III Star
NASA Astrophysics Data System (ADS)
Chen, Ke-Jung; Heger, Alexander; Woosley, Stan; Almgren, Ann; Whalen, Daniel J.; Johnson, Jarrett L.
2014-08-01
The formation of supermassive Population III stars with masses gsim10,000 M ⊙ in primeval galaxies in strong ultraviolet backgrounds at z ~ 15 may be the most viable pathway to the formation of supermassive black holes by z ~ 7. Most of these stars are expected to live for short times and then directly collapse to black holes, with little or no mass loss over their lives. However, we have now discovered that non-rotating primordial stars with masses close to 55,000 M ⊙ can instead die as highly energetic thermonuclear supernovae powered by explosive helium burning, releasing up to 1055 erg, or about 10,000 times the energy of a Type Ia supernova. The explosion is triggered by the general relativistic contribution of thermal photons to gravity in the core of the star, which causes the core to contract and explosively burn. The energy release completely unbinds the star, leaving no compact remnant, and about half of the mass of the star is ejected into the early cosmos in the form of heavy elements. The explosion would be visible in the near infrared at z <~ 20 to Euclid and the Wide-Field Infrared Survey Telescope, perhaps signaling the birth of supermassive black hole seeds and the first quasars.
General Relativistic Simulations of Low-Mass Magnetized Binary Neutron Star Mergers
NASA Astrophysics Data System (ADS)
Giacomazzo, Bruno
2017-01-01
We will present general relativistic magnetohydrodynamic (GRMHD) simulations of binary neutron star (BNS) systems that produce long-lived neutron stars (NSs) after merger. While the standard scenario for short gamma-ray bursts (SGRBs) requires the formation after merger of a spinning black hole surrounded by an accretion disk, other theoretical models, such as the time-reversal scenario, predict the formation of a long-lived magnetar. The formation of a long-lived magnetar could in particular explain the X-ray plateaus that have been observed in some SGRBs. Moreover, observations of NSs with masses of 2 solar masses indicate that the equation of state of NS matter should support masses larger than that. Therefore a significant fraction of BNS mergers will produce long-lived NSs. This has important consequences both on the emission of gravitational wave signals and on their electromagnetic counterparts. We will discuss GRMHD simulations of ``low-mass'' magnetized BNS systems with different equations of state and mass ratios. We will describe the properties of their post-merger remnants and of their gravitational and electromagnetic emission.
Odyssey: A Public GPU-based Code for General Relativistic Radiative Transfer in Kerr Spacetime
NASA Astrophysics Data System (ADS)
Pu, Hung-Yi; Yun, Kiyun; Younsi, Ziri; Yoon, Suk-Jin
2016-04-01
General relativistic radiative transfer calculations coupled with the calculation of geodesics in the Kerr spacetime are an essential tool for determining the images, spectra, and light curves from matter in the vicinity of black holes. Such studies are especially important for ongoing and upcoming millimeter/submillimeter very long baseline interferometry observations of the supermassive black holes at the centers of Sgr A* and M87. To this end we introduce Odyssey, a graphics processing unit (GPU) based code for ray tracing and radiative transfer in the Kerr spacetime. On a single GPU, the performance of Odyssey can exceed 1 ns per photon, per Runge-Kutta integration step. Odyssey is publicly available, fast, accurate, and flexible enough to be modified to suit the specific needs of new users. Along with a Graphical User Interface powered by a video-accelerated display architecture, we also present an educational software tool, Odyssey_Edu, for showing in real time how null geodesics around a Kerr black hole vary as a function of black hole spin and angle of incidence onto the black hole.
Distorted turbulence in axisymmetric flow
NASA Technical Reports Server (NTRS)
Durbin, P. A.
1981-01-01
A solution to the rapid-distortion theory for small-scale turbulence in flow round an axisymmetric obstacle is derived. General formulae for velocity covariances and Eulerian time scales are obtained and are evaluated for the particular case of flow round a sphere. The large-scale limit for this flow is also discussed.
General-relativistic approach to the nonlinear evolution of collisionless matter
Matarrese, S.; Pantano, O. ); Saez, D. )
1993-02-15
A new general-relativistic algorithm is developed to study the nonlinear evolution of scalar (density) perturbations of an irrotational collisionless fluid up to shell crossing, under the approximation of neglecting the interaction with tensor (gravitational-wave) perturbations. The dynamics of each fluid element is separately followed in its own inertial rest frame by a system of twelve coupled first-order ordinary differential equations, which can be further reduced to six under very general conditions. Initial conditions are obtained in a cosmological framework, from linear theory, in terms of a single gauge-invariant potential. Physical observables, which are expressed in the Lagrangian form at different times, can be traced back to the Eulerian picture by solving supplementary first-order differential equations for the relative position vectors of neighboring fluid elements. Similarly to the Zel'dovich approximation, in our approach the evolution of each fluid element is completely determined by the local initial conditions and can be independently followed up to the time when it enters a multistream region. Unlike the Zel'dovich approximation, however, our approach is correct also in three dimensions (except for the possible role of gravitational waves). The accuracy of our numerical procedure is tested by integrating the nonlinear evolution of a spherical perturbation in an otherwise spatially flat Friedmann-Robertson-Walker universe and comparing the results with the exact Tolman-Bondi solution for the same initial profile. An exact solution for the planar symmetric case is also given, which turns out to be locally identical to the Zel'dovich solution.
NASA Astrophysics Data System (ADS)
Lou, Yu-Qing; Xia, Yu-Kai
2017-05-01
We study magnetohydrodynamic (MHD) self-similar collapses and void evolution, with or without shocks, of a general polytropic quasi-spherical magnetofluid permeated by random transverse magnetic fields under the Paczynski-Wiita gravity that captures essential general relativistic effects of a Schwarzschild black hole (BH) with a growing mass. Based on the derived set of non-linear MHD ordinary differential equations, we obtain various asymptotic MHD solutions, the geometric and analytical properties of the magnetosonic critical curve (MSCC) and MHD shock jump conditions. Novel asymptotic MHD solution behaviours near the rim of central expanding voids are derived analytically. By exploring numerical global MHD solutions, we identify allowable boundary conditions at large radii that accommodate a smooth solution and show that a reasonable amount of magnetization significantly increases the mass accretion rate in the expansion-wave-collapse solution scenario. We also construct the counterparts of envelope-expansion-core-collapse solutions that cross the MSCC twice, which are found to be closely paired with a sequence of global smooth solutions satisfying a novel type of central MHD behaviours. MHD shocks with static outer and various inner flow profiles are also examined. Astrophysical applications include dynamic core collapses of magnetized massive stars and compact objects as well as formation of supermassive, hypermassive, dark matter and mixed matter BHs in the Universe, including the early Universe. Such gigantic BHs can be detected in X-ray/gamma-ray sources, quasars, ultraluminous infrared galaxies or extremely luminous infrared galaxies and dark matter overwhelmingly dominated elliptical galaxies as well as massive dark matter halos, etc. Gravitational waves and electromagnetic wave emissions in broad band (including e.g., gamma-ray bursts and fast radio bursts) can result from this type of dynamic collapses of forming BHs involving magnetized media.
Relativistic Jets and Collapsars
NASA Astrophysics Data System (ADS)
Zhang, W.; Woosley, S. E.
2001-05-01
In order to study the relativistic jets from collapsars, we have developed a special relativistic multiple-dimensional hydrodynamics code similar to the GENESIS code (Aloy et al., ApJS, 122, 151). The code is based on the PPM interpolation algorithm and Marquina's Riemann solver. Using this code, we have simulated the propagation of axisymmetric jets along the rotational axis of collapsed rotating stars (collapsars). Using the progenitors of MacFadyen, Woosley, and Heger, a relativistic jet is injected at a given inner boundary radius. This radius, the opening angle of the jet, its Lorentz factor, and its total energy are parameters of the problem. A highly collimated, relativistic outflow is observed at the surface of the star several seconds later. We will discuss the hydrodynamical focusing of the jet, it's break out properties, time evolution, and sensitivity to the adopted parameters.
Verma, Bhupesh; Mishra, Tarun Kumar; Balasubramaniam, Krishnan; Rajagopal, Prabhu
2014-03-01
The use of ultrasonic guided waves for the inspection of pipes with elbow and U-type bends has received much attention in recent years, but studies for more general bend angles which may also occur commonly, for example in cross-country pipes, are limited. Here, we address this topic considering a general bend angle φ, a more general mean bend radius R in terms of the wavelength of the mode studied and pipe thickness b. We use 3D Finite Element (FE) simulation to understand the propagation of fundamental axisymmetric L(0,2) mode across bends of different angles φ. The effect of the ratio of the mean bend radius to the wavelength of the mode studied, on the transmission and reflection of incident wave is also considered. The studies show that as the bend angle is reduced, a progressively larger extent of mode-conversion affects the transmission and velocity characteristics of the L(0,2) mode. However the overall message on the potential of guided waves for inspection and monitoring of bent pipes remains positive, as bends seem to impact mode transmission only to the extent of 20% even at low bend angles. The conclusions seem to be valid for different typical pipe thicknesses b and bend radii. The modeling approach is validated by experiments and discussed in light of physics of guided waves.
NASA Astrophysics Data System (ADS)
Iorio, Lorenzo
2011-02-01
We analytically work out the cumulative, i.e. averaged over one orbital revolution, time variations ? of the radial velocity vρ of a typical S star orbiting the supermassive (M•≈ 106 M⊙) black hole (SBH) hosted by the Galactic Centre (GC) in Sgr A* caused by several dynamical effects. They are the general relativistic gravitoelectromagnetic (GEM) fields of the SBH, its quadrupole mass moment Q2 and a diffuse dark matter distribution around the SBH. All of them induce non-zero long-term radial accelerations proportional to the eccentricity e of the orbit. By taking the S2 star, orbiting the SBH along a highly eccentric (e= 0.8831) ellipse with a period Pb= 15.9 yr and semimajor axis a= 1031.69 au, we numerically compute the magnitudes of its radial accelerations. The largest effects are due to the general relativistic Schwarzschild-like gravitoelectric (GE) field, with ?, and the diffuse material distribution, modelled with a Plummer-type mass density profile, with ?. The effects caused by the general relativistic Kerr-type gravitomagnetic (GM) field and by Q2 are smaller by orders of magnitude. By assuming an uncertainty in measuring the radial velocities of about 15 km s-1, the future accuracy in measuring ? can be evaluated to be of the order of 2.4 × 10-5 m s-2 over an observational time-span Δt= 20 yr. Currently, the available radial velocity measurements cover just 7 yr.
Kuroda, Takami; Kotake, Kei; Takiwaki, Tomoya
2012-08-10
We present results from the first generation of multi-dimensional hydrodynamic core-collapse simulations in full general relativity (GR) that include an approximate treatment of neutrino transport. Using an M1 closure scheme with an analytic variable Eddington factor, we solve the energy-independent set of radiation energy and momentum based on the Thorne's momentum formalism. Our newly developed code is designed to evolve the Einstein field equation together with the GR radiation hydrodynamic equations. We follow the dynamics starting from the onset of gravitational core collapse of a 15 M{sub Sun} star, through bounce, up to about 100 ms postbounce in this study. By computing four models that differ according to 1D to 3D and by switching from special relativistic (SR) to GR hydrodynamics, we study how the spacial multi-dimensionality and GR would affect the dynamics in the early postbounce phase. Our 3D results support the anticipation in previous 1D results that the neutrino luminosity and average neutrino energy of any neutrino flavor in the postbounce phase increase when switching from SR to GR hydrodynamics. This is because the deeper gravitational well of GR produces more compact core structures, and thus hotter neutrino spheres at smaller radii. By analyzing the residency timescale to the neutrino-heating timescale in the gain region, we show that the criterion to initiate neutrino-driven explosions can be most easily satisfied in 3D models, irrespective of SR or GR hydrodynamics. Our results suggest that the combination of GR and 3D hydrodynamics provides the most favorable condition to drive a robust neutrino-driven explosion.
NASA Astrophysics Data System (ADS)
Liebendörfer, Matthias; Messer, O. E. Bronson; Mezzacappa, Anthony; Bruenn, Stephen W.; Cardall, Christian Y.; Thielemann, F.-K.
2004-01-01
We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, AGILE-BOLTZTRAN, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in self-consistent simulations of stellar core collapse and postbounce evolution. It implements a dynamically adaptive grid in comoving coordinates. A comoving frame in the momentum phase space facilitates the evaluation and tabulation of neutrino-matter interaction cross sections but produces a multitude of observer corrections in the transport equation. Most macroscopically interesting physical quantities are defined by expectation values of the distribution function. We optimize the finite differencing of the microscopic transport equation for a consistent evolution of important expectation values. We test our code in simulations launched from progenitor stars with 13 solar masses and 40 solar masses. Half a second after core collapse and bounce, the protoneutron star in the latter case reaches its maximum mass and collapses further to form a black hole. When the hydrostatic gravitational contraction sets in, we find a transient increase in electron flavor neutrino luminosities due to a change in the accretion rate. The μ- and τ-neutrino luminosities and rms energies, however, continue to rise because previously shock-heated material with a nondegenerate electron gas starts to replace the cool degenerate material at their production site. We demonstrate this by supplementing the concept of neutrinospheres with a more detailed statistical description of the origin of escaping neutrinos. Adhering to our tradition, we compare the evolution of the 13 Msolar progenitor star to corresponding simulations with the multigroup flux-limited diffusion approximation, based on a recently developed flux limiter. We find similar results in the postbounce phase and validate this MGFLD approach for the spherically symmetric
Change in general relativistic precession rates due to Lidov-Kozai oscillations in Solar system
NASA Astrophysics Data System (ADS)
Sekhar, A.; Asher, D. J.; Werner, S. C.; Vaubaillon, J.; Li, G.
2017-06-01
Both general relativistic (GR) precession and the Lidov-Kozai mechanism, separately, are known to play an important role in the orbital evolution of Solar system bodies. Previous works have studied these two mechanisms independently in great detail. However, both these phenomena occurring at the same time in real Solar system bodies have rarely been explored. In this work, we find a continuum connecting the GR precession dominant and Lidov-Kozai-like mechanism dominant regimes, i.e. an intermediate regime where the competing effects of GR precession and Lidov-Kozai-like oscillations coexist simultaneously. We find some real examples in the Solar system in this intermediate regime. Moreover, we identify a rare example among them, comet 96P/Machholz 1, which shows significant changes in the rates of GR precession (an order of magnitude higher than Mercury's GR precession rate) due to sungrazing and sun-colliding phases induced by Lidov-Kozai-like oscillations. This comet's combination of orbital elements and initial conditions (at the present epoch) favour this measurable rapid change in GR precession (at some points peaking up to 60 times Mercury's GR precession rate) along with prograde-retrograde inclination flip (due to Lidov-Kozai-like oscillations). Similar tests are performed for hundreds of bodies lying in the moderately low perihelion distance and moderately low semimajor axis phase space in the Solar system, the present lowest perihelion distance asteroid 322P/SOHO 1, and further examples connected with 96P/Machholz 1 namely, the Marsden and Kracht families of sungrazing comets plus low perihelion meteoroid streams like Daytime Arietids and Southern Delta Aquariids.
NASA Astrophysics Data System (ADS)
Ciolfi, Riccardo; Kastaun, Wolfgang; Giacomazzo, Bruno; Endrizzi, Andrea; Siegel, Daniel M.; Perna, Rosalba
2017-03-01
Merging binary neutron stars (BNSs) represent the ultimate targets for multimessenger astronomy, being among the most promising sources of gravitational waves (GWs), and, at the same time, likely accompanied by a variety of electromagnetic counterparts across the entire spectrum, possibly including short gamma-ray bursts (SGRBs) and kilonova/macronova transients. Numerical relativity simulations play a central role in the study of these events. In particular, given the importance of magnetic fields, various aspects of this investigation require general relativistic magnetohydrodynamics (GRMHD). So far, most GRMHD simulations focused the attention on BNS mergers leading to the formation of a hypermassive neutron star (NS), which, in turn, collapses within few tens of ms into a black hole surrounded by an accretion disk. However, recent observations suggest that a significant fraction of these systems could form a long-lived NS remnant, which will either collapse on much longer time scales or remain indefinitely stable. Despite the profound implications for the evolution and the emission properties of the system, a detailed investigation of this alternative evolution channel is still missing. Here, we follow this direction and present a first detailed GRMHD study of BNS mergers forming a long-lived NS. We consider magnetized binaries with different mass ratios and equations of state and analyze the structure of the NS remnants, the rotation profiles, the accretion disks, the evolution and amplification of magnetic fields, and the ejection of matter. Moreover, we discuss the connection with the central engine of SGRBs and provide order-of-magnitude estimates for the kilonova/macronova signal. Finally, we study the GW emission, with particular attention to the post-merger phase.
Non-linear generalization of the relativistic Schrödinger equations.
NASA Astrophysics Data System (ADS)
Ochs, U.; Sorg, M.
1996-09-01
The theory of the relativistic Schrödinger equations is further developped and extended to non-linear field equations. The technical advantage of the relativistic Schroedinger approach is demonstrated explicitly by solving the coupled Einstein-Klein-Gordon equations including a non-linear Higgs potential in case of a Robertson-Walker universe. The numerical results yield the effect of dynamical self-diagonalization of the Hamiltonian which corresponds to a kind of quantum de-coherence being enabled by the inflation of the universe.
NASA Astrophysics Data System (ADS)
Sekhar, Aswin; Asher, David; Morbidelli, Alessandro; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie
2017-06-01
Two well known phenomena in orbital dynamics associated with low perihelion distance bodies are general relativistic (GR) precession and Lidov-Kozai (LK) oscillations.In this work, we are interested to identify bodies evolving in the near future (i.e. thousands of years in this case) into rapid sungrazing and sun colliding phases and undergoing inclination flips, due to LK like oscillations and being GR active at the same time. We find that LK mechanism leads to secular lowering of perihelion distance which in turn leads to a huge increase in GR precession of the argument of pericentre depending on the initial orbital elements. This in turn gives feedback to the LK mechanism as the eccentricity, inclination and argument of pericentre in Kozai cycles are closely correlated. In this work, we find real examples of solar system bodies which show rapid enhancement in GR precession rates due to LK like oscillations and there are cases where GR precession rate peaks to about 60 times that of the GR precession of Mercury thus showing the strength and complementary nature between these two dynamical phenomena.An analytical treatment is done on few bodies to understand the difference in their orbital evolution in the context of LK mechanism with and without GR precession term by incorporating suitable Hamiltonian dynamics. This result is subsequently matched using numerical integrations to find direct correlations. Real solar system bodies showing both GR precession and LK like oscillations are identified using compiled observational records from IAU-Minor Planet Center, Cometary Catalogue, IAU-Meteor Data Center and performing analytical plus numerical tests on them. This intermediate state (where GR and LK effects are comparable and co-exist) brings up the interesting possibility of drastic changes in GR precession rates during orbital evolution due to sungrazing and sun colliding phases induced by the LK like mechanism, thus combining both these important effects in a
Axisymmetric fully spectral code for hyperbolic equations
NASA Astrophysics Data System (ADS)
Panosso Macedo, Rodrigo; Ansorg, Marcus
2014-11-01
We present a fully pseudo-spectral scheme to solve axisymmetric hyperbolic equations of second order. With the Chebyshev polynomials as basis functions, the numerical grid is based on the Lobbato (for two spatial directions) and Radau (for the time direction) collocation points. The method solves two issues of previous algorithms which were restricted to one spatial dimension, namely, (i) the inversion of a dense matrix and (ii) the acquisition of a sufficiently good initial-guess for non-linear systems of equations. For the first issue, we use the iterative bi-conjugate gradient stabilized method, which we equip with a pre-conditioner based on a singly diagonally implicit Runge-Kutta (“SDIRK”-) method. In this paper, the SDIRK-method is also used to solve issue (ii). The numerical solutions are correct up to machine precision and we do not observe any restriction concerning the time step in comparison with the spatial resolution. As an application, we solve general-relativistic wave equations on a black-hole space-time in so-called hyperboloidal slices and reproduce some recent results available in the literature.
NASA Astrophysics Data System (ADS)
Hindman, R. G.
1985-09-01
Theoretical background and several basic test cases are presented for a new, time dependent Navier-Stokes solver for two-dimensional and axisymmetric flows. The goal of the effort is to invoke state-of-the-art computational fluid dynamics (CFD) technology to improve modeling of viscous phenomenal and to increase the robustness of CFD analysis. The original motivation was inadequate representation of supersonic ramp-induced separation by existing CFD codes. The present work addresses that inadequacy by using modern numerical methods which accurately model signal propagation in high-speed fluid flow. This technique solves the Navier-Stokes equations in general curvilinear coordinates in a four-sided domain bounded by a wall, and upper boundary opposite the wall, an inflow boundary, and an outflow boundary. The interior algorithm is a flux-difference splitting method similar to that of Yang, Lombard, and Bershader, but is blended into a second order, implicit factored delta form. With implicitly treated boundary conditions, the solution is performed using a block tridiagonal method followed by an explicit updating of the boundaries. The resulting scheme satisfies the global conversation requirement to within the order of accuracy of the algorithm. The grid is generated using a relaxation Poisson solver. A systematic and rigorous development of the complete method is presented. Initial steps in code validation include successful reproduction of Couette and Blasius solutions.
GPU-based four-dimensional general-relativistic ray tracing
NASA Astrophysics Data System (ADS)
Kuchelmeister, Daniel; Müller, Thomas; Ament, Marco; Wunner, Günter; Weiskopf, Daniel
2012-10-01
This paper presents a new general-relativistic ray tracer that enables image synthesis on an interactive basis by exploiting the performance of graphics processing units (GPUs). The application is capable of visualizing the distortion of the stellar background as well as trajectories of moving astronomical objects orbiting a compact mass. Its source code includes metric definitions for the Schwarzschild and Kerr spacetimes that can be easily extended to other metric definitions, relying on its object-oriented design. The basic functionality features a scene description interface based on the scripting language Lua, real-time image output, and the ability to edit almost every parameter at runtime. The ray tracing code itself is implemented for parallel execution on the GPU using NVidia's Compute Unified Device Architecture (CUDA), which leads to performance improvement of an order of magnitude compared to a single CPU and makes the application competitive with small CPU cluster architectures. Program summary Program title: GpuRay4D Catalog identifier: AEMV_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMV_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 73649 No. of bytes in distributed program, including test data, etc.: 1334251 Distribution format: tar.gz Programming language: C++, CUDA. Computer: Linux platforms with a NVidia CUDA enabled GPU (Compute Capability 1.3 or higher), C++ compiler, NVCC (The CUDA Compiler Driver). Operating system: Linux. RAM: 2 GB Classification: 1.5. External routines: OpenGL Utility Toolkit development files, NVidia CUDA Toolkit 3.2, Lua5.2 Nature of problem: Ray tracing in four-dimensional Lorentzian spacetimes. Solution method: Numerical integration of light rays, GPU-based parallel programming using CUDA, 3D
Change in General Relativistic precession rates due to Lidov-Kozai oscillations in the Solar System
NASA Astrophysics Data System (ADS)
Sekhar, Aswin; Asher, David J.; Werner, Stephanie C.; Vaubaillon, Jeremie; Li, Gongjie
2017-04-01
Introduction: Two well known phenomena associated with low perihelion distance bodies in orbital dynamics are general relativistic (GR) precession and Lidov-Kozai (LK) oscillations. The accurate prediction of the perihelion shift of Mercury in accord with real observations is one of the significant triumphs of the general theory of relativity developed by Einstein. The Lidov-Kozai mechanism was first proposed and derived by Kozai and independently by Lidov explaining the periodic exchange between eccentricities e and inclinations i thereby increasing or decreasing the perihelion distance q secularly in the orbiting body. Co-existence of GR Precession and LK Oscillations: In this work, we were interested to identify bodies evolving in the near future (i.e. thousands of years in this case) into rapid sungrazing and sun colliding phases and undergoing inclination flips, due to LK oscillations and being GR active at the same time. Of all the bodies we checked from the IAU-Minor Planet Center, and Marsden plus Kracht families from the comet catalogue, 96P/Machholz 1 stands out because it shows all these trends in the near future. LK leads to secular lowering of q which in turn leads to a huge increase in GR precession of argument of pericentre. This in turn gives feedback to the LK mechanism as the e,i and argument of pericentre in Kozai cycles are closely correlated. In this work, we find real examples of solar system bodies which show the continuum nature between GR precession domi-nant and LK mechanism dominant regimes. Results and Discussion: We have shown that there are bodies in the solar system in which both GR precession and LK mechanism can co-exist at the same time and for which these effects can be measured and identified using analytical and numerical techniques. Thus there is a continuum of bodies encompassing, firstly GR precession dominant, secondly GR precession plus LK mechanism co-existing and finally LK mechanism dominant states which are all
Optimal strokes for axisymmetric microswimmers
NASA Astrophysics Data System (ADS)
Alouges, F.; Desimone, A.; Lefebvre, A.
2009-03-01
We present a theory for low-Reynolds-number axisymmetric swimmers and a general strategy for the computation of strokes of maximal efficiency. An explicit equation characterizing optimal strokes is derived, and numerical strategies to obtain solutions are discussed. The merits of this approach are demonstrated by applying it to two concrete examples: the three linked spheres of Najafi and Golestanian and the pushmepullyou of Avron, Kenneth, and Oakmin.
NASA Astrophysics Data System (ADS)
Xu, Chongming
2009-05-01
The approximation method in multiple coordinate systems at first post Newtonian (1 PN) level has been established by Darmour, Soffel and Xu (Phys. Rev. D(PRD) 43, 3273 (1991);D 45, 1017(1992);D 47, 3124 (1993);D 49, 618 (1994)). Normally, to discuss an astronomical object (e.g. a star in binary systems or the earth in solar system) we need multiple coordinate systems, especially for precise astrometry 1 PN (some time even 2 PN) approximate method is required. As we know up to now the ideas on elastic body, fluid, rigid body and liquid in the framework of Newtonian physics are still very useful for understanding and calculating some practical problems. Although the general relativistic theories of elastic body, general relativistic hydrodynamics and post-Newtonian quasi-rigid body have been discussed by many authors (including our papers (PRD63, 043002(2001); D63, 064001(2001); D68, 064009(2003); D69, 024003(2004); D71,024030 (2005))), but there is no completing discussion on all of these ideas in a unified point view. The applications of these ideas in the general relativity are important in the research fields of astrometry and geophysics, especially in case precise measurements reach so higher level (millimicro arc sec). The extended relativistic versions of these ideas should be revised the Newtonian results. In this paper, we shall give a complete discussion on all of these ideas in 1 PN approximation. We shall clarify the ideas on perfect elastic material, quasi-rigid body, quasi-liquid and so on with some precise mathematical forms. For fluid we show the hydrodynamic equations of a non-perfect fluid in multiple coordinates systems (both local and global).
NASA Astrophysics Data System (ADS)
Novak, Jerome; Dimmelmeier, Harrald; Font-Roda, Jose A.
2004-12-01
We present a new three-dimensional general relativistic hydrodynamics code which can be applied to study stellar core collapses and the resulting gravitational radiation. This code uses two different numerical techniques to solve partial differential equations arising in the model: high-resolution shock capturing (HRSC) schemes for the evolution of hydrodynamic quantities and spectral methods for the solution of Einstein equations. The equations are written and solved using spherical polar coordinates, best suited to stellar topology. Einstein equations are formulated within the 3+1 formalism and conformal flat condition (CFC) for the 3-metric and gravitational radiation is extracted using Newtonian quadrupole formulation.
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas
2014-06-01
Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M ⊙, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, langErang, of \\bar{\
General Relativistic Hydrodynamic Simulation of Accretion Flow from a Stellar Tidal Disruption
NASA Astrophysics Data System (ADS)
Shiokawa, Hotaka; Krolik, Julian H.; Cheng, Roseanne M.; Piran, Tsvi; Noble, Scott C.
2015-05-01
We study how the matter dispersed when a supermassive black hole tidally disrupts a star joins an accretion flow. Combining a relativistic hydrodynamic simulation of the stellar disruption with a relativistic hydrodynamics simulation of the subsequent debris motion, we track the evolution of such a system until ≃ 80% of the stellar mass bound to the black hole has settled into an accretion flow. Shocks near the stellar pericenter and also near the apocenter of the most tightly bound debris dissipate orbital energy, but only enough to make its characteristic radius comparable to the semimajor axis of the most bound material, not the tidal radius as previously envisioned. The outer shocks are caused by post-Newtonian relativistic effects, both on the stellar orbit during its disruption and on the tidal forces. Accumulation of mass into the accretion flow is both non-monotonic and slow, requiring several to 10 times the orbital period of the most tightly bound tidal streams, while the inflow time for most of the mass may be comparable to or longer than the mass accumulation time. Deflection by shocks does, however, cause some mass to lose both angular momentum and energy, permitting it to move inward even before most of the mass is accumulated into the accretion flow. Although the accretion rate still rises sharply and then decays roughly as a power law, its maximum is ≃ 0.1× the previous expectation, and the timescale of the peak is ≃ 5× longer than previously predicted. The geometric mean of the black hole mass and stellar mass inferred from a measured event timescale is therefore ≃ 0.2× the value given by classical theory.
Stability of axisymmetric liquid bridges
NASA Astrophysics Data System (ADS)
Fel, Leonid G.; Rubinstein, Boris Y.
2015-12-01
Based on the Weierstrass representation of second variation, we develop a non-spectral theory of stability for isoperimetric problem with minimized and constrained two-dimensional functionals of general type and free endpoints allowed to move along two given planar curves. We establish the stability criterion and apply this theory to the axisymmetric liquid bridge between two axisymmetric solid bodies without gravity to determine the stability of menisci with free contact lines. For catenoid and cylinder menisci and different solid shapes, we determine the stability domain. The other menisci (unduloid, nodoid and sphere) are considered in a simple setup between two plates. We find the existence conditions of stable unduloid menisci with and without inflection points.
NASA Astrophysics Data System (ADS)
Bagayoko, Diola
In 2014, 50 years following the introduction of density functional theory (DFT), a rigorous understanding of it was published [AIP Advances, 4, 127104 (2014)]. This understanding included necessary steps ab initio electronic structure calculations have to take if their results are to possess the full physical content of DFT. These steps guarantee the fulfillment of conditions of validity of DFT; not surprisingly, they have led to accurate descriptions of several dozens of semiconductors, from first principle, without invoking derivative discontinuity or self-interaction correction. This presentation shows the mathematically and physically rigorous understanding of the relativistic extension of DFT by Rajagopal and Callaway {Phys. Rev. B 7, 1912 (1973)]. As in the non-relativistic case, the attainment of the absolute minima of the occupied energies is a necessary condition for the corresponding current density to be that of the ground state of the system and for computational results to agree with corresponding, experimental ones. Acknowledgments:This work was funded in part by the US National Science Foundation [NSF, Award Nos. EPS-1003897, NSF (2010-2015)-RII-SUBR, and HRD-1002541], the US Department of Energy, National Nuclear Security Administration (NNSA, Award No. DE-NA0002630), LaSPACE, and LONI-SUBR.
NASA Astrophysics Data System (ADS)
Petrucci, P. O.; Henri, G.
1997-10-01
In a previous paper (Henri & Petrucci, 1997A&A...326...87H, hereafter Paper I), we have derived a new model in order to explain the UV and X-ray emission of radio quiet AGNs. This model assumes that a point source of relativistic leptons (e^+^,e^-^) illuminates the accretion disk of the AGN by Inverse Compton process. This disk is supposed to be simply represented by a finite slab which radiates only the energy reprocessed from the hot source. The radiation field within the hot source region is therefore highly anisotropic, which strongly influences the Inverse Compton process. The different Eddington parameters characterizing the radiative balance of this system have been calculated self-consistently in the Newtonian case (Paper I) giving a universal spectrum for a given inclination angle. In this paper, we take into account relativistic effects by including the gravitational redshift, the Doppler boosting and the gravitational focusing due to the central supermassive black hole. This has the effect of modifying the radial temperature profile in the innermost region of the disk (at some gravitational radii). However, the spectrum is hardly different from that obtained in the Newtonian case, unless the hot source is very close to the black hole. These results are clearly different from standard accretion disk models where the gravitational energy is mainly released in the vicinity of the black hole.
NASA Astrophysics Data System (ADS)
Nobili, Anna M.
2016-12-01
The universality of free fall and the weak equivalence principle, which are at the basis of general relativity, have been confirmed to 1 part in 1 013. Space experiments with macroscopic test masses of different composition orbiting Earth inside a low altitude satellite aim to improve this precision by 2 orders of magnitude (with the Microscope satellite launched on April 25, 2016) and up to 4 orders of magnitude (with the Galileo Galilei satellite). At such a high precision, many tiny effects must be taken into account in order to be ruled out as the source of a spurious violation signal. In this work, we investigate the general relativistic effects, including those which involve the rotation of both Earth and the test masses, and show that they are by far too small to be considered even in the most challenging experiment.
Hawke, Ian; Loeffler, Frank; Nerozzi, Andrea
2005-05-15
We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of reconstruction-evolution methods, a standard class of high-resolution shock-capturing methods. We test three different reconstruction schemes, namely, total variation diminishing, piecewise parabolic method (PPM) and essentially nonoscillatory. The method does not require that the coordinate system is adapted to the excision boundary. We demonstrate the effectiveness of our method using tests containing discontinuities, static test fluid solutions with black holes, and full dynamical collapse of a neutron star to a black hole. A modified PPM scheme is introduced because of problems arisen when matching excision with the original PPM reconstruction scheme.
A general relativistic approach to the Navarro Frenk White galactic halos
NASA Astrophysics Data System (ADS)
Matos, Tonatiuh; Núñez, Darío; Sussman, Roberto A.
2004-11-01
Although galactic dark matter halos are basically Newtonian structures, the study of their interplay with large-scale cosmic evolution and with relativistic effects, such as gravitational lenses, quintessence sources or gravitational waves, makes it necessary to obtain adequate relativistic descriptions for these self-gravitating systems. With this purpose in mind, we construct a post-Newtonian fluid framework for the 'Navarro Frenk White' (NFW) models of galactic halos that follow from N-body numerical simulations. Since these simulations are unable to resolve regions very near the halo centre, the extrapolation of the fitting formula leads to a spherically averaged 'universal' density profile that diverges at the origin. We remove this inconvenient feature by replacing a small central region of the NFW halo with an interior Schwarzschild solution with constant density, continuously matched to the remaining NFW spacetime. A model of a single halo, as an isolated object with finite mass, follows by smoothly matching the NFW spacetime to a Schwarzschild vacuum exterior along the virial radius, the physical 'cut-off' customarily imposed, as the mass associated with NFW profiles diverges asymptotically. Numerical simulations assume weakly interacting collisionless particles, hence we suggest that NFW halos approximately satisfy an 'ideal gas' type of equation of state, where mass-density is the dominant rest-mass contribution to matter-energy, with the internal energy contribution associated with an anisotropic kinetic pressure. We show that, outside the central core, this pressure and the mass density roughly satisfy a polytropic relation. Since stellar polytropes are the equilibrium configurations in Tsallis' non-extensive formalism of statistical mechanics, we argue that NFW halos might provide a rough empirical estimate of the free parameter q of Tsallis' formalism.
NASA Astrophysics Data System (ADS)
Wu, Kailiang; Tang, Huazhong
2017-01-01
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 the 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 L1-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.
NASA Astrophysics Data System (ADS)
Kállay, Mihály; Nataraj, H. S.; Sahoo, B. K.; Das, B. P.; Visscher, Lucas
2011-03-01
We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the black-body radiation shift of the Al+ clock has been estimated precisely. The computed shift relative to the frequency of the 3s21S0e→3s3p3P0o clock transition given by (-3.66±0.60)×10-18 calls for an improvement over the recent measurement with a reported result of (-9±3)×10-18 [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.104.070802 104, 070802 (2010)].
NASA Astrophysics Data System (ADS)
Murad, Mohammad Hassan; Pant, Neeraj
2014-03-01
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/ c 2 R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538-52, LMC X-4, SAX J1808.4-3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
General relativistic considerations of the field shedding model of fast radio bursts
NASA Astrophysics Data System (ADS)
Punsly, Brian; Bini, Donato
2016-06-01
Popular models of fast radio bursts (FRBs) involve the gravitational collapse of neutron star progenitors to black holes. It has been proposed that the shedding of the strong neutron star magnetic field (B) during the collapse is the power source for the radio emission. Previously, these models have utilized the simplicity of the Schwarzschild metric which has the restriction that the magnetic flux is magnetic `hair' that must be shed before final collapse. But neutron stars have angular momentum and charge and a fully relativistic Kerr-Newman solution exists in which B has its source inside of the event horizon. In this Letter, we consider the magnetic flux to be shed as a consequence of the electric discharge of a metastable collapsed state of a Kerr-Newman black hole. It has also been argued that the shedding model will not operate due to pair creation. By considering the pulsar death line, we find that for a neutron star with B = 1011-1013 G and a long rotation period, >1s this is not a concern. We also discuss the observational evidence supporting the plausibility of magnetic flux shedding models of FRBs that are spawned from rapidly rotating progenitors.
General Relativistic Magnetohydrodynamic Simulations of Jet Formation with a Thin Keplerian Disk
NASA Technical Reports Server (NTRS)
Mizuno, Yosuke; Nishikawa, Ken-Ichi; Koide, Shinji; Hardee, Philip; Gerald, J. Fishman
2006-01-01
We have performed several simulations of black hole systems (non-rotating, black hole spin parameter a = 0.0 and rapidly rotating, a = 0.95) with a geometrically thin Keplerian disk using the newly developed RAISHIN code. The simulation results show the formation of jets driven by the Lorentz force and the gas pressure gradient. The jets have mildly relativistic speed (greater than or equal to 0.4 c). The matter is continuously supplied from the accretion disk and the jet propagates outward until each applicable terminal simulation time (non-rotating: t/tau S = 275 and rotating: t/tau S = 200, tau s equivalent to r(sub s/c). It appears that a rotating black hole creates an additional, faster, and more collimated inner outflow (greater than or equal to 0.5 c) formed and accelerated by the twisted magnetic field resulting from frame-dragging in the black hole ergosphere. This new result indicates that jet kinematic structure depends on black hole rotation.
Galaxies, Axisymmetric Systems and Relativity
NASA Astrophysics Data System (ADS)
MacCallum, M. A. H.
2011-06-01
List of contributors; Preface; Prof. W. B. Bonnor: a biological sketch; Part I. Galaxies and Cosmology: 1. The origin of large scale cosmic structure B. J. T. Jones and P. L. Palmer; 2. The problem of origin of the primordial pertubations and the modern cosmology V. N. Lukash and I. D. Novikov; 3. The automorphism group and field equations for Bianchi universes W. L. Rogue and G. F. R. Ellis; 4. New perspectives on galaxy formation J. Silk; Part II. Axisymmetric Systems: 5. On exact radiative solutions representing finite sources J. Bicak; 6. Proof of a generalized Geroch conjecture I. Hauser and F. J. Ernst; 7. Limits of the double Kerr solution C. Hoenselaers; 8. Non-inheritance of static symmetry by Maxwell fields M. A. H. MacCallum and N. Van den Bergh; 9. Stationary axisymmetric electrovacuum fields in general relativity G. Neugebauer and D. Kramer; 10. An almost conformal approach to axial symmetry Z. Perjes; 11. Conformally stationary axisymmetric space-times J. Winicour; Part III. Relativity: 12. A family of conformally flat space-times having the same curvature tensor in a given co-ordinate frame C. D. Collinson; 13. On the Bell-Szekeres solution for colliding electromagnetic waves J. B. Griffiths; 14. A remark on the Hauser metric A. Held; 15. Numerical relativity by power series R. Penrose; 16. Projective relativity and the equation of motion E. Schmutzer; 17. On generalized equations of goedesic deviation B. F. Schutz; 18. Lobatchevski plane gravitational waves S. T. C. Siklos; 19. Perfect fluid and vacuum solutions of Einstein's field equations with flat 3-dimensional slices H. Stephani and Th. Wolf; 20. Self-similar solutions of Einstein's equations J. Wainwright.
Properties of relativistically rotating quark stars
NASA Astrophysics Data System (ADS)
Zhou, Enping
2017-06-01
In this work, quasi-equilibrium models of rapidly rotating triaxially deformed quark stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polynomial equation of state. Especially, since we are using a full 3-D numerical relativity initial data code, we are able to consider the triaxially deformed rotating quark stars at very high spins. Such triaxially deformed stars are possible gravitational radiation sources detectable by ground based gravitational wave observatories. Additionally, the bifurcation from axisymmetric rotating sequence to triaxially rotating sequence hints a more realistic spin up limit for rotating compact stars compared with the mass-shedding limit. With future observations such as sub-millisecond pulsars, we could possibly distinguish between equation of states of compact stars, thus better understanding strong interaction in the low energy regime.
NASA Astrophysics Data System (ADS)
Harko, T.; Mak, M. K.
2016-09-01
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index n. The explicit form of the solution is presented for the polytropic index n=1, and for the indexes n=1/2 and n=1/5, respectively. The case of n=3 is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.
NASA Astrophysics Data System (ADS)
Heller, René
2017-09-01
As new concepts of sending interstellar spacecraft to the nearest stars are now being investigated by various research teams, crucial questions about the timing of such a vast financial and labour investment arise. If humanity could build high-speed interstellar lightsails and reach α Centauri 20 yr after launch, would it be better to wait a few years, then take advantage of further technology improvements and arrive earlier despite waiting? The risk of being overtaken by a future, faster probe has been described earlier as the incentive trap. Based on 211 yr of historical data, we find that the speed growth of artificial vehicles, from steam-driven locomotives to Voyager 1, is much faster than previously believed, about 4.72 per cent annually or a doubling every 15 yr. We derive the mathematical framework to calculate the minimum of the wait time to launch t plus travel time τ(t) and extend it into the relativistic regime. We show that the t + τ(t) minimum disappears for nearby targets. There is no use of waiting once we can reach an object within about 20 yr of travel, irrespective of the actual speed. In terms of speed, the t + τ(t) minimum for a travel to α Centauri occurs at 19.6 per cent the speed of light (c), in agreement with the 20 per cent c proposed by the Breakthrough Starshot initiative. If interstellar travel at 20 per cent c could be achieved within 45 yr from today and the kinetic energy be increased at a rate consistent with the historical record, then humans can reach the 10 most nearby stars within 100 yr from today.
Teraki, Yuto; Takahara, Fumio
2014-05-20
Using a numerical method, we examine the radiation spectra from relativistic electrons moving in Langmuir turbulence, which are expected to exist in high energy astrophysical objects. The spectral shape is characterized by the spatial scale λ, field strength σ, and frequency of the Langmuir waves, and in terms of frequency they are represented by ω{sub 0} = 2πc/λ, ω{sub st} = eσ/mc, and ω{sub p}, respectively. We normalize ω{sub st} and ω {sub p} by ω{sub 0} as a ≡ ω{sub st}/ω{sub 0} and b ≡ ω{sub p}/ω{sub 0}, and examine the spectral shape in the a–b plane. An earlier study based on the diffusive radiation in Langmuir turbulence (DRL) theory by Fleishman and Toptygin showed that the typical frequency is γ{sup 2}ω{sub p} and that the low frequency spectrum behaves as F {sub ω}∝ω{sup 1} for b > 1 irrespective of a. Here, we adopt the first principle numerical approach to obtain the radiation spectra in more detail. We generate Langmuir turbulence by superposing Fourier modes, injecting monoenergetic electrons, solving the equation of motion, and calculating the radiation spectra using a Lienard-Wiechert potential. We find different features from the DRL theory for a > b > 1. The peak frequency turns out to be γ{sup 2}ω{sub st}, which is higher than the γ{sup 2}ω{sub p} predicted by the DRL theory, and the spectral index of the low frequency region is not 1 but 1/3. This is because the typical deflection angle of electrons is larger than the angle of the beaming cone ∼1/γ. We call the radiation for this case 'wiggler radiation in Langmuir turbulence'.
NASA Astrophysics Data System (ADS)
Mitra, Abhas
2011-11-01
Hoyle & Folwler (1963a,b) suggested that quasars may contain Radiation Pressure Supported Stars (RPSS), which are quasi-Newtonian (surface redshitf z ≪ 1) and supermassive. This proposal however did not work and one of the reasons was that such quasi-Newtonian PRSSs are unstable to gravitational contraction to become extremely general relativistic RPSSs. And since trapped surfaces are not allowed, (Mitra 2009a) these relativistic RPSSs are bound to hover around their instantaneous "Schwarzschild Radius" Rs = 2GM/c2. In view of the fact that they have z ≫ 1, they appear as "Black Holes" (BH) to distant observers. However since, they are always radiating, in a strict sense, they are always contracting. During such extreme compatification, RPSSs are likely to acquire extremely large magnetic field due to magnetic flux freezing, and hence they have strong magnetosphere around them by which they may arrest the accretion disk surrounding them at "Alfven Radius", Ra ≫ Rs. In contrast, for an accreting Schwarzschild black hole, one expects the inner edge of the accretion disk to be at Ri = 3Rs. Consequently, such ultramagnetized RPSSs have been nick named as Magnetospheric Eternally Collapsing Objects" (MECOs). Microlensing studies of several quasar structures have shown that indeed Ri ˜ 35Rs rather that R1 = 3Rs, and which confirms that quasars harbor MECOs rather than true black holes (Schild et al. 2006, 2008, Lovegrove et al. 2011). Further the recent proof that the true BHs have M = 0 confirms that the BH candidates are not true BHs (Mitra 2004a,b; 2009b). Here we highlight the facts (i) outflows from quasars and (ii) their ability to recycle cosmic matter for having new stars and galaxies are best understood by realizing that they contain MECOs rather than true BHs.
NASA Astrophysics Data System (ADS)
Rowland, D. R.
2006-01-01
Introductory courses covering modern physics sometimes introduce some elementary ideas from general relativity, though the idea of a geodesic is generally limited to shortest Euclidean length on a curved surface of two spatial dimensions rather than extremal aging in spacetime. It is shown that Epstein charts provide a simple geometric picture of geodesics in one space and one time dimension and that for a hypothetical uniform gravitational field, geodesics are straight lines on a planar diagram. This means that the properties of geodesics in a uniform field can be calculated with only a knowledge of elementary geometry and trigonometry, thus making the calculation of some basic results of general relativity accessible to students even in an algebra-based survey course on physics.
General relativistic simulations of compact binary mergers as engines for short gamma-ray bursts
NASA Astrophysics Data System (ADS)
Paschalidis, Vasileios
2017-04-01
Black hole—neutron star (BHNS) and neutron star—neutron star (NSNS) binaries are among the favored candidates for the progenitors of the black hole—disk systems that may be the engines powering short-hard gamma ray bursts. After almost two decades of simulations of binary NSNSs and BHNSs in full general relativity we are now beginning to understand the ingredients that may be necessary for these systems to launch incipient jets. Here, we review our current understanding, and summarize the surprises and lessons learned from state-of-the-art (magnetohydrodynamic) simulations in full general relativity of BHNS and NSNS mergers as jet engines for short-hard gamma-ray bursts. We also propose a new approach to probing the nuclear equation of state by virtue of multimessenger observations.
Schumaker, B.L.
1985-01-01
This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum-mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and momentum variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the output modes arise from two-proton transitions, i.e., are created or destroyed two at a time. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed. The fifth paper considers the validity of the standard quantum limit (SQL) for measurements that monitor the position of a free mass. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models and of the gravitational waves they emit.
NASA Astrophysics Data System (ADS)
Roberts, Luke F.; Ott, Christian D.; Haas, Roland; O'Connor, Evan P.; Diener, Peter; Schnetter, Erik
2016-11-01
We report on a set of long-term general-relativistic three-dimensional (3D) multi-group (energy-dependent) neutrino radiation-hydrodynamics simulations of core-collapse supernovae. We employ a full 3D two-moment scheme with the local M1 closure, three neutrino species, and 12 energy groups per species. With this, we follow the post-core-bounce evolution of the core of a nonrotating 27 - {M}⊙ progenitor in full unconstrained 3D and in octant symmetry for ≳380 ms. We find the development of an asymmetric runaway explosion in our unconstrained simulation. We test the resolution dependence of our results and, in agreement with previous work, find that low resolution artificially aids explosion and leads to an earlier runaway expansion of the shock. At low resolution, the octant and full 3D dynamics are qualitatively very similar, but at high resolution, only the full 3D simulation exhibits the onset of explosion.
Pu, Hung-Yi; Nakamura, Masanori; Hirotani, Kouichi; Asada, Keiichi; Wu, Kinwah
2015-03-01
General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields threading a black hole can be divided into inflow and outflow parts, according to the result of the competition between the black hole gravity and magneto-centrifugal forces along the field line. Here we present the first self-consistent, semi-analytical solution for a cold, Poynting flux–dominated (PFD) GRMHD flow, which passes all four critical (inner and outer, Alfvén, and fast magnetosonic) points along a parabolic streamline. By assuming that the dominating (electromagnetic) component of the energy flux per flux tube is conserved at the surface where the inflow and outflow are separated, the outflow part of the solution can be constrained by the inflow part. The semi-analytical method can provide fiducial and complementary solutions for GRMHD simulations around the rotating black hole, given that the black hole spin, global streamline, and magnetizaion (i.e., a mass loading at the inflow/outflow separation) are prescribed. For reference, we demonstrate a self-consistent result with the work by McKinney in a quantitative level.
NASA Astrophysics Data System (ADS)
Takahashi, Hiroyuki R.; Ohsuga, Ken
2017-08-01
By performing 2.5-dimensional general relativistic radiation magnetohydrodynamic simulations, we demonstrate supercritical accretion onto a non-rotating, magnetized neutron star, where the magnetic field strength of dipole fields is 1010 G on the star surface. We found the supercritical accretion flow consists of two parts: the accretion columns and the truncated accretion disk. The supercritical accretion disk, which appears far from the neutron star, is truncated at around ≃3 R * (R * = 106 cm is the neutron star radius), where the magnetic pressure via the dipole magnetic fields balances with the radiation pressure of the disks. The angular momentum of the disk around the truncation radius is effectively transported inward through magnetic torque by dipole fields, inducing the spin up of a neutron star. The evaluated spin-up rate, ˜-10-11 s s-1, is consistent with the recent observations of the ultraluminous X-ray pulsars. Within the truncation radius, the gas falls onto a neutron star along the dipole fields, which results in a formation of accretion columns onto the northern and southern hemispheres. The net accretion rate and the luminosity of the column are ≃66 L Edd/c 2 and ≲10 L Edd, where L Edd is the Eddington luminosity and c is the light speed. Our simulations support a hypothesis whereby the ultraluminous X-ray pulsars are powered by the supercritical accretion onto the magnetized neutron stars.
NASA Astrophysics Data System (ADS)
Yamamoto, Shigeyoshi; Tatewaki, Hiroshi; Saue, Trond
2008-12-01
A four-component relativistic study of electronic transitions in the gadolinium monofluoride molecule (GdF) is presented. The electronic spectra of GdF have been investigated with a general open-shell configuration interaction method, where active electrons are distributed among molecular spinors mainly consisting of the Gd 4f, 5d, and 6s atomic spinors. The near-degeneracy effects of these spinors on the molecular electronic structure are considered by the valence full-CI-like approach. By the magnitudes of calculated transition dipole moments, the candidates for the observable transitions were selected. The present result is complementary to our previous study based on multireference configuration interaction singles and doubles calculations, which identified the electronic excited states of GdF by comparing the calculated excitation energies and angular momenta with those given by the laser spectroscopy. The spectra of the excited states less than 3.0 eV have been refined with the help of the calculated transition probabilities. The transitions between the excited states are newly analyzed and a rearrangement is proposed.
Troxel, M. A.; Ishak, Mustapha; Peel, Austin E-mail: mishak@utdallas.edu
2014-03-01
The study of relativistic, higher order, and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are thus naturally included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observables like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of such clusters. The resulting relative difference in various geometries can be as large as approximately 2%, 8%, and 24% in the measure of convergence (1−κ) for levels of anisotropy of 5%, 10%, and 15%, respectively, as a fraction of total cluster mass. For the total magnitude of shear, the relative difference can grow near the center of the structure to be as large as 15%, 32%, and 44% for the same levels of anisotropy, averaged over the two extreme geometries. The convergence is impacted most strongly for rays which pass in directions along the axis of maximum dipole anisotropy in the structure, while the shear is most strongly impacted for rays which pass in directions orthogonal to this axis, as expected. The rich features found in the lensing signal due to anisotropic substructure are nearly entirely lost when one treats the cluster in the traditional FLRW lensing framework. These effects due to anisotropic structures are thus likely to
NASA Astrophysics Data System (ADS)
Sridhar, S.; Touma, Jihad R.
2017-02-01
We study the resonant relaxation (RR) of an axisymmetric, low-mass (or Keplerian) stellar disc orbiting a more massive black hole (MBH). Our recent work on the general kinetic theory of RR is simplified in the standard manner by the neglect of 'gravitational polarization' and applied to a razor-thin axisymmetric disc. The wake of a stellar orbit is expressed in terms of the angular momenta exchanged with other orbits, and used to derive a kinetic equation for RR under the combined actions of self-gravity, 1 PN and 1.5 PN general relativistic effects of the MBH and an arbitrary external axisymmetric potential. This is a Fokker-Planck equation for the stellar distribution function (DF), wherein the diffusion coefficients are given self-consistently in terms of contributions from apsidal resonances between pairs of stellar orbits. The physical kinetics is studied for the two main cases of interest. (1) 'Lossless' discs in which the MBH is not a sink of stars, and disc mass, angular momentum and energy are conserved: we prove that general H-functions can increase or decrease during RR, but the Boltzmann entropy is (essentially) unique in being a non-decreasing function of time. Therefore, secular thermal equilibria are maximum entropy states, with DFs of the Boltzmann form; the two-ring correlation function at equilibrium is computed. (2) Discs that lose stars to the MBH through an 'empty loss cone': we derive expressions for the MBH feeding rates of mass, angular momentum and energy in terms of the diffusive fluxes at the loss-cone boundaries.
The relativistic transformation for an electromagnetic plane wave with general time dependence
NASA Astrophysics Data System (ADS)
Smith, Glenn S.
2012-03-01
In special relativity, the transformation between inertial frames for an electromagnetic plane wave is usually derived for the time-harmonic case (the field is a sinusoid of infinite duration), even though all practical waves are of finite duration and may not even contain a dominant sinusoid. This paper presents an alternative derivation in which the time dependence of the field is general; for example, it could be a Gaussian pulse in time. The changes that occur on transformation in the quantities that describe the wave are obtained and discussed. These changes include the temporal behaviour, direction of propagation, electromagnetic field, energy, and linear momentum. The derivation uses only elementary principles from special relativity, so it is suitable for an introductory course on the subject or a course on electrodynamics.
NASA Astrophysics Data System (ADS)
Lucchesi, David M.; Peron, Roberto
2014-04-01
The aim of this paper is to extend, clarify, and deepen the results of our previous work [D. M. Lucchesi and R. Peron, Phys. Rev. Lett. 105, 231103 (2010)], related to the precise measurement of LAGEOS (LAser GEOdynamics Satellite) II pericenter shift. A 13-year time span of LAGEOS satellites' laser tracking data has been considered, obtaining a very precise orbit and correspondingly residuals time series from which to extract the relevant signals. A thorough description is provided of the data analysis strategy and the dynamical models employed, along with a detailed discussion of the known sources of error in the experiment, both statistical and systematic. From this analysis, a confirmation of the predictions of Einstein's general relativity, as well as strong bounds on alternative theories of gravitation, clearly emerge. In particular, taking conservatively into account the stricter error bound due to systematic effects, general relativity has been confirmed in the Earth's field at the 98% level (meaning the measurement of a suitable combination of β and γ PPN parameters in weak-field conditions). This bound has been used to constrain possible deviations from the inverse-square law parameterized by a Yukawa-like new long range interaction with strength |α|≲1×10-10 at a characteristic range λ ≃1 Earth radius, a possible nonsymmetric gravitation theory with the interaction parameter C⊕LAGEOS II≲(9 × 10-2 km)4, and a possible spacetime torsion with a characteristic parameter combination |2t2+t3|≲7×10-2. Conversely, if we consider the results obtained from our best fit of the LAGEOS II orbit, the constraints in fundamental physics improve by at least 2 orders of magnitude.
Uniqueness of the equilibrium configurations of slowy rotating relativistic fluids
Kuenzle, H.P.; Savage, J.R.
1980-11-01
We consider the equations of a general relativistic space-time that is stationary, asymptotically Euclidean, diffeomorphic to R/sup 4/ and consists of an exterior vacuum solution and an interior perfect fluid in rigid motion. If one requires further that the solution be close to the static spherically symmetric ones (in the sense of a suitable topology on the set of stationary space--time metrics) it is shown that for a given equation of state rho( p) and given total mass m and (small) angular momentum J there are no smooth curves of physically distinct global axially symmetric solutions. In view of a recent result of Lindblom that all such space-times are axisymmetric this result is quite general. The method is a generalization of the one used to prove (in a ''local'' sense) the uniqueness of the spherical solution in the static case.
NASA Astrophysics Data System (ADS)
Dunkel, Jörn; Hänggi, Peter
2009-02-01
Over the past one hundred years, Brownian motion theory has contributed substantially to our understanding of various microscopic phenomena. Originally proposed as a phenomenological paradigm for atomistic matter interactions, the theory has since evolved into a broad and vivid research area, with an ever increasing number of applications in biology, chemistry, finance, and physics. The mathematical description of stochastic processes has led to new approaches in other fields, culminating in the path integral formulation of modern quantum theory. Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special relativity, we review, here, recent progress in the phenomenological description of relativistic diffusion processes. After a brief historical overview, we will summarize basic concepts from the Langevin theory of nonrelativistic Brownian motions and discuss relevant aspects of relativistic equilibrium thermostatistics. The introductory parts are followed by a detailed discussion of relativistic Langevin equations in phase space. We address the choice of time parameters, discretization rules, relativistic fluctuation-dissipation theorems, and Lorentz transformations of stochastic differential equations. The general theory is illustrated through analytical and numerical results for the diffusion of free relativistic Brownian particles. Subsequently, we discuss how Langevin-type equations can be obtained as approximations to microscopic models. The final part of the article is dedicated to relativistic diffusion processes in Minkowski spacetime. Since the velocities of relativistic particles are bounded by the speed of light, nontrivial relativistic Markov processes in spacetime do not exist; i.e., relativistic generalizations of the nonrelativistic diffusion equation and its Gaussian solutions
Psaltis, Dimitrios; Özel, Feryal; Chan, Chi-Kwan; Marrone, Daniel P.
2015-12-01
The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc{sup 2}, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%.
NASA Astrophysics Data System (ADS)
Psaltis, Dimitrios; Özel, Feryal; Chan, Chi-Kwan; Marrone, Daniel P.
2015-12-01
The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc2, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest that our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%.
Well behaved parametric class of relativistic charged fluid ball in general relativity
NASA Astrophysics Data System (ADS)
Pant, Neeraj
2011-04-01
The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤ K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).
General-relativistic Large-eddy Simulations of Binary Neutron Star Mergers
NASA Astrophysics Data System (ADS)
Radice, David
2017-03-01
The flow inside remnants of binary neutron star (NS) mergers is expected to be turbulent, because of magnetohydrodynamics instability activated at scales too small to be resolved in simulations. To study the large-scale impact of these instabilities, we develop a new formalism, based on the large-eddy simulation technique, for the modeling of subgrid-scale turbulent transport in general relativity. We apply it, for the first time, to the simulation of the late-inspiral and merger of two NSs. We find that turbulence can significantly affect the structure and survival time of the merger remnant, as well as its gravitational-wave (GW) and neutrino emissions. The former will be relevant for GW observation of merging NSs. The latter will affect the composition of the outflow driven by the merger and might influence its nucleosynthetic yields. The accretion rate after black hole formation is also affected. Nevertheless, we find that, for the most likely values of the turbulence mixing efficiency, these effects are relatively small and the GW signal will be affected only weakly by the turbulence. Thus, our simulations provide a first validation of all existing post-merger GW models.
GENERAL RELATIVISTIC SIMULATIONS OF ACCRETION INDUCED COLLAPSE OF NEUTRON STARS TO BLACK HOLES
Giacomazzo, Bruno; Perna, Rosalba
2012-10-10
Neutron stars (NSs) in the astrophysical universe are often surrounded by accretion disks. Accretion of matter onto an NS may increase its mass above the maximum value allowed by its equation of state, inducing its collapse to a black hole (BH). Here we study this process for the first time, in three-dimensions, and in full general relativity. By considering three initial NS configurations, each with and without a surrounding disk (of mass {approx}7% M{sub NS}), we investigate the effect of the accretion disk on the dynamics of the collapse and its imprint on both the gravitational wave (GW) and electromagnetic (EM) signals that can be emitted by these sources. We show in particular that, even if the GW signal is similar for the accretion induced collapse (AIC) and the collapse of an NS in vacuum (and detectable only for Galactic sources), the EM counterpart could allow us to discriminate between these two types of events. In fact, our simulations show that, while the collapse of an NS in vacuum leaves no appreciable baryonic matter outside the event horizon, an AIC is followed by a phase of rapid accretion of the surviving disk onto the newly formed BH. The post-collapse accretion rates, on the order of {approx}10{sup -2} M{sub Sun} s{sup -1}, make these events tantalizing candidates as engines of short gamma-ray bursts.
NASA Astrophysics Data System (ADS)
Mitra, Abhas
2013-04-01
It is widely believed that though pressure resists gravitational collapse in Newtonian gravity, it aids the same in general relativity (GR) so that GR collapse should eventually be similar to the monotonous free fall case. But we show that, even in the context of radiationless adiabatic collapse of a perfect fluid, pressure tends to resist GR collapse in a manner which is more pronounced than the corresponding Newtonian case and formation of trapped surfaces is inhibited. In fact there are many works which show such collapse to rebound or become oscillatory implying a tug of war between attractive gravity and repulsive pressure gradient. Furthermore, for an imperfect fluid, the resistive effect of pressure could be significant due to likely dramatic increase of tangential pressure beyond the "photon sphere." Indeed, with inclusion of tangential pressure, in principle, there can be static objects with surface gravitational redshift z → ∞. Therefore, pressure can certainly oppose gravitational contraction in GR in a significant manner in contradiction to the idea of Roger Penrose that GR continued collapse must be unstoppable.
A GENERAL RELATIVISTIC EXTERNAL COMPTON-SCATTERING MODEL FOR TeV EMISSION FROM M87
Cui Yudong; Yuan Yefei; Li Yanrong; Wang Jianmin
2012-02-20
M87 is the first detected non-blazar extragalactic tera-electron-volt (TeV) source with rapid variation and a very flat spectrum in the TeV band. To explain the two peaks in the spectral energy distribution of the nucleus of M87, which is similar to that of blazars, the most commonly adopted models are the synchrotron self-Compton-scattering models and the external inverse Compton (EIC) scattering models. Considering that there is no correlated variation in the soft band (from radio to X-ray) matching the TeV variation and that the TeV sources should not suffer from {gamma}{gamma} absorption due to the flat TeV spectrum, the EIC models are advantageous in modeling the TeV emission from M87. In this paper, we propose a self-consistent EIC model to explain the flat TeV spectrum of M87 within the framework of fully general relativity, where the background soft photons are from the advection-dominated accretion flow around the central black hole, and the high-energy electrons are from the mini-jets that are powered by the magnetic reconnection in the main jet. In our model, both the TeV flares observed in the years 2005 and 2008 could be well explained: the {gamma}{gamma} absorption for TeV photons is very low, even inside the region very close to the black hole 20R{sub g} {approx} 50R{sub g} ; at the same region, the average EIC cooling time ({approx}10{sup 2} {approx} 10{sup 3} s) is short, which is consistent with the observed timescale of the TeV variation. Furthermore, we also discuss the possibility that the accompanying X-ray flare in 2008 is due to the direct synchrotron radiation of the mini-jets.
NASA Astrophysics Data System (ADS)
Pant, Neeraj; Rajasekhara, S.
2011-05-01
The paper presents a variety of classes of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I1) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ b =2×1014 g/cm3 corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5 M Θ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.
NASA Astrophysics Data System (ADS)
Sekhar, Aswin; Valsecchi, Giovanni B.; Asher, David; Werner, Stephanie; Vaubaillon, Jeremie; Li, Gongjie
2017-06-01
One of the greatest successes of Einstein's General Theory of Relativity (GR) was the correct prediction of the perihelion precession of Mercury. The closed form expression to compute this precession tells us that substantial GR precession would occur only if the bodies have a combination of both moderately small perihelion distance and semi-major axis. Minimum Orbit Intersection Distance (MOID) is a quantity which helps us to understand the closest proximity of two orbits in space. Hence evaluating MOID is crucial to understand close encounters and collision scenarios better. In this work, we look at the possible scenarios where a small GR precession in argument of pericentre can create substantial changes in MOID for small bodies ranging from meteoroids to comets and asteroids.Previous works have looked into neat analytical techniques to understand different collision scenarios and we use those standard expressions to compute MOID analytically. We find the nature of this mathematical function is such that a relatively small GR precession can lead to drastic changes in MOID values depending on the initial value of argument of pericentre. Numerical integrations were done with the MERCURY package incorporating GR code to test the same effects. A numerical approach showed the same interesting relationship (as shown by analytical theory) between values of argument of pericentre and the peaks or dips in MOID values. There is an overall agreement between both analytical and numerical methods.We find that GR precession could play an important role in the calculations pertaining to MOID and close encounter scenarios in the case of certain small solar system bodies (depending on their initial orbital elements) when long term impact risk possibilities are considered. Previous works have looked into impact probabilities and collision scenarios on planets from different small body populations. This work aims to find certain sub-sets of small bodies where GR could play an
NASA Astrophysics Data System (ADS)
Valente, Giovanni; Owen Weatherall, James
2014-11-01
Relativity theory is often taken to include, or to imply, a prohibition on superluminal propagation of causal processes. Yet, what exactly the prohibition on superluminal propagation amounts to and how one should deal with its possible violation have remained open philosophical problems, both in the context of the metaphysics of causation and the foundations of physics. In particular, recent work in philosophy of physics has focused on the causal structure of spacetime in relativity theory and on how this causal structure manifests itself in our most fundamental theories of matter. These topics were the subject of a workshop on "Relativistic Causality in Quantum Field Theory and General Relativity" that we organized (along with John Earman) at the Center for Philosophy of Science in Pittsburgh on April 5-7, 2013. The present Special Issue comprises contributions by speakers in that workshop as well as several other experts exploring different aspects of relativistic causality. We are grateful to the journal for hosting this Special Issue, to the journal's managing editor, Femke Kuiling, for her help and support in putting the issue together, and to the authors and the referees for their excellent work.
NASA Astrophysics Data System (ADS)
Kovács, Z.; Harko, T.
2011-11-01
We present a full general relativistic numerical code for estimating the energy-momentum deposition rate (EMDR) from neutrino pair annihilation (?). The source of the neutrinos is assumed to be a neutrino-cooled accretion disc around neutron and quark stars. We calculate the neutrino trajectories by using a ray-tracing algorithm with the general relativistic Hamilton's equations for neutrinos and derive the spatial distribution of the EMDR due to the annihilations of neutrinos and antineutrinos around rotating neutron and quark stars. We obtain the EMDR for several classes of rotating neutron stars, described by different equations of state of the neutron matter, and for quark stars, described by the Massachusetts Institute of Technology (MIT) bag model equation of state and in the colour-flavour-locked (CFL) phase. The distribution of the total annihilation rate of the neutrino-antineutrino pairs around rotating neutron and quark stars is studied for isothermal discs and accretion discs in thermodynamical equilibrium. We demonstrate both the differences in the equations of state for neutron and quark matter and rotation with the general relativistic effects significantly modify the EMDR of the electrons and positrons generated by the neutrino-antineutrino pair annihilation around compact stellar objects, as measured at infinity.
Müller, Bernhard; Janka, Hans-Thomas E-mail: bjmuellr@mpa-garching.mpg.de
2014-06-10
Considering six general relativistic, two-dimensional (2D) supernova (SN) explosion models of progenitor stars between 8.1 and 27 M {sub ☉}, we systematically analyze the properties of the neutrino emission from core collapse and bounce to the post-explosion phase. The models were computed with the VERTEX-COCONUT code, using three-flavor, energy-dependent neutrino transport in the ray-by-ray-plus approximation. Our results confirm the close similarity of the mean energies, (E), of ν-bar {sub e} and heavy-lepton neutrinos and even their crossing during the accretion phase for stars with M ≳ 10 M {sub ☉} as observed in previous 1D and 2D simulations with state-of-the-art neutrino transport. We establish a roughly linear scaling of 〈E{sub ν-bar{sub e}}〉 with the proto-neutron star (PNS) mass, which holds in time as well as for different progenitors. Convection inside the PNS affects the neutrino emission on the 10%-20% level, and accretion continuing beyond the onset of the explosion prevents the abrupt drop of the neutrino luminosities seen in artificially exploded 1D models. We demonstrate that a wavelet-based time-frequency analysis of SN neutrino signals in IceCube will offer sensitive diagnostics for the SN core dynamics up to at least ∼10 kpc distance. Strong, narrow-band signal modulations indicate quasi-periodic shock sloshing motions due to the standing accretion shock instability (SASI), and the frequency evolution of such 'SASI neutrino chirps' reveals shock expansion or contraction. The onset of the explosion is accompanied by a shift of the modulation frequency below 40-50 Hz, and post-explosion, episodic accretion downflows will be signaled by activity intervals stretching over an extended frequency range in the wavelet spectrogram.
NASA Astrophysics Data System (ADS)
Takahashi, Hiroyuki R.; Ohsuga, Ken; Kawashima, Tomohisa; Sekiguchi, Yuichiro
2016-07-01
Using three-dimensional general relativistic radiation-magnetohydrodynamics simulations of accretion flows around stellar mass black holes, we report that the relatively cold disk (≳ {10}7 {{K}}) is truncated near the black hole. Hot and less dense regions, of which the gas temperature is ≳ {10}9 {{K}} and more than 10 times higher than the radiation temperature (overheated regions), appear within the truncation radius. The overheated regions also appear above as well as below the disk, sandwiching the cold disk, leading to the effective Compton upscattering. The truncation radius is ˜ 30{r}{{g}} for \\dot{M}˜ {L}{{Edd}}/{c}2, where {r}{{g}},\\dot{M},{L}{Edd},c are the gravitational radius, mass accretion rate, Eddington luminosity, and light speed, respectively. Our results are consistent with observations of a very high state, whereby the truncated disk is thought to be embedded in the hot rarefied regions. The truncation radius shifts inward to ˜ 10{r}{{g}} with increasing mass accretion rate \\dot{M}˜ 100{L}{{Edd}}/{c}2, which is very close to an innermost stable circular orbit. This model corresponds to the slim disk state observed in ultraluminous X-ray sources. Although the overheated regions shrink if the Compton cooling effectively reduces the gas temperature, the sandwich structure does not disappear at the range of \\dot{M}≲ 100{L}{{Edd}}/{c}2. Our simulations also reveal that the gas temperature in the overheated regions depends on black hole spin, which would be due to efficient energy transport from black hole to disks through the Poynting flux, resulting in gas heating.
Axisymmetric multiwormholes revisited
NASA Astrophysics Data System (ADS)
Clément, Gérard
2016-06-01
The construction of stationary axisymmetric multiwormhole solutions to gravitating field theories admitting toroidal reductions to three-dimensional gravitating sigma models is reviewed. We show that, as in the multi-black hole case, strut singularities always appear in this construction, except for very special configurations with an odd number of centers. We also review the analytical continuation of the multicenter solution across the n cuts associated with the wormhole mouths. The resulting Riemann manifold has 2^n sheets interconnected by 2^{n-1}n wormholes. We find that the maximally extended multicenter solution can never be asymptotically locally flat in all the Riemann sheets.
The mechanics of relativistic space flights
NASA Astrophysics Data System (ADS)
Zakirov, U. N.
The relativistic mechanics of an artificial space body with a variable rest mass is presented in a systematic manner. In particular, attention is given to the principles of Lobachevskii geometry, Riemann geometry, and relativity; general Lorentz transformations and relativistic kinematics; the principal theorems of the relativistic mechanics of a space vehicle in spherically symmetric gravitational fields; and the relativistic motion of a space vehicle with jet propulsion. Possible applications of relativistic mechanics are examined.
The field lines of an axisymmetric magnetic field
NASA Technical Reports Server (NTRS)
Backus, George E.
1988-01-01
The equations of Willis and Young (1987) for the field lines of an arbitrary axisymmetric multipole are generalized to an arbitrary linear combination of multipoles, i.e., to an arbitrary axisymmetric magnetic field B outside a sphere of radius a, S(a), centered on the origin, and containing all the sources of B. For this field, axisymmetric Stokes stream function is expressed in terms of the Gauss coefficients. It is shown that if only one Gauss coefficient is nonzero, the field line equations are identical to those obtained by Willis and Young.
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.
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.
NASA Astrophysics Data System (ADS)
Mohammadi, Vahid; Chenaghlou, Alireza
2017-09-01
The two-dimensional Dirac equation with spin and pseudo-spin symmetries is investigated in the presence of the maximally superintegrable potentials. The integrals of motion and the quadratic algebras of the superintegrable quantum E3‧, anisotropic oscillator and the Holt potentials are studied. The corresponding Casimir operators and the structure functions of the mentioned superintegrable systems are found. Also, we obtain the relativistic energy spectra of the corresponding superintegrable systems. Finally, the relativistic energy eigenvalues of the generalized Yang-Coulomb monopole (YCM) superintegrable system (a SU(2) non-Abelian monopole) are calculated by the energy spectrum of the eight-dimensional oscillator which is dual to the former system by Hurwitz transformation.
Logunov, A.A.; Loskutov, Yu.M.
1986-10-01
The orbital period of a satellite revolving around a planet is calculated in the framework of the relativistic theory of gravitation and in general relativity. The difference between the theoretical predictions is amenable to experimental verification.
Henisey, Ken B.; Blaes, Omer M.; Fragile, P. Chris
2012-12-10
We study the spatial and temporal behavior of fluid in fully three-dimensional, general relativistic, magnetohydrodynamical simulations of both tilted and untilted black hole accretion flows. We uncover characteristically greater variability in tilted simulations at frequencies similar to those predicted by the formalism of trapped modes, but ultimately conclude that its spatial structure is inconsistent with a modal interpretation. We find instead that previously identified, transient, overdense clumps orbiting on roughly Keplerian trajectories appear generically in our global simulations, independent of tilt. Associated with these fluctuations are acoustic spiral waves interior to the orbits of the clumps. We show that the two non-axisymmetric standing shock structures that exist in the inner regions of these tilted flows effectively amplify the variability caused by these spiral waves to markedly higher levels than in untilted flows, which lack standing shocks. Our identification of clumps, spirals, and spiral-shock interactions in these fully general relativistic, magnetohydrodynamical simulations suggests that these features may be important dynamical elements in models that incorporate tilt as a way to explain the observed variability in black hole accretion flows.
Exact axisymmetric Taylor states for shaped plasmas
Cerfon, Antoine J. O'Neil, Michael
2014-06-15
We present a general construction for exact analytic Taylor states in axisymmetric toroidal geometries. In this construction, the Taylor equilibria are fully determined by specifying the aspect ratio, elongation, and triangularity of the desired plasma geometry. For equilibria with a magnetic X-point, the location of the X-point must also be specified. The flexibility and simplicity of these solutions make them useful for verifying the accuracy of numerical solvers and for theoretical studies of Taylor states in laboratory experiments.
Harikae, Seiji; Kotake, Kei; Sekiguchi, Yu-ichiro; Takiwaki, Tomoya
2010-09-01
Bearing in mind the application to the collapsar models of gamma-ray bursts (GRBs), we develop a numerical scheme and code for estimating the deposition of energy and momentum due to the neutrino pair annihilation ({nu}+{nu}-bar{yields}e{sup -}+e{sup +}) in the vicinity of an accretion tori around a Kerr black hole. Our code is designed to solve the general relativistic (GR) neutrino transfer by a ray-tracing method. To solve the collisional Boltzmann equation in curved spacetime, we numerically integrate the so-called rendering equation along the null geodesics. We employ the Fehlberg (4,5) adaptive integrator in the Runge-Kutta method to perform the numerical integration accurately. For the neutrino opacity, the charged-current {beta}-processes, which are dominant in the vicinity of the accretion tori, are taken into account. The numerical accuracy of the developed code is certified by several tests in which we show comparisons with the corresponding analytical solutions. In order to solve the energy-dependent ray-tracing transport, we propose that an adaptive-mesh-refinement approach, which we take for the two radiation angles ({theta}, {phi}) and the neutrino energy, is useful in reducing the computational cost significantly. Based on the hydrodynamical data in our collapsar simulation, we estimate the annihilation rates in a post-processing manner. Increasing the Kerr parameter from 0 to 1, it is found that the GR effect can increase the local energy deposition rate by about one order of magnitude, and the net energy deposition rate by several tens of percent. After the accretion disk settles into a stationary state (typically later than {approx}9 s from the onset of gravitational collapse), we point out that the neutrino-heating timescale in the vicinity of the polar funnel region can be shorter than the dynamical timescale. Our results suggest that the neutrino pair annihilation is potentially as important as the conventional magnetohydrodynamic mechanism
NASA Astrophysics Data System (ADS)
Hollywood, J. M.; Melia, Fulvio
1997-10-01
The possibility that some portion of the infrared (IR) radiation emanating from active galactic nuclei (AGNs) may arise from disklike structures of ionized plasma accreting onto massive black holes motivates the investigation of the effects of strong gravitational fields in the vicinity of emitting particles on the observed radiation. Numerous previous studies have been incomplete in several respects: (1) they have neglected to take into account the observed specific power flux contribution of radiation emitted from the underside of the disk and gravitationally lensed into the upper half-hemisphere, (2) they have considered only a limited range of observing positions and hole spins, and (3) many have been restricted to examination of the steady state flux arising from homogeneous disks. The present study develops, within the context of the optically thick, geometrically thin accretion disk model, a set of new calculational techniques based on an analysis of the algebraic properties of the effective potential functions governing photon propagation in the Kerr metric; ancillary techniques, such as that of ``extended images,'' are introduced and employed to illustrate aspects of general relativistic image formation that affect the observed time-dependent flux arising from a thermally inhomogeneous accretion disk. The contribution of the first-orbit disk images, including the effects of disk self-blocking, to the observed flux are fully taken into account for the entire range of observing positions and hole spins for both the steady state and time-dependent cases. The procedure is illustrated by application of the results to the paradigm case of the Galactic center black hole candidate Sagittarius A*. Current observations are somewhat contaminated because of poor angular resolution, making this exercise still only an illustrative examination of the method. However, the future deployment of the Near-Infrared Camera and Multiobject Spectrometer (NICMOS) on HST should
Relativistic viscoelastic fluid mechanics.
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
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 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.
Mueller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald E-mail: thj@mpa-garching.mpg.d
2010-07-15
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 point 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
NASA Astrophysics Data System (ADS)
Müller, Bernhard; Janka, Hans-Thomas; Dimmelmeier, Harald
2010-07-01
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 point 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
Structure of axisymmetric mantle plumes
NASA Technical Reports Server (NTRS)
Olson, Peter; Schubert, Gerald; Anderson, Charles
1993-01-01
The structure of axisymmetric subsolidus thermal plumes in the earth's lower mantle is inferred from calculations of axisymmetric thermal plumes in an infinite Prandtl number fluid with thermally activated viscosity. The velocity and temperature distribution is determined for axisymmetric convection above a heated disk in an incompressible fluid cylinder 2,400 km in height and 1,200 km in diameter. Several calculations of plumes with heat transport in the range 100-400 GW, similar to the advective heat transport at the Hawaiian hotspot, are presented. Hotspot formation by plumes originating at the base of the mantle requires both large viscosity variations and a minimum heat transport.
Attitude stability criteria of axisymmetric solar sail
NASA Astrophysics Data System (ADS)
Hu, Xiaosai; Gong, Shengping; Li, Junfeng
2014-07-01
Passive attitude stability criteria of a solar sail whose membrane surface is axisymmetric are studied in this paper under a general SRP model. This paper proves that arbitrary attitude equilibrium position can be designed through adjusting the deviation between the pressure center and the mass center of the sail. The linearized method is applied to inspect analytically the stability of the equilibrium point from two different points of views. The results show that the attitude stability depends on the membrane surface shape and area. The results of simulation with full dynamic equations confirm that the two stability criteria are effective in judging the attitude stability for axisymmetric solar sail. Several possible applications of the study are also mentioned.
Relativistic magnetohydrodynamics in one dimension
NASA Astrophysics Data System (ADS)
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Relativistic magnetohydrodynamics in one dimension.
Lyutikov, Maxim; Hadden, Samuel
2012-02-01
We derive a number of solutions for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of simple waves of fast modes propagating orthogonally to the magnetic field in relativistically hot plasma. The magnetic and kinetic pressures obey different equations of state, so that the system behaves as a mixture of gases with different polytropic indices. We find the self-similar solutions for the expansion of hot strongly magnetized plasma into vacuum. Second, we derive linear hodograph and Darboux equations for the relativistic Khalatnikov potential, which describe arbitrary one-dimensional isentropic relativistic motion of cold magnetized plasma and find their general and particular solutions. The obtained hodograph and Darboux equations are very powerful: A system of highly nonlinear, relativistic, time-dependent equations describing arbitrary (not necessarily self-similar) dynamics of highly magnetized plasma reduces to a single linear differential equation.
Modeling axisymmetric flow and transport.
Langevin, Christian D
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.
Modeling axisymmetric flow and transport
Langevin, C.D.
2008-01-01
Unmodified versions of common computer programs such as MODFLOW, MT3DMS, and SEAWAT that use Cartesian geometry can accurately simulate axially symmetric ground water flow and solute transport. Axisymmetric flow and transport are simulated by adjusting several input parameters to account for the increase in flow area with radial distance from the injection or extraction well. Logarithmic weighting of interblock transmissivity, a standard option in MODFLOW, can be used for axisymmetric models to represent the linear change in hydraulic conductance within a single finite-difference cell. Results from three test problems (ground water extraction, an aquifer push-pull test, and upconing of saline water into an extraction well) show good agreement with analytical solutions or with results from other numerical models designed specifically to simulate the axisymmetric geometry. Axisymmetric models are not commonly used but can offer an efficient alternative to full three-dimensional models, provided the assumption of axial symmetry can be justified. For the upconing problem, the axisymmetric model was more than 1000 times faster than an equivalent three-dimensional model. Computational gains with the axisymmetric models may be useful for quickly determining appropriate levels of grid resolution for three-dimensional models and for estimating aquifer parameters from field tests.
NASA Astrophysics Data System (ADS)
Blair, D. G.; Buckingham, M. J.
Contents: Part A. 1. Rigorous and exact. Classical general relativity: highly non-linear behaviour. Spin, geometry and topology. Approximation methods. Exact solutions. Black hole physics. Alternative theories and torsion. 2. Quantum gravity. Critical accelerations. Quantum gravity. String theories. Cosmic strings, superstrings and supergravity. Quantum cosmology: wavefunction of the universe. Quantum cosmology. 3. Cosmology. Early cosmology and quantum field theory. Supersymmetry, multidimensional cosmology and Kaluza-Klein theory. Theoretical cosmology. Large-scale structure of the universe. Dark matter. Part B. 4. Mathematical astrophysics. Algebraic computing. Numerical relativity. Astrophysics of collapsed objects. Self gravitating systems. History of general relativity. 5. Observational astrophysics. Sources of gravitational radiation. Relativistic astrophysics. Supernovae. Observation of collapsed objects. Cosmic background. 5. Precision experiments. The fifth force. Measuring the gravitational interaction in precision space experiments. Resonant bar antennas. Laser interferometer antennas. Detection of gravitational radiation. Quantum technology for gravitational radiation detection. Precision clocks in general relativity.
Axisymmetric Coanda-assisted vectoring
NASA Astrophysics Data System (ADS)
Allen, Dustin; Smith, Barton L.
2009-01-01
An experimental demonstration of a jet vectoring technique used in our novel spray method called Coanda-assisted Spray Manipulation (CSM) is presented. CSM makes use of the Coanda effect on axisymmetric geometries through the interaction of two jets: a primary jet and a control jet. The primary jet has larger volume flow rate but generally a smaller momentum flux than the control jet. The primary jet flows through the center of a rounded collar. The control jet is parallel to the primary and is adjacent to the convex collar. The Reynolds number range for the primary jet at the exit plane was between 20,000 and 80,000. The flow was in the incompressible Mach number range (Mach < 0.3). The control jet attaches to the convex wall and vectors according to known Coanda effect principles, entraining and vectoring the primary jet, resulting in controllable r - θ directional spraying. Several annular control slots and collar radii were tested over a range of momentum flux ratios to determine the effects of these variables on the vectored jet angle and spreading. Two and Three-component Particle Image Velocimetry systems were used to determine the vectoring angle and the profile of the combined jet in each experiment. The experiments show that the control slot and expansion radius, along with the momentum ratios of the two jets predominantly affected the vectoring angle and profile of the combined jets.
The Formation of Relativistic Jets from Kerr Black Holes
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Richardson, G.; Preece, R.; Hardee, P.; Koide, S.; Shibata, K.; Kudoh, T.; Sol, H.; Fishman, G. J.
2003-01-01
We have performed the first fully three-dimensional general relativistic magnetohydrodynamics (GRMHD) simulation for Schwarzschild and Kerr black holes with a free falling corona and thin accretion disk. The initial simulation results with a Schwarzschild metric show that a jet is created as in the previous axisymmetric simulations with mirror symmetry at the equator. However, the time to form the jet is slightly longer than in the 2-D axisymmetric simulation. We expect that the dynamics of jet formation are modified due to the additional freedom in the azimuth dimension without axisymmetry with respect to the Z axis and reflection symmetry respect to the equatorial plane. The jet which is initially formed due to the twisted magnetic fields and shocks becomes a wind at the later time. The wind flows out with a much wider angle than the initial jet. The twisted magnetic fields at the earlier time were untwisted and less pinched. The accretion disk became thicker than the initial condition. Further simulations with initial perturbations will provide insights for accretion dynamics with instabilities such as magneto-rotational instability (MRI) and accretion-eject instability (AEI). These instabilities may contribute to variabilities observed in microquasars and AGN jets.
Axisymmetric annular curtain stability
NASA Astrophysics Data System (ADS)
Ahmed, Zahir U.; Khayat, Roger E.; Maissa, Philippe; Mathis, Christian
2012-06-01
A temporal stability analysis was carried out to investigate the stability of an axially moving viscous annular liquid jet subject to axisymmetric disturbances in surrounding co-flowing viscous gas media. We investigated in this study the effects of inertia, surface tension, the gas-to-liquid density ratio, the inner-to-outer radius ratio and the gas-to-liquid viscosity ratio on the stability of the jet. With an increase in inertia, the growth rate of the unstable disturbances is found to increase. The dominant (or most unstable) wavenumber decreases with increasing Reynolds number for larger values of the gas-to-liquid viscosity ratio. However, an opposite tendency for the most unstable wavenumber is predicted for small viscosity ratio in the same inertia range. The surrounding gas density, in the presence of viscosity, always reduces the growth rate, hence stabilizing the flow. There exists a critical value of the density ratio above which the flow becomes stable for very small viscosity ratio, whereas for large viscosity ratio, no stable flow appears in the same range of the density ratio. The curvature has a significant destabilizing effect on the thin annular jet, whereas for a relatively thick jet, the maximum growth rate decreases as the inner radius increases, irrespective of the surrounding gas viscosity. The degree of instability increases with Weber number for a relatively large viscosity ratio. In contrast, for small viscosity ratio, the growth rate exhibits a dramatic dependence on the surface tension. There is a small Weber number range, which depends on the viscosity ratio, where the flow is stable. The viscosity ratio always stabilizes the flow. However, the dominant wavenumber increases with increasing viscosity ratio. The range of unstable wavenumbers is affected only by the curvature effect.
NASA Astrophysics Data System (ADS)
McNair, S. Lauren; Tragesser, Steven
2017-03-01
A unique formulation of the solution to a spinning, nearly axisymmetric rigid-body is presented. Direct integration of the linearized equations of motion gives accurate results for nearly axisymmetric inertia ellipsoids while avoiding the complexity of more general formulations. The simplicity of the formulation lends itself to a better understanding of the system behavior. Specifically, the motion of the spin axis for this nearly axisymmetric case is described by an oblate epicycloid, providing an extension of the classic epicycloid solution for axisymmetric objects.
Rotating and binary relativistic stars with magnetic field
NASA Astrophysics Data System (ADS)
Markakis, Charalampos
We develop a geometrical treatment of general relativistic magnetohydrodynamics for perfectly conducting fluids in Einstein--Maxwell--Euler spacetimes. The theory is applied to describe a neutron star that is rotating or is orbiting a black hole or another neutron star. Under the hypotheses of stationarity and axisymmetry, we obtain the equations governing magnetohydrodynamic equilibria of rotating neutron stars with poloidal, toroidal or mixed magnetic fields. Under the hypothesis of an approximate helical symmetry, we obtain the first law of thermodynamics governing magnetized equilibria of double neutron star or black hole - neutron star systems in close circular orbits. The first law is written as a relation between the change in the asymptotic Noether charge deltaQ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetofluid. In an attempt to provide a better theoretical understanding of the methods used to construct models of isolated rotating stars and corotating or irrotational binaries and their unexplained convergence properties, we analytically examine the behavior of different iterative schemes near a static solution. We find the spectrum of the linearized iteration operator and show for self-consistent field methods that iterative instability corresponds to unstable modes of this operator. On the other hand, we show that the success of iteratively stable methods is due to (quasi-)nilpotency of this operator. Finally, we examine the integrability of motion of test particles in a stationary axisymmetric gravitational field. We use a direct approach to seek nontrivial constants of motion polynomial in the momenta---in addition to energy and angular momentum about the symmetry axis. We establish the existence and uniqueness of quadratic constants and the nonexistence of quartic constants for stationary axisymmetric Newtonian potentials with equatorial symmetry
Fast electron bremsstrahlung in axisymmetric magnetic configuration
NASA Astrophysics Data System (ADS)
Peysson, Y.; Decker, J.
2008-09-01
The nonthermal bremsstrahlung is calculated in a plasma with arbitrary axisymmetric magnetic configuration, taking into account the relativistic angular anisotropy of the radiation cross section at high photon energies, the helical winding of the field lines on the magnetic flux surfaces, and the poloidal variation of the electron distribution function including particle trapping effects. The fast electron dynamics during current drive in tokamaks and reverse field pinches can be investigated in detail by coupling this calculation to a bounce-averaged relativistic Fokker-Planck solver, which calculates the electron distribution function. The asymmetry between high- and low-field side hard x-ray emission intensity that has been measured on the Tore-Supra tokamak [Equipe TORE SUPRA, in Proceedings of the 15th Conference on Plasma Physics and Controlled Nuclear Fusion Research, Seville (International Atomic Energy Agency, Vienna, 1995) Vol. 1, IAEA-CN-60/A1-5 (Institute of Physics, Bristol, U.K., 1995), p. 105] is explained for the first time by the role of trapped electrons. A much stronger poloidal asymmetry is predicted for the line-integrated fast electron bremsstrahlung in the poloidal plane of the Madison Symmetric Torus [R. N. Dexter et al., Fusion Tech. 19, 131 (1991)], since the helical winding of the magnetic field lines is much larger for a reverse field pinch configuration. In this case, the hard x-ray emission is no longer a flux surface quantity, which prevents local reconstructions using a standard Abel inversion, whatever the geometrical arrangement of the lines of sight.
ACCELERATION AND COLLIMATION OF RELATIVISTIC MAGNETOHYDRODYNAMIC DISK WINDS
Porth, Oliver; Fendt, Christian E-mail: fendt@mpia.d
2010-02-01
We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 x 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied-an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically-implying three relativistically distinct regimes in the flow-an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface-similar to the spine-sheath structure currently
Acceleration and Collimation of Relativistic Magnetohydrodynamic Disk Winds
NASA Astrophysics Data System (ADS)
Porth, Oliver; Fendt, Christian
2010-02-01
We perform axisymmetric relativistic magnetohydrodynamic simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. Newtonian gravity is added to the relativistic treatment in order to establish the physical boundary condition of an underlying accretion disk in centrifugal and pressure equilibrium. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Substantial effort has been made to implement a current-free, numerical outflow boundary condition in order to avoid artificial collimation present in the standard outflow conditions. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100 × 200 inner disk radii. The simulations evolve from an initial state in hydrostatic equilibrium and an initially force-free magnetic field configuration. Two options for the initial field geometries are applied—an hourglass-shaped potential magnetic field and a split monopole field. Most of our parameter runs evolve into a steady state solution which can be further analyzed concerning the physical mechanism at work. In general, we obtain collimated beams of mildly relativistic speed with Lorentz factors up to 6 and mass-weighted half-opening angles of 3-7 deg. The split-monopole initial setup usually results in less collimated outflows. The light surface of the outflow magnetosphere tends to align vertically—implying three relativistically distinct regimes in the flow—an inner subrelativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface—similar to the spine-sheath structure
Particle acceleration in axisymmetric pulsar current sheets
NASA Astrophysics Data System (ADS)
Cerutti, Benoît; Philippov, Alexander; Parfrey, Kyle; Spitkovsky, Anatoly
2015-03-01
The equatorial current sheet in pulsar magnetospheres is often regarded as an ideal site for particle acceleration via relativistic reconnection. Using 2D spherical particle-in-cell simulations, we investigate particle acceleration in the axisymmetric pulsar magnetosphere as a function of the injected plasma multiplicity and magnetization. We observe a clear transition from a highly charge-separated magnetosphere for low plasma injection with little current and spin-down power, to a nearly force-free solution for high plasma multiplicity characterized by a prominent equatorial current sheet and high spin-down power. We find significant magnetic dissipation in the current sheet, up to 30 per cent within 5 light-cylinder radii in the high-multiplicity regime. The simulations unambiguously demonstrate that the dissipated Poynting flux is efficiently channelled to the particles in the sheet, close to the Y-point within about 1-2 light-cylinder radii from the star. The mean particle energy in the sheet is given by the upstream plasma magnetization at the light cylinder. The study of particle orbits shows that all energetic particles originate from the boundary layer between the open and the closed field lines. Energetic positrons always stream outwards, while high-energy electrons precipitate back towards the star through the sheet and along the separatrices, which may result in auroral-like emission. Our results suggest that the current sheet and the separatrices may be the main source of high-energy radiation in young pulsars.
Kallay, Mihaly; Nataraj, H. S.; Sahoo, B. K.; Das, B. P.; Visscher, Lucas
2011-03-15
We report the implementation of a general-order relativistic coupled-cluster method for performing high-precision calculations of atomic and molecular properties. As a first application, the black-body radiation shift of the Al{sup +} clock has been estimated precisely. The computed shift relative to the frequency of the 3s{sup 2} {sup 1}S{sub 0}{sup e}{yields}3s3p {sup 3}P{sub 0}{sup o} clock transition given by (-3.66{+-}0.60)x10{sup -18} calls for an improvement over the recent measurement with a reported result of (-9{+-}3)x10{sup -18}[Phys. Rev. Lett. 104, 070802 (2010)].
The relativistic equations of stellar structure and evolution
NASA Technical Reports Server (NTRS)
Thorne, K. S.
1977-01-01
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.
The relation between relativistic and non-relativistic continuum thermodynamics
NASA Astrophysics Data System (ADS)
Schellstede, G. O.; von Borzeszkowski, H.-H.; Chrobok, T.; Muschik, W.
2014-01-01
We consider the relativistic theory of irreversible processes with the aim to answer the following questions: (1) Under which conditions is this theory a relativistic generalization of the non-relativistic theory of irreversible processes (in particular, this implies to ask for the conditions under which the first law of thermodynamics can be recovered from the relativistic conservation law of total energy), and (2) how do the relativistic corrections look like? To this end, we perform a low-energy approximation for the balance equations underlying the theory, i.e., for the balances of the particle number, the energy-momentum and the entropy. It is shown that, going up to the 3rd order in the expansion series of the balances, the non-relativistic theory can be derived when one assumes that the 4-current of the particle flow is purely convective and the product of the 3-dimensional acceleration and velocity is equal to zero. Afterwards, the higher-order terms are discussed. Since our discussion mainly makes use of those balance equations that lie on the basis of most versions of continuum thermodynamics, the results do not only refer to early TIP presented by Eckart (Phys Rev 58:919,
REVIEW ARTICLE: Control of non-axisymmetric toroidal plasmas
NASA Astrophysics Data System (ADS)
Boozer, Allen H.
2010-10-01
The control of non-axisymmetric toroidal plasmas, stellarators, has a different character than the control of tokamaks for two reasons. Non-axisymmetric magnetic fields (1) can provide an arbitrarily large fraction of the poloidal magnetic field and (2) can strongly center the plasma in the chamber making it impossible to lose position control. The focus of stellarator design is on plasmas that are stable without feedback, need little or no change in the external magnetic field as the plasma evolves, and require no external power to maintain the desired magnetic configuration. The physics of non-axisymmetric fields is the same whether in a tokamak or a stellarator and whether introduced intentionally or accidentally. Fundamental physics indicates that plasma shape, which is controlled by the distribution of the external magnetic field that is normal to the plasma surface, is the primary control for fusion plasmas. The importance of non-axisymmetric control is set by the importance of toroidal plasma physics. Informed decisions on the development strategy of tokamaks, as well as magnetic fusion in general, require an understanding of the capabilities and difficulties of plasma control at various levels of non-axisymmetric shaping.
Radiative configuration factors from cylinders to coaxial axisymmetric bodies
NASA Technical Reports Server (NTRS)
Saltiel, C.; Naraghi, M. H. N.
1990-01-01
Exact solutions are obtained for the radiative configuration factor between differential elements of arbitrary orientation and cylinders. A general method is then proposed for calculating the view factor from a cylinder to a coaxial axisymmetric body using only a single numerical integration. The method is illustrated for axisymmetric bodies with function generators described by a power law equation. The method may be useful in calculating radiative heat transfer between cylindrical bodies and high-density exhaust gases and between annular radiative fins and their bases.
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.
Relativistic Jets from Collapsars
NASA Astrophysics Data System (ADS)
Aloy, M. A.; Müller, E.; Ibáñez, J. M.; Martí, J. M.; MacFadyen, A.
2000-03-01
Using a collapsar progenitor model of MacFadyen & Woosley, we have simulated the propagation of an axisymmetric jet through a collapsing rotating massive star with the GENESIS multidimensional relativistic hydrodynamic code. The jet forms as a consequence of an assumed (constant or variable) energy deposition in the range of 1050-1051 ergs s-1 within a 30 deg cone around the rotation axis. The jet flow is strongly beamed (approximately less than a few degrees), spatially inhomogeneous, and time dependent. The jet reaches the surface of the stellar progenitor (R*=2.98x1010 cm) intact. At breakout, the maximum Lorentz factor of the jet flow is 33. After breakout, the jet accelerates into the circumstellar medium, whose density is assumed to decrease exponentially and then become constant, ρext=10-5 g cm-3. Outside the star, the flow begins to expand laterally also (v~c), but the beam remains very well collimated. At a distance of 2.54 R*, where the simulation ends, the Lorentz factor has increased to 44.
Relativistic radiation transport in dispersive media
Kichenassamy, S.; Krikorian, R.A.
1985-10-15
A general-relativistic radiative transfer equation in an isotropic, weakly absorbing, nonmagnetized dispersive medium is derived using the kinetic-theoretical approach and the relativistic Hamiltonian theory of geometrical optics in those media. It yields the generally accepted classical equation in the special-relativistic approximation and in stationary conditions. The influence of the gravitational field and of space-time variations of the refractive index n on the radiation distribution is made explicit in the case of spherical symmetry.
Allen, M.A.; Azuma, O.; Callin, R.S.; Deruyter, H.; Eppley, K.R.; Fant, K.S.; Fowkes, W.R.; Herrmannsfeldt, W.B.; Hoag, H.A.; Koontz, R.F.
1989-03-01
Experimental work is underway by a SLAC-LLNL-LBL collaboration to investigate the feasibility of using relativistic klystrons as a power source for future high gradient accelerators. Two different relativistic klystron configurations have been built and tested to date: a high grain multicavity klystron at 11.4 GHz and a low gain two cavity subharmonic buncher driven at 5.7 GHz. In both configurations power is extracted at 11.4 GHz. In order to understand the basic physics issues involved in extracting RF from a high power beam, we have used both a single resonant cavity and a multi-cell traveling wave structure for energy extraction. We have learned how to overcome our previously reported problem of high power RF pulse shortening, and have achieved peak RF power levels of 170 MW with the RF pulse of the same duration as the beam current pulse. 6 refs., 3 figs., 3 tabs.
NASA Astrophysics Data System (ADS)
Flury, J.
2016-06-01
Quantum metrology enables new applications in geodesy, including relativistic geodesy. The recent progress in optical atomic clocks and in long-distance frequency transfer by optical fiber together pave the way for using measurements of the gravitational frequency redshift for geodesy. The remote comparison of frequencies generated by calibrated clocks will allow for a purely relativistic determination of differences in gravitational potential and height between stations on Earth surface (chronometric leveling). The long-term perspective is to tie potential and height differences to atomic standards in order to overcome the weaknesses and inhomogeneity of height systems determined by classical spirit leveling. Complementarily, gravity measurements with atom interferometric setups, and satellite gravimetry with space borne laser interferometers allow for new sensitivities in the measurement of the Earth's gravity field.
Relativistic effects in atom gravimeters
NASA Astrophysics Data System (ADS)
Tan, Yu-Jie; Shao, Cheng-Gang; Hu, Zhong-Kun
2017-01-01
Atom interferometry is currently developing rapidly, which is now reaching sufficient precision to motivate laboratory tests of general relativity. Thus, it is extremely significant to develop a general relativistic model for atom interferometers. In this paper, we mainly present an analytical derivation process and first give a complete vectorial expression for the relativistic interferometric phase shift in an atom interferometer. The dynamics of the interferometer are studied, where both the atoms and the light are treated relativistically. Then, an appropriate coordinate transformation for the light is performed crucially to simplify the calculation. In addition, the Bordé A B C D matrix combined with quantum mechanics and the "perturbation" approach are applied to make a methodical calculation for the total phase shift. Finally, we derive the relativistic phase shift kept up to a sensitivity of the acceleration ˜1 0-14 m/s 2 for a 10 -m -long atom interferometer.
Post-Newtonian reference ellipsoid for relativistic geodesy
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena
2016-02-01
We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to
NASA Astrophysics Data System (ADS)
Jones, Bernard J. T.; Markovic, Dragoljub
1997-06-01
Preface; Prologue: Conference overview Bernard Carr; Part I. The Universe At Large and Very Large Redshifts: 2. The size and age of the Universe Gustav A. Tammann; 3. Active galaxies at large redshifts Malcolm S. Longair; 4. Observational cosmology with the cosmic microwave background George F. Smoot; 5. Future prospects in measuring the CMB power spectrum Philip M. Lubin; 6. Inflationary cosmology Michael S. Turner; 7. The signature of the Universe Bernard J. T. Jones; 8. Theory of large-scale structure Sergei F. Shandarin; 9. The origin of matter in the universe Lev A. Kofman; 10. New guises for cold-dark matter suspects Edward W. Kolb; Part II. Physics and Astrophysics Of Relativistic Compact Objects: 11. On the unification of gravitational and inertial forces Donald Lynden-Bell; 12. Internal structure of astrophysical black holes Werner Israel; 13. Black hole entropy: external facade and internal reality Valery Frolov; 14. Accretion disks around black holes Marek A. Abramowicz; 15. Black hole X-ray transients J. Craig Wheeler; 16. X-rays and gamma rays from active galactic nuclei Roland Svensson; 17. Gamma-ray bursts: a challenge to relativistic astrophysics Martin Rees; 18. Probing black holes and other exotic objects with gravitational waves Kip Thorne; Epilogue: the past and future of relativistic astrophysics Igor D. Novikov; I. D. Novikov's scientific papers and books.
Homoclinic chaos in axisymmetric Bianchi-IX cosmological models with an ad hoc quantum potential
Correa, G. C.; Stuchi, T. J.; Joras, S. E.
2010-04-15
In this work we study the dynamics of the axisymmetric Bianchi-IX cosmological model with a term of quantum potential added. As it is well known, this class of Bianchi-IX models is homogeneous and anisotropic with two scale factors, A(t) and B(t), derived from the solution of Einstein's equation for general relativity. The model we use in this work has a cosmological constant and the matter content is dust. To this model we add a quantum-inspired potential that is intended to represent short-range effects due to the general relativistic behavior of matter in small scales and play the role of a repulsive force near the singularity. We find that this potential restricts the dynamics of the model to positive values of A(t) and B(t) and alters some qualitative and quantitative characteristics of the dynamics studied previously by several authors. We make a complete analysis of the phase space of the model finding critical points, periodic orbits, stable/unstable manifolds using numerical techniques such as Poincare section, numerical continuation of orbits, and numerical globalization of invariant manifolds. We compare the classical and the quantum models. Our main result is the existence of homoclinic crossings of the stable and unstable manifolds in the physically meaningful region of the phase space [where both A(t) and B(t) are positive], indicating chaotic escape to inflation and bouncing near the singularity.
Axisymmetric Vortices with Swirl
NASA Astrophysics Data System (ADS)
Elcrat, A.
2007-11-01
This talk is concerned with finding solutions of the Euler equations by solving elliptic boundary value problems for the Bragg-Hawthorne equation L u= -urr -(1/r)ur - = r^2f (u) + h(u). Theoretical results have been given for previously (Elcrat and Miller, Differential and Integral Equations 16(4) 2003, 949-968) for problems with swirl and general classes of profile functions f, h by iterating Lu(n+1)= rf(u)n)) + h(u(n)), and showing u(n) converges montonically to a solution. The solutions obtained depend on the initial guess, which can be thought of as prescribing level sets of the vortex. When a computational program was attempted these monotone iterations turned out to be numerically unstable, and a stable computation was acheived by fixing the moment of the cross section of a vortex in the merideanal plane. (This generalizes previous computational results in Elcrat, Fornberg and Miller, JFM 433 2001, (315-328) We obtain famillies of vortices related to vortex rings with swirl, Moffatt's generalization of Hill's vortex and tubes of vorticity with swirl wrapped around the symmetry axis. The vortices are embedded in either an irrotational flow or a flow with shear, and we deal with the transition form no swirl in the vortex to flow with only swirl, a Beltrami flow.
A minimal axisymmetric hurricane model
NASA Astrophysics Data System (ADS)
Mai, Nguyen Chi; Smith, Roger K.; Zhu, Hongyan; Ulrich, Wolfgang
2002-10-01
Solutions of an axisymmetric version of the minimal three-dimensional numerical model of a tropical cyclone developed by Zhu et al. (2001) are described and compared with those of the three-dimensional model. Vortex evolution is similar in the two models during the early stages of intensification, but the period of rapid intensification occurs earlier in the axisymmetric model due to the higher effective resolution obtained using a staggered grid. There are marked differences at later times, when, in the three-dimensional model, asymmetric structures develop. The findings are compared with those of an earlier study by Anthes (1972). The axisymmetric model is used to investigate certain fundamental aspects of tropical-cyclone dynamics, including the emergence of a region of supergradient winds in the boundary layer and the evolution of regions satisfying necessary conditions for inertial and barotropic instability.Supergradient winds develop in the boundary layer within a radius of about 100 km of the vortex axis at an early stage of evolution and appear to be a natural feature of the vortex boundary layer. The development of flow regions satisfying necessary conditions for inertial and barotropic instability occur later, and may be attributed inter alia to the upward transfer of air with relatively high angular momentum, from the boundary layer to the middle and upper layers, by the secondary circulation of the vortex, and the downward transfer of air with relatively low angular momentum to the middle layer. A linear analysis of a two-layer slab-symmetric flow suggests why inertial instability does not occur in the axisymmetric model. Barotropic instability does not appear to be the mechanism responsible for the growth of asymmetries in the calculations using the three-dimensional version of the model.
Relativistic Bernstein waves in a degenerate plasma
Ali, Muddasir; Hussain, Azhar; Murtaza, G.
2011-09-15
Bernstein mode for a relativistic degenerate electron plasma is investigated. Using relativistic Vlasov-Maxwell equations, a general expression for the conductivity tensor is derived and then employing Fermi-Dirac distribution function a generalized dispersion relation for the Bernstein mode is obtained. Two limiting cases, i.e., non-relativistic and ultra-relativistic are discussed. The dispersion relations obtained are also graphically presented for some specific values of the parameters depicting how the propagation characteristics of Bernstein waves as well as the Upper Hybrid oscillations are modified with the increase in plasma number density.
Greenwald, Jared; Satheeshkumar, V.H.; Wang, Anzhong E-mail: VHSatheeshkumar@baylor.edu
2010-12-01
We study spherically symmetric static spacetimes generally filled with an anisotropic fluid in the nonrelativistic general covariant theory of gravity. In particular, we find that the vacuum solutions are not unique, and can be expressed in terms of the U(1) gauge field A. When solar system tests are considered, severe constraints on A are obtained, which seemingly pick up the Schwarzschild solution uniquely. In contrast to other versions of the Horava-Lifshitz theory, non-singular static stars made of a perfect fluid without heat flow can be constructed, due to the coupling of the fluid with the gauge field. These include the solutions with a constant pressure. We also study the general junction conditions across the surface of a star. In general, the conditions allow the existence of a thin matter shell on the surface. When applying these conditions to the perfect fluid solutions with the vacuum ones as describing their external spacetimes, we find explicitly the matching conditions in terms of the parameters appearing in the solutions. Such matching is possible even without the presence of a thin matter shell.
Relativistic gravity gradiometry
NASA Astrophysics Data System (ADS)
Bini, Donato; Mashhoon, Bahram
2016-12-01
In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck [Proc. R. Soc. A 385, 431 (1983)]. We are interested in the measured components of the curvature tensor along the inclined "circular" geodesic orbit of a test mass about a slowly rotating astronomical object of mass M and angular momentum J . Therefore, we specialize Marck's results to such a "circular" orbit that is tilted with respect to the equatorial plane of the Kerr source. To linear order in J , we recover the gravitomagnetic beating phenomenon [B. Mashhoon and D. S. Theiss, Phys. Rev. Lett. 49, 1542 (1982)], where the beat frequency is the frequency of geodetic precession. The beat effect shows up as a special long-period gravitomagnetic part of the relativistic tidal matrix; moreover, the effect's short-term manifestations are contained in certain post-Newtonian secular terms. The physical interpretation of this effect is briefly discussed.
Transition from gas to plasma kinetic equilibria in gravitating axisymmetric structures
Cremaschini, Claudio; Stuchlík, Zdeněk
2014-04-15
The problem of the transition from gas to plasma in gravitating axisymmetric structures is addressed under the assumption of having initial and final states realized by kinetic Maxwellian-like equilibria. In astrophysics, the theory applies to accretion-disc scenarios around compact objects. A formulation based on non-relativistic kinetic theory for collisionless systems is adopted. Equilibrium solutions for the kinetic distribution functions describing the initial neutral matter and the resulting plasma state are constructed in terms of single-particle invariants and expressed by generalized Maxwellian distributions. The final plasma configuration is related to the initial gas distribution by the introduction of appropriate functional constraints. Qualitative aspects of the solution are investigated and physical properties of the system are pointed out. In particular, the admitted functional dependences of the fluid fields carried by the corresponding equilibrium distributions are determined. Then, the plasma is proved to violate the condition of quasi-neutrality, implying a net charge separation between ions and electrons. This result is shown to be independent of the precise realization of the plasma distribution function, while a physical mechanism able to support a non-neutral equilibrium state is proposed.
Knecht, Stefan; Jensen, Hans Jorgen Aa; Fleig, Timo
2008-01-07
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5x10(9) Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10 days to less than 1 day.
NASA Astrophysics Data System (ADS)
Knecht, Stefan; Jensen, Hans Jørgen Aa.; Fleig, Timo
2008-01-01
We present a parallel implementation of a string-driven general active space configuration interaction program for nonrelativistic and scalar-relativistic electronic-structure calculations. The code has been modularly incorporated in the DIRAC quantum chemistry program package. The implementation is based on the message passing interface and a distributed data model in order to efficiently exploit key features of various modern computer architectures. We exemplify the nearly linear scalability of our parallel code in large-scale multireference configuration interaction (MRCI) calculations, and we discuss the parallel speedup with respect to machine-dependent aspects. The largest sample MRCI calculation includes 1.5×109 Slater determinants. Using the new code we determine for the first time the full short-range electronic potentials and spectroscopic constants for the ground state and for eight low-lying excited states of the weakly bound molecular system (Rb-Ba)+ with the spin-orbit-free Dirac formalism and using extensive uncontracted basis sets. The time required to compute to full convergence these electronic states for (Rb-Ba)+ in a single-point MRCI calculation correlating 18 electrons and using 16 cores was reduced from more than 10days to less than 1day.
NASA Astrophysics Data System (ADS)
Mondragon-Suarez, J. H.; Brun-Battistini, D.; Sandoval-Villalbazo, A.; Garcia-Perciante, A. L.
2015-11-01
In this paper tensor transport processes present in single-component dilute fluids are discussed within the framework of irreversible thermodynamics using elements of general relativity. The formalism suggests the existence of a tensor analog of Tolman's effect. In this case, the traceless symmetric part of the local hydrodynamic velocity gradient is compensated (in principle) with the terms containing sources of curvature in the case of null entropy production. This result is obtained only if the field effects are included in the treatment of the Boltzmann equation through the use of geodesics. The authors acknowledge support from CONACyT through grant CB2011/167563.
The r-process in black hole-neutron star mergers based on a fully general-relativistic simulation
NASA Astrophysics Data System (ADS)
Nishimura, N.; Wanajo, S.; Sekiguchi, Y.; Kiuchi, K.; Kyutoku, K.; Shibata, M.
2016-01-01
We investigate the black hole-neutron star binary merger in the contest of the r-process nucleosynthesis. Employing a hydrodynamical model simulated in the framework of full general relativity, we perform nuclear reaction network calculations. The extremely neutron-rich matter with the total mass 0.01 M⊙ is ejected, in which a strong r-process with fission cycling proceeds due to the high neutron number density. We discuss relevant astrophysical issues such as the origin of r-process elements as well as the r-process powered electromagnetic transients.
NASA Astrophysics Data System (ADS)
Ghosh, Shubhrangshu; Banik, Prabir
2015-07-01
In this paper, we present a complete work on steady state spherically symmetric Bondi type accretion flow in the presence of cosmological constant (Λ) in both Schwarzschild-de Sitter (SDS) and Schwarzschild anti-de Sitter (SADS) backgrounds considering an isolated supermassive black hole (SMBH), with the inclusion of a simple radiative transfer scheme, in the pseudo-general relativistic paradigm. We do an extensive analysis on the transonic behavior of the Bondi type accretion flow onto the cosmological BHs including a complete analysis of the global parameter space and the stability of flow, and do a complete study of the global family of solutions for a generic polytropic flow. Bondi type accretion flow in SADS background renders multiplicity in its transonic behavior with inner "saddle" type and outer "center" type sonic points, with the transonic solutions forming closed loops or contours. There is always a limiting value for ∣Λ∣ up to which we obtain valid stationary transonic solutions, which correspond to both SDS and SADS geometries; this limiting value moderately increases with the increasing radiative efficiency of the flow, especially correspond to Bondi type accretion flow in SADS background. Repulsive Λ suppresses the Bondi accretion rate by an order of magnitude for relativistic Bondi type accretion flow for a certain range in temperature, and with a marginal increase in the Bondi accretion rate if the corresponding accretion flow occurs in SADS background. However, for a strongly radiative Bondi type accretion flow with high mass accretion rate, the presence of cosmological constant do not much influence the corresponding Bondi accretion rate of the flow. Our analysis show that the relic cosmological constant has a substantial effect on Bondi type accretion flow onto isolated SMBHs and their transonic solutions beyond length-scale of kiloparsecs, especially if the Bondi type accretion occurs onto the host supergiant ellipticals or central
Multispecies transport theory for axisymmetric rotating plasmas
Tessarotto, M.; White, R.B.
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to ``explicit`` velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer`s inductive terms.
Multispecies transport theory for axisymmetric rotating plasmas
Tessarotto, M. . Dipt. di Scienze Matematiche); White, R.B. . Plasma Physics Lab.)
1992-01-01
A reduced gyrokinetic equation is derived for a multi-species toroidal axisymmetric plasma with arbitrary toroidal differential rotation speeds and in the presence of a finite induced electric field. The kinetic equation obtained, extending previous results obtained by Hinton and Wong and by Catto, Bernstein and Tessarotto, has a form suited for transport applications, via variational techniques; in particular it exhibits the feature that all source terms, including the Spitzer source term, carrying the contribution due to the inductive electric field, appear to be acted upon by the collision operator. Moreover, the equation displays a new contribution due to explicit'' velocity perturbations, here proven to be consistent with transport ordering, whose evaluation appears relevant for transport calculations. In addition, general expressions are obtained for the neoclassical fluxes in terms of a variational principle, as well as for the classical ones, retaining, in both cases, the contributions due to the Spitzer's inductive terms.
Axisymmetric supersonic flow in rotating impellers
NASA Technical Reports Server (NTRS)
Goldstein, Arthur W
1952-01-01
General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.
Reintjes, Moritz; Temple, Blake
2015-01-01
We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C0,1 to C1,1 in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C1,1, cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein–Euler equations remains open. PMID:27547092
Reintjes, Moritz; Temple, Blake
2015-05-08
We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from C(0,1) to C(1,1) in a neighbourhood of points of shock wave collision in general relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier Proc. R. Soc. A publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to C(1,1), cannot exist. Thus, our result implies that regularity singularities (a type of mild singularity introduced in our Proc. R. Soc. A paper) do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original Proc. R. Soc. A publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein-Euler equations remains open.
Carter-like constants of motion in the Newtonian and relativistic two-center problems
NASA Astrophysics Data System (ADS)
Mirshekari, Saeed; Will, Clifford M.
2010-12-01
In Newtonian gravity, a stationary axisymmetric system admits a third, Carter-like constant of motion if its mass multipole moments are related to each other in exactly the same manner as for the Kerr black-hole spacetime. The Newtonian source with this property consists of two point masses at rest a fixed distance apart. The integrability of motion about this source was first studied in the 1760s by Euler. We show that the general relativistic analog of the Euler problem, the Bach-Weyl solution, does not admit a Carter-like constant of motion, first, by showing that it does not possess a non-trivial Killing tensor, and secondly, by showing that the existence of a Carter-like constant for the two-center problem fails at the first post-Newtonian order.
The Case for General Relativistic Effects in the Fe K(alpha) Profile of an Active Galaxy
NASA Technical Reports Server (NTRS)
Turner, T. J.; Mushotzky, R.; Yaqoob, T.; George, I. M.; Snowden, S. L.; Netzer, H.; Kraemer, S. B.; Nandra, K.; Chelouche, D.; White, Nicholas E. (Technical Monitor)
2002-01-01
We present results from a simultaneous Chandra HETG (High Energy Transmission Grating) and XMM (X-ray Multi-mirror Mission)-Newton observation of NGC 3516. We find evidence for several narrow components of Fe K(alpha) along with a broad line. We consider the possibility that the lines arise in a blob of material ejected from the nucleus with velocity of approximately 0.25c. We also consider an origin in a neutral accretion disk, suffering enhanced illumination at 35 and 175 R(sub g), perhaps due to magnetic reconnection. The presence of these narrow features indicates there is no Comptonizing region along the line-of-sight to the nucleus. This in turn is compelling support for the hypothesis that broad Fe K(alpha) components are, in general, produced by strong gravity.
NASA Astrophysics Data System (ADS)
Hehl, Friedrich W.; McCrea, J. Dermott
1986-03-01
Automatic conservation of energy-momentum and angular momentum is guaranteed in a gravitational theory if, via the field equations, the conservation laws for the material currents are reduced to the contracted Bianchi identities. We first execute an irreducible decomposition of the Bianchi identities in a Riemann-Cartan space-time. Then, starting from a Riemannian space-time with or without torsion, we determine those gravitational theories which have automatic conservation: general relativity and the Einstein-Cartan-Sciama-Kibble theory, both with cosmological constant, and the nonviable pseudoscalar model. The Poincaré gauge theory of gravity, like gauge theories of internal groups, has no automatic conservation in the sense defined above. This does not lead to any difficulties in principle. Analogies to 3-dimensional continuum mechanics are stressed throughout the article.
Oscillations of rapidly rotating relativistic stars
Gaertig, Erich; Kokkotas, Kostas D.
2008-09-15
Nonaxisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This is the first study of its kind and provides information on the effect of fast rotation on the oscillation spectra while it offers the possibility of studying the complete problem by including space-time perturbations. Our study includes both axisymmetric and nonaxisymmetric perturbations and provides limits for the onset of the secular bar mode rotational instability. We also present approximate formulas for the dependence of the oscillation spectrum from rotation. The results suggest that it is possible to extract the relativistic star's parameters from the observed gravitational wave spectrum.
Relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Hernandez, Juan; Kovtun, Pavel
2017-05-01
We present the equations of relativistic hydrodynamics coupled to dynamical electromagnetic fields, including the effects of polarization, electric fields, and the derivative expansion. We enumerate the transport coefficients at leading order in derivatives, including electrical conductivities, viscosities, and thermodynamic coefficients. We find the constraints on transport coefficients due to the positivity of entropy production, and derive the corresponding Kubo formulas. For the neutral state in a magnetic field, small fluctuations include Alfvén waves, magnetosonic waves, and the dissipative modes. For the state with a non-zero dynamical charge density in a magnetic field, plasma oscillations gap out all propagating modes, except for Alfvén-like waves with a quadratic dispersion relation. We relate the transport coefficients in the "conventional" magnetohydrodynamics (formulated using Maxwell's equations in matter) to those in the "dual" version of magnetohydrodynamics (formulated using the conserved magnetic flux).
Definition of the relativistic geoid in terms of isochronometric surfaces
NASA Astrophysics Data System (ADS)
Philipp, Dennis; Perlick, Volker; Puetzfeld, Dirk; Hackmann, Eva; Lämmerzahl, Claus
2017-05-01
We present a definition of the geoid that is based on the formalism of general relativity without approximations; i.e., it allows for arbitrarily strong gravitational fields. For this reason, it applies not only to the Earth and other planets but also to compact objects such as neutron stars. We define the geoid as a level surface of a time-independent redshift potential. Such a redshift potential exists in any stationary spacetime. Therefore, our geoid is well defined for any rigidly rotating object with constant angular velocity and a fixed rotation axis that is not subject to external forces. Our definition is operational because the level surfaces of a redshift potential can be realized with the help of standard clocks, which may be connected by optical fibers. Therefore, these surfaces are also called "isochronometric surfaces." We deliberately base our definition of a relativistic geoid on the use of clocks since we believe that clock geodesy offers the best methods for probing gravitational fields with highest precision in the future. However, we also point out that our definition of the geoid is mathematically equivalent to a definition in terms of an acceleration potential, i.e., that our geoid may also be viewed as a level surface orthogonal to plumb lines. Moreover, we demonstrate that our definition reduces to the known Newtonian and post-Newtonian notions in the appropriate limits. As an illustration, we determine the isochronometric surfaces for rotating observers in axisymmetric static and axisymmetric stationary solutions to Einstein's vacuum field equation, with the Schwarzschild metric, the Erez-Rosen metric, the q metric, and the Kerr metric as particular examples.
Short and long term simulations of relativistic, magnetized jets
NASA Astrophysics Data System (ADS)
Aloy, M. A.
2004-12-01
We will present a series of numerical simulations addressed to understand the morphology and dynamics of relativistic, magnetized, axisymmetric jets. Some of the simulations have been specifically set up to follow the long term evolution of extragalactic jets under idealized conditions. The simulations have been done with an extension of the GENESIS code (Aloy et al 1999a} suitable for relativistic magnetohydrodynamcs applications. The code is based on a Godunov-type scheme whose building block is a method of lines. The numerical algorithm can provide up to third order of accuracy and makes use of a constrained transport method in order to keep the divergence--free condition of the magnetic field.
Dissipation in relativistic pair-plasma reconnection
Hesse, Michael; Zenitani, Seiji
2007-11-15
An investigation into the relativistic dissipation in magnetic reconnection is presented. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. A set of numerical simulations is analyzed, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For antiparallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.
Dissipation in Relativistic Pair-Plasma Reconnection
NASA Technical Reports Server (NTRS)
Hesse, Michael; Zenitani, Seiji
2007-01-01
We present an investigation of the relativistic dissipation in magnetic reconnection. The investigated system consists of an electron-positron plasma. A relativistic generalization of Ohm's law is derived. We analyze a set of numerical simulations, composed of runs with and without guide magnetic field, and of runs with different species temperatures. The calculations indicate that the thermal inertia-based dissipation process survives in relativistic plasmas. For anti-parallel reconnection, it is found that the pressure tensor divergence remains the sole contributor to the reconnection electric field, whereas relativistic guide field reconnection exhibits a similarly important role of the bulk inertia terms.
NASA Astrophysics Data System (ADS)
Barai, Paramita; Das, Tapas K.; Wiita, Paul J.
2006-03-01
In the course of performing an extension of this work, we discovered an error in the metric component gtφ. The value of gtφ in equation (3) must be divided by 2, and the corrected equations (3) and (4) are, respectively,Ω=-(gtφ+λgtt)/(gφφ+λgtφ)=((2a/r)-[λ(4a2-r2Δ)/A])/((A/r2)-(2λa/r)), (3)vt=(Ar2Δ)/((1-u2)[A2-4λarA+λ2r2(4a2-r2Δ)])1/2. (4) The forms of no other equations as displayed in the Letter are affected as they are written in terms of vt, Ω, gtφ, etc. However, the numerical results presented earlier are modified, as are some of our conclusions. The general topology of the flows remains the same, but there are small changes to the inner and middle sonic point locations for given initial assumptions. For example, in Figure 1, the identical parameters a=0.2, E=1.0003, λ=3.1, and γ=4/3 yield nearly identical curves, but they give new values for ri (=5.0847), rm (=13.564), and ro (=1093.8, which is only slightly different). The correction to gtφ produces results that are in many respects more desirable than those reported earlier and are summarized here. The replacement Figure 2 shows that a more limited range of λ-values completely spans the full range of positive spin parameters. For counterrotating flows through ro, the variations of Aδ with a are not monotonic; Mδ shows a maximum, and Tδ, ρδ, pδ show minima at a~=0.5. Now we get common [P3 solutions for both a and -a, up to a<~0.57. For prograde (positive a) flows through ri (relevant during shock formation), the general profiles for the variations of ρδ and pδ with a remain exactly the same as that for flow through ro. Mδ and Tδ also show a similar overall trend for flows through ri and ro. However, for flows through ri, the variations of Mδ and Tδ with a are not monotonic; Mδ has a minimum, and Tδ has a maximum, at some intermediate a-value (near the highest a of their valid multitransonicity range, for fixed E, λ, γ). The comparisons of magnitude for fixed E, λ, γ, a
Relativistic rotation curve for cosmological structures
NASA Astrophysics Data System (ADS)
Razbin, Mohammadhosein; Firouzjaee, Javad T.; Mansouri, Reza
2014-08-01
Using a general relativistic exact model for spherical structures in a cosmological background, we have put forward an algorithm to calculate the test particle geodesics within such cosmological structures in order to obtain the velocity profile of stars or galaxies. The rotation curve thus obtained is based on a density profile and is independent of any mass definition which is not unique in general relativity. It is then shown that this general relativistic rotation curves for a toy model and a NFW density profile are almost identical to the corresponding Newtonian one, although the general relativistic masses may be quite different.
NASA Technical Reports Server (NTRS)
Buschman, Albert J., Jr.; Pittman, Claud M.
1961-01-01
Radiation-interchange configuration factors are derived for axisymmetrical sections of cylinders, cones, and hemispheres radiating internally to annular and circular sections of their bases and to other axisymmetrical sections. The general procedure of obtaining configuration factors is outlined and the results are presented in the form of equations, tables, and figures.
Local stability of axisymmetric plumes
NASA Astrophysics Data System (ADS)
R. v. K., Chakravarthy; Lesshafft, Lutz; Huerre, Patrick
2014-11-01
A linear stability analysis of a forced plume with non-zero momentum at the inlet is performed for Pr = 1 , Re = 100 and Ri near 1. The steady base flow is obtained as a laminar solution of the steady Navier Stokes equations. The base flow asymptotes to a self-similar solution as it evolves downstream. In the non-self-similar regime close to the inlet, both axisymmetric mode (m = 0) and the helical mode (m = 1) are convectively unstable at sufficiently low Richardson number. In the self-similar regime, only the helical mode is absolutely unstable and the axisymmetric mode is stable. Higher helical modes (m >= 2) are seen to be convectively unstable very close to the inlet and become stable as the flow evolves downstream. The transition from convective to absolute instability makes the flow a good candidate for observing steep nonlinear global modes associated with buoyancy. This work is supported by a PhD scholarship from Ecole polytechnique.
Special Relativistic Hydrodynamics with Gravitation
NASA Astrophysics Data System (ADS)
Hwang, Jai-chan; Noh, Hyerim
2016-12-01
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.
Axisymmetric Bending Oscillations of Stellar Disks
NASA Astrophysics Data System (ADS)
Sellwood, J. A.
1996-12-01
Self-gravitating stellar disks with random motion support both exponentially growing and, in some cases, purely oscillatory axisymmetric bending modes, unlike their cold disk counterparts. A razor-thin disk with even a very small degree of random motion in the plane is both unstable and possesses a discrete spectrum of neutral modes, irrespective of the sharpness of the edge. Random motion normal to the disk plane is stabilizing but at the same time allows bending waves to couple to the internal vibrations of the particles, which causes the formerly neutral modes to decay through Landau damping. Focusing first on instabilities, I here determine the degree of random motion normal to the plane needed to suppress global, axisymmetric, bending instabilities in a family of self-gravitating disks. As found previously, bending instabilities are suppressed only when the thickness exceeds that expected from a local criterion when the degree of pressure support within the disk plane is comparable to, or exceeds, the support from rotation. Nevertheless, a modest disk thickness would seem to be adequate for the bending stability of most disk galaxies, except perhaps near their centers. The discretization of the neutral spectrum in a zero-thickness disk is due to the existence of a turning point for bending waves in a warm disk, which is absent when the disk is cold. When the disk is given a finite thickness, the discrete neutral modes generally become strongly damped through wave-particle interactions. It is surprising therefore that I find some simulations of warm, stable disks can support (quasi-)neutral, large-scale, bending modes that decay very slowly, if at all.
NASA Astrophysics Data System (ADS)
Iorio, Lorenzo
2012-03-01
We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit leading-order interactions. Concerning the spin-orbit term, we compute the long-term variations due to the particle's spin by finding secular precessions for the inclination I of the particle's orbit, its longitude of the ascending node Ω and the longitude of pericenter {\\varpi} . Moreover, we generalize the well-known Lense-Thirring precessions to a generic orientation of the source's angular momentum by obtaining an entirely new effect represented by a secular precession of I, and additional secular precessions of Ω and {\\varpi} as well. The spin-spin interaction is responsible of gravitational effects à la Stern-Gerlach consisting of secular precessions of {I, Ω, \\varpi} and the mean anomaly {M} . Such results are obtained without resorting to any approximations either in the particle's eccentricity e or in its inclination I; moreover, no preferred orientations of both the system's angular momenta are adopted. Their generality allows them to be applied to a variety of astronomical and astrophysical scenarios like, e.g., the Sun and its planets and the double pulsar PSR J0737-3039A/B. It turns out that the orbital precessions caused by the spin-spin and the spin-orbit perturbations due to the less massive body are below the current measurability level, especially for the solar system and the Stern-Gerlach effects. Concerning the solar Lense-Thirring precessions, the slight misalignment of the solar equator with respect to the ecliptic reduces the gravitomagnetic node precession of Mercury down to a 0.08 mas per century level with respect to the standard value of 1 mas per century obtained by aligning the z axis with the Sun's angular momentum. The new inclination precession is as large as 0.06 mas per century, while the perihelion's rate remains
Republication of: Relativistic cosmology
NASA Astrophysics Data System (ADS)
Robertson, H. P.
2012-08-01
This is a reprinting of the paper by Howard Percy Robertson, first published in 1933 in Rev. Mod. Phys., that is a very authoritative summary of relativistic cosmology at the stage at which it was up to 1933. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by George Ellis, and by Robertson's biography, compiled by Andrzej Krasinski from printed sources.
An annular superposition integral for axisymmetric radiators
Kelly, James F.; McGough, Robert J.
2007-01-01
A fast integral expression for computing the nearfield pressure is derived for axisymmetric radiators. This method replaces the sum of contributions from concentric annuli with an exact double integral that converges much faster than methods that evaluate the Rayleigh-Sommerfeld integral or the generalized King integral. Expressions are derived for plane circular pistons using both continuous wave and pulsed excitations. Several commonly used apodization schemes for the surface velocity distribution are considered, including polynomial functions and a “smooth piston” function. The effect of different apodization functions on the spectral content of the wave field is explored. Quantitative error and time comparisons between the new method, the Rayleigh-Sommerfeld integral, and the generalized King integral are discussed. At all error levels considered, the annular superposition method achieves a speed-up of at least a factor of 4 relative to the point-source method and a factor of 3 relative to the generalized King integral without increasing the computational complexity. PMID:17348500
Guided waves by axisymmetric and non-axisymmetric surface loading on hollow cylinders
Shin; Rose
1999-06-01
Guided waves generated by axisymmetric and non-axisymmetric surface loading on a hollow cylinder are studied. For the theoretical analysis of the superposed guided waves, a normal mode concept is employed. The amplitude factors of individual guided wave modes are studied with respect to varying surface pressure loading profiles. Both theoretical and experimental focus is given to the guided waves generated by both axisymmetric and non-axisymmetric excitation. For the experiments, a comb transducer and high power tone burst function generator system are used on a sample Inconel tube. Surface loading conditions, such as circumferential loading angles and axial loading lengths, are used with the frequency and phase velocity to control the axisymmetric and non-axisymmetric mode excitations. The experimental study demonstrates the use of a practical non-axisymmetric partial loading technique in generating axisymmetric modes, particularly useful in the inspection of tubing and piping with limited circumferential access. From both theoretical and experimental studies, it also could be said that the amount of flexural modes reflected from a defect contains information on the reflector's circumferential angle, as well as potentially other classification and sizing feature information. The axisymmetric and non-axisymmetric guided wave modes should both be carefully considered for improvement of the overall analysis of guided waves generated in hollow cylinders.
Dynamo Models for Saturn's Axisymmetric Magnetic Field
NASA Astrophysics Data System (ADS)
Stanley, S.; Tajdaran, K.
2012-12-01
Magnetic field measurements by the Cassini mission have confirmed the earlier Pioneer 11 and Voyager missions' results that Saturn's observed magnetic field is extremely axisymmetric . For example, Saturn's dipole tilt is less than 0.06 degrees (Cao et al., 2011) . The nearly-perfect axisymmetry of Saturn's dipole is troubling because of Cowling's Theorem which states that an axisymmetric magnetic field cannot be maintained by a dynamo. However, Cowling's Theorem applies to the magnetic field generated inside the dynamo source region and we can avert any contradiction with Cowling's Theorem if we can find reason for a non-axisymmetric field generated inside the dynamo region to have an axisymmetrized potential field observed at satellite altitude. Stevenson (1980) proposed a mechanism for this axisymmetrization. He suggested that differential rotation in a stably-stratified electrically conducting layer (i.e. the helium rain-out layer) surrounding the dynamo could act to shear out the non-axisymmetry and hence produce an axisymmetric observed magnetic field. In previous work, we used three-dimensional self-consistent numerical dynamo models to demonstrate that a thin helium rain-out layer can produce a more axisymmetrized field (Stanley, 2010). We also found that the direction of the zonal flows in the layer is a crucial factor for magnetic field axisymmetry. Here we investigate the influence of the thickness of the helium rain-out layer and the intensity of the thermal winds on the axisymmetrization of the field. We search for optimal regions in parameter space for producing axisymmetric magnetic fields with similar spectral properties to the observed Saturnian field.
Action Principle for Relativistic Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
D'Avignon, Eric; Morrison, Philip; Pegoraro, Francesco
2015-11-01
A covariant action principle for ideal relativistic magnetohydrodynamics in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al., which uses a noncanonical bracket to implement constrained variations of an action functional. Various implications and extensions of this action principle are also discussed.
Non-axisymmetric local magnetostatic equilibrium
Candy, Jefferey M.; Belli, Emily A.
2015-03-24
In this study, we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas. Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozer coordinates is clarified.
Stable photon orbits in stationary axisymmetric electrovacuum spacetimes
NASA Astrophysics Data System (ADS)
Dolan, Sam R.; Shipley, Jake O.
2016-08-01
We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordström diholes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a dihole, via a selection of Poincaré sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electro vacuum, but not in pure vacuum.
1612 MHz OH maser emission from axisymmetric circumstellar envelopes - Miras
NASA Technical Reports Server (NTRS)
Collison, Alan J.; Fix, John D.
1992-01-01
Radiative transfer calculations are performed using a modified form of the Sobolev approximation to determine the inversion of the 1612 MHz line of OH in axisymmetric circumstellar envelopes around Miras. The mass loss is assumed to be occurring in the form of a smooth wind. Line profiles and maps are presented for three models of varying degrees of asymmetry and for various orientations of the envelopes. It is concluded that the axisymmetric models can reproduce many of the features of observed profiles and maps which both the standard, spherically symmetric model and the discrete emission model cannot easily explain. The model profiles reproduce all of the general features seen in the line profiles of real sources.
Non-Relativistic Superstring Theories
Kim, Bom Soo
2007-12-14
We construct a supersymmetric version of the 'critical' non-relativistic bosonic string theory [1] with its manifest global symmetry. We introduce the anticommuting bc CFT which is the super partner of the {beta}{gamma} CFT. The conformal weights of the b and c fields are both 1/2. The action of the fermionic sector can be transformed into that of the relativistic superstring theory. We explicitly quantize the theory with manifest SO(8) symmetry and find that the spectrum is similar to that of Type IIB superstring theory. There is one notable difference: the fermions are non-chiral. We further consider 'noncritical' generalizations of the supersymmetric theory using the superspace formulation. There is an infinite range of possible string theories similar to the supercritical string theories. We comment on the connection between the critical non-relativistic string theory and the lightlike Linear Dilaton theory.
Relativistic quantum information
NASA Astrophysics Data System (ADS)
Mann, R. B.; Ralph, T. C.
2012-11-01
Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from
Relativistic electron beam generator
Mooney, L.J.; Hyatt, H.M.
1975-11-11
A relativistic electron beam generator for laser media excitation is described. The device employs a diode type relativistic electron beam source having a cathode shape which provides a rectangular output beam with uniform current density.
Non-axisymmetric viscous lower-branch modes in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Hall, Philip
1990-01-01
A previous paper by Duck and Hall (1989) considered the weakly nonlinear interaction of a pair of axisymmetric lower-branch Tollmien-Schlichting instabilities in cylindrical supersonic flows. Here, the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius a less than some critical value a(c). This critical value a(c) is found to increase monotonically with the azimuthal wavenumber n of the disturbance, and it is found that unstable modes always occur in pairs. It is shown that, in general, instability in the form of lower-branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that, in the unstable regime, the largest growth rates correspond to the latter modes.
Non-axisymmetric viscous lower-branch modes in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Hall, Philip
1990-01-01
A previous paper by Duck and Hall (1989) considered the weakly nonlinear interaction of a pair of axisymmetric lower-branch Tollmien-Schlichting instabilities in cylindrical supersonic flows. Here, the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius a less than some critical value a(c). This critical value a(c) is found to increase monotonically with the azimuthal wavenumber n of the disturbance, and it is found that unstable modes always occur in pairs. It is shown that, in general, instability in the form of lower-branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that, in the unstable regime, the largest growth rates correspond to the latter modes.
Axisymmetric and non-axisymmetric modulated MHD waves in magnetic flux tubes
NASA Astrophysics Data System (ADS)
Chargeishvili, B. B.; Japaridze, D. R.
2016-02-01
Nonlinear modulated both axisymmetric and non-axisymmetric MHD wave propagation in magnetic flux tubes is studied. In the cylindrical coordinates, ordinary differential equation with cubic nonlinearity is derived. In both cases of symmetry, the equation has solitary solutions. Modulation stability of the solutions is studied. The results of the study show that the propagation of axisymmetric soliton causes rising of plasma temperature in peripheral regions of a magnetic flux tube. In the non-axisymmetric case, it gives also temperature rising effect. Results of theoretical study are examined on idealized model of chromospheric spicule.
Radiation from Axisymmetric Waveguide Fed Horns
NASA Technical Reports Server (NTRS)
Chinn, G. C.; Hoppe, D. J.; Epp, L. W.
1995-01-01
Return losses and radiation patterns for axisymmetric waveguide fed horns are calculated with the finite element method (FEM) in conjunction with the method of moments (MoM) and the mode matching technique (MM).
Radiation from Axisymmetric Waveguide Fed Horns
NASA Technical Reports Server (NTRS)
Chinn, G. C.; Hoppe, D. J.; Epp, L. W.
1995-01-01
Return losses and radiation patterns for axisymmetric waveguide fed horns are calculated with the finite element method (FEM) in conjunction with the method of moments (MoM) and the mode matching technique (MM).
Cremaschini, Claudio; Kovář, Jiří; Slaný, Petr; Stuchlík, Zdeněk; Karas, Vladimír
2013-11-01
The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal magnetohydrodynamic theory. These stationary structures can represent plausible candidates for the modeling of coronal plasmas expected to arise in association with accretion disks. However, accretion disk coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can also be determined in the case of collisionless plasmas for which treatment based on kinetic theory, rather than a fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic, multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically, kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.
NASA Astrophysics Data System (ADS)
Cremaschini, Claudio; Kovář, Jiří; Slaný, Petr; Stuchlík, Zdeněk; Karas, Vladimír
2013-11-01
The possible occurrence of equilibrium off-equatorial tori in the gravitational and electromagnetic fields of astrophysical compact objects has been recently proved based on non-ideal magnetohydrodynamic theory. These stationary structures can represent plausible candidates for the modeling of coronal plasmas expected to arise in association with accretion disks. However, accretion disk coronae are formed by a highly diluted environment, and so the fluid description may be inappropriate. The question is posed of whether similar off-equatorial solutions can also be determined in the case of collisionless plasmas for which treatment based on kinetic theory, rather than a fluid one, is demanded. In this paper the issue is addressed in the framework of the Vlasov-Maxwell description for non-relativistic, multi-species axisymmetric plasmas subject to an external dominant spherical gravitational and dipolar magnetic field. Equilibrium configurations are investigated and explicit solutions for the species kinetic distribution function are constructed, which are expressed in terms of generalized Maxwellian functions characterized by isotropic temperature and non-uniform fluid fields. The conditions for the existence of off-equatorial tori are investigated. It is proved that these levitating systems are admitted under general conditions when both gravitational and magnetic fields contribute to shaping the spatial profiles of equilibrium plasma fluid fields. Then, specifically, kinetic effects carried by the equilibrium solution are explicitly provided and identified here with diamagnetic energy-correction and electrostatic contributions. It is shown that these kinetic terms characterize the plasma equation of state by introducing non-vanishing deviations from the assumption of thermal pressure.
Bypassing Cowling's Theorem in Axisymmetric Fluid Dynamos
Gissinger, Christophe; Fauve, Stephan; Dormy, Emmanuel
2008-10-03
We present a numerical study of the magnetic field generated by an axisymmetrically forced flow in a spherical domain. We show that, even in the absence of nonaxisymmetric velocity fluctuations, a mean magnetic field with a dominant axisymmetric dipolar component can be generated via a secondary bifurcation from an equatorial dipole. We understand the dynamical behaviors that result from the interaction of equatorial and axial dipolar modes using simple model equations for their amplitudes derived from symmetry arguments.
Transition and mixing in axisymmetric jets and vortex rings
NASA Technical Reports Server (NTRS)
Allen, G. A., Jr.; Cantwell, B. J.
1986-01-01
A class of impulsively started, axisymmetric, laminar jets produced by a time dependent joint source of momentum are considered. These jets are different flows, each initially at rest in an unbounded fluid. The study is conducted at three levels of detail. First, a generalized set of analytic creeping flow solutions are derived with a method of flow classification. Second, from this set, three specific creeping flow solutions are studied in detail: the vortex ring, the round jet, and the ramp jet. This study involves derivation of vorticity, stream function, entrainment diagrams, and evolution of time lines through computer animation. From entrainment diagrams, critical points are derived and analyzed. The flow geometry is dictated by the properties and location of critical points which undergo bifurcation and topological transformation (a form of transition) with changing Reynolds number. Transition Reynolds numbers were calculated. A state space trajectory was derived describing the topological behavior of these critical points. This state space derivation yielded three states of motion which are universal for all axisymmetric jets. Third, the axisymmetric round jet is solved numerically using the unsteady laminar Navier Stokes equations. These equations were shown to be self similar for the round jet. Numerical calculations were performed up to a Reynolds number of 30 for a 60x60 point mesh. Animations generated from numerical solution showed each of the three states of motion for the round jet, including the Re = 30 case.
Asymmetric and axisymmetric dynamics of tropical cyclones
NASA Astrophysics Data System (ADS)
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
2013-05-01
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f-plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally-averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics and are generally not represented properly by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast time scales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since during the 3-D intensification process the convection has not yet organized into annular rings
Newtonian and relativistic cosmologies
NASA Astrophysics Data System (ADS)
Green, Stephen R.; Wald, Robert M.
2012-03-01
Cosmological N-body simulations are now being performed using Newtonian gravity on scales larger than the Hubble radius. It is well known that a uniformly expanding, homogeneous ball of dust in Newtonian gravity satisfies the same equations as arise in relativistic Friedmann-Lemaître-Robinson-Walker cosmology, and it also is known that a correspondence between Newtonian and relativistic dust cosmologies continues to hold in linearized perturbation theory in the marginally bound/spatially flat case. Nevertheless, it is far from obvious that Newtonian gravity can provide a good global description of an inhomogeneous cosmology when there is significant nonlinear dynamical behavior at small scales. We investigate this issue in the light of a perturbative framework that we have recently developed [S. R. Green and R. M. Wald, Phys. Rev. DPRVDAQ1550-7998 83, 084020 (2011).10.1103/PhysRevD.83.084020], which allows for such nonlinearity at small scales. We propose a relatively straightforward dictionary—which is exact at the linearized level—that maps Newtonian dust cosmologies into general relativistic dust cosmologies, and we use our “ordering scheme” to determine the degree to which the resulting metric and matter distribution solve Einstein’s equation. We find that, within our ordering scheme, Einstein’s equation fails to hold at “order 1” at small scales and at “order ɛ” at large scales. We then find the additional corrections to the metric and matter distribution needed to satisfy Einstein’s equation to these orders. While these corrections are of some interest in their own right, our main purpose in calculating them is that their smallness should provide a criterion for the validity of the original dictionary (as well as simplified versions of this dictionary). We expect that, in realistic Newtonian cosmologies, these additional corrections will be very small; if so, this should provide strong justification for the use of Newtonian simulations
Axisymmetric MHD Instabilities in Solar/Stellar Tachoclines
NASA Astrophysics Data System (ADS)
Dikpati, Mausumi; Gilman, Peter A.; Cally, Paul S.; Miesch, Mark S.
2009-02-01
Extensive studies over the past decade showed that HD and MHD nonaxisymmetric instabilities exist in the solar tachocline for a wide range of toroidal field profiles, amplitudes, and latitude locations. Axisymmetric instabilities (m = 0) do not exist in two dimensions, and are excited in quasi-three-dimensional shallow-water systems only for very high field strengths (2 mG). We investigate here MHD axisymmetric instabilities in a three-dimensional thin-shell model of the solar/stellar tachocline, employing a hydrostatic, non-Boussinesq system of equations. We deduce a number of general properties of the instability by use of an integral theorem, as well as finding detailed numerical solutions for unstable modes. Toroidal bands become unstable to axisymmetric perturbations for solar-like field strengths (100 kG). The e-folding time can be months down to a few hours if the field strength is 1 mG or higher, which might occur in the solar core, white dwarfs, or neutron stars. These instabilities exist without rotation, with rotation, and with differential rotation, although both rotation and differential rotation have stabilizing effects. Broad toroidal fields are stable. The instability for modes with m = 0 is driven from the poleward shoulder of banded profiles by a perturbation magnetic curvature stress that overcomes the stabilizing Coriolis force. The nonaxisymmetric instability tips or deforms a band; with axisymmetric instability, the fluid can roll in latitude and radius, and can convert bands into tubes stacked in radius. The velocity produced by this instability in the case of low-latitude bands crosses the equator, and hence can provide a mechanism for interhemispheric coupling.
The inviscid stability of supersonic flow past axisymmetric bodies
NASA Technical Reports Server (NTRS)
Duck, Peter W.
1990-01-01
The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).
The inviscid stability of supersonic flow past axisymmetric bodies
NASA Technical Reports Server (NTRS)
Duck, Peter W.
1990-01-01
The supersonic flow past a sharp cone is studied. The associated boundary layer flow (i.e., the velocity and temperature field) is computed. The inviscid linear temporal stability of axisymmetric boundary layers in general is considered, and in particular, a so-called 'triply generalized' inflection condition for 'subsonic' nonaxisymmetric neutral modes is presented. Preliminary numerical results for the stability of the cone boundary layer are presented for a freestream Mach number of 3.8. In particular, a new inviscid mode of instability is seen to occur in certain regimes, and this is shown to be related to a viscous mode found by Duck and Hall (1988).
Four motional invariants in axisymmetric tori equilibria
A ring gren, O.; Moiseenko, V.E.
2006-05-15
In addition to the standard set ({epsilon},{mu},p{sub {phi}}) of three invariants in axisymmetric tori, there exists a fourth independent radial drift invariant I{sub r}. For confined particles, the net radial drift has to be zero, whereby the drift orbit average I{sub r}=
Relativistic radiative transfer in relativistic spherical flows
NASA Astrophysics Data System (ADS)
Fukue, Jun
2017-02-01
Relativistic radiative transfer in relativistic spherical flows is numerically examined under the fully special relativistic treatment. We first derive relativistic formal solutions for the relativistic radiative transfer equation in relativistic spherical flows. We then iteratively solve the relativistic radiative transfer equation, using an impact parameter method/tangent ray method, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities, and the Eddington factor. We consider several cases; a scattering wind with a luminous central core, an isothermal wind without a core, a scattering accretion on to a luminous core, and an adiabatic accretion on to a dark core. In the typical wind case with a luminous core, the emergent intensity is enhanced at the center due to the Doppler boost, while it reduces at the outskirts due to the transverse Doppler effect. In contrast to the plane-parallel case, the behavior of the Eddington factor is rather complicated in each case, since the Eddington factor depends on the optical depth, the flow velocity, and other parameters.
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.
Relativistic linear restoring force
NASA Astrophysics Data System (ADS)
Clark, D.; Franklin, J.; Mann, N.
2012-09-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke’s law to be the force appearing on the right-hand side of the relativistic expressions: dp/dt or dp/dτ. Either formulation recovers Hooke’s law in the non-relativistic limit. In addition to these two forces, we introduce a form of retardation appropriate for the description of a linear (in displacement) force arising from the interaction of a pair of particles with a relativistic field. The procedure is akin to replacing Coulomb’s law in electromagnetism with a retarded form (the first correction in the full relativistic case). This retardation leads to the expected oscillation, but with amplitude growth in both its relativistic and non-relativistic incarnations.
NASA Astrophysics Data System (ADS)
Fukue, Jun
2014-07-01
Relativistic radiative transfer in a relativistic plane-parallel flow which is accelerated from its base, like an accretion disk wind, is numerically examined under a fully special-relativistic treatment. We first derive relativistic formal solutions. We then iteratively solve the relativistic transfer equation for several cases such as radiative equilibrium or local thermodynamic equilibrium, and obtain specific intensities in the inertial and comoving frames, as well as moment quantities and the Eddington factor. Moment quantities are rather different in each case, but the behavior of the Eddington factor for the plane-parallel case is quite similar in all cases. The Eddington factor generally depends on the flow velocity v as well as the optical depth τ. In the case of relativistic plane-parallel flows, in an optically thin regime of τ ≲ 1, it is slightly larger than 1/3 at very slow speed, it becomes smaller than 1/3 at mildly relativistic speed, and it again increases up to unity in the highly relativistic case. At highly relativistic speed, on the other hand, it becomes larger than 1/3 even in an optically thick regime. We find the Eddington approximation is fairly good, except for τ ≲ 1 or v/c ≳ 0.9, although the moment formalism under the Eddington approximation has some defects at v/c=1/√{3}.
Nagakura, Hiroki; Takahashi, Rohta
2010-03-01
We show for the first time the direct time-variable radio images in the context of shocked accretion flows around a black hole under the general relativistic treatment of both hydrodynamics and radiation transfer. Time variability around a black hole can be induced by the non-axisymmetric standing accretion shock instability (namely, black hole SASI). Since the spiral arm shock waves generate the density and temperature waves at the post-shock region, they cause time variability in the black hole vicinity. Based on our dynamical simulations, we discuss a possibility of detection for the time-variable radio images of M87 by the future space telescope VSOP2/ASTRO-G satellite. The most luminous part of the images is predicted to be near 15 Schwarzschild radii for some snapshots. We show that our results are consistent with existing observational data such as time-averaged radio spectra, Very Long Baseline Array images, and variability timescale for M87. We also discuss observations of M87 with millimeter and submillimeter interferometers.
NASA Astrophysics Data System (ADS)
Zhang, Fupeng; Lu, Youjun; Yu, Qingjuan
2015-08-01
S-stars, discovered in the vicinity of the massive black hole (MBH) in the Galactic center (GC), are anticipated to provide unique dynamical constraints on the MBH spin and metric, in addition to the mass. In this paper, we develop a fast full general relativistic method to simultaneously constrain the MBH mass, spin, and spin direction by considering both the orbital motion of a star close to the GC MBH and the propagation of photons from the star to a distant observer. Based on the current observations and dynamical model predictions, we assume six example stars with different semimajor axes ({a}{orb}) and eccentricities ({e}{orb}) and numerically calculate their projected trajectories in the sky plane and redshift curves. Two of those stars are set to have orbital configurations similar to that of S0-2/S2 and S0-102. We find that the spin-induced effects on the projected trajectory and redshift curve of a given star, including the leading term by the Lense-Thirring precession and the frame dragging, and the high-order precession due to the quadruple moment, depend on both the absolute value and the direction of the spin. The maximum values of the spin-induced position displacement and the redshift differences of the star over a full orbit may differ by a factor of several to more than one order of magnitude for two cases with significantly different spin directions. The dependence patterns of the position displacements and redshift differences on the spin direction are different, and thus the position and the redshift data are complementary for constraining the MBH spin and its direction. Adopting the Markov Chain Monte Carlo fitting technique, we illustrate that the spin of the GC MBH is likely to be well constrained by using the motion of S0-2/S2 over a period of ˜45 years if the spin is close to one and if the astrometric and spectroscopic precisions can be as high as ({σ }{{p}},{σ }Z)˜ (10 μ {as},1 {km} {{{s}}}-1), which is expected to be realized by
Cremaschini, Claudio; Stuchlík, Zdeněk; Tessarotto, Massimo
2013-05-15
The problem of formulating a kinetic treatment for quasi-stationary collisionless plasmas in axisymmetric systems subject to the possibly independent presence of local strong velocity-shear and supersonic rotation velocities is posed. The theory is developed in the framework of the Vlasov-Maxwell description for multi-species non-relativistic plasmas. Applications to astrophysical accretion discs arising around compact objects and to plasmas in laboratory devices are considered. Explicit solutions for the equilibrium kinetic distribution function (KDF) are constructed based on the identification of the relevant particle adiabatic invariants. These are shown to be expressed in terms of generalized non-isotropic Gaussian distributions. A suitable perturbative theory is then developed which allows for the treatment of non-uniform strong velocity-shear/supersonic plasmas. This yields a series representation for the equilibrium KDF in which the leading-order term depends on both a finite set of fluid fields as well as on the gradients of an appropriate rotational frequency. Constitutive equations for the fluid number density, flow velocity, and pressure tensor are explicitly calculated. As a notable outcome, the discovery of a new mechanism for generating temperature and pressure anisotropies is pointed out, which represents a characteristic feature of plasmas considered here. This is shown to arise as a consequence of the canonical momentum conservation and to contribute to the occurrence of temperature anisotropy in combination with the adiabatic conservation of the particle magnetic moment. The physical relevance of the result and the implications of the kinetic solution for the self-generation of quasi-stationary electrostatic and magnetic fields through a kinetic dynamo are discussed.
Analytic models of relativistic accretion disks
NASA Astrophysics Data System (ADS)
Zhuravlev, V. V.
2015-06-01
We present not a literature review but a description, as detailed and consistent as possible, of two analytic models of disk accretion onto a rotating black hole: a standard relativistic disk and a twisted relativistic disk. Although one of these models is older than the other, both are of topical interest for black hole studies. The treatment is such that the reader with only a limited knowledge of general relativity and relativistic hydrodynamics, with little or no use of additional sources, can gain insight into many technical details lacking in the original papers.
Relativistic Celestial Mechanics
NASA Astrophysics Data System (ADS)
Brumberg, Victor A.
2010-08-01
Relativistic celestial mechanics (RCM) refers to a science to study the motion of celestial bodies within the framework of general relativity theory (GRT) by Einstein. Being a straightforward successor of Newtonian celestial mechanics RCM embraces all aspects of motion of celestial bodies including (1) physics of motion, i.e. investigation of the physical nature of all effects influencing the motion of celestial bodies and formulation of a physical model for a specific problem; (2) mathematics of motion, i.e. investigation of the mathematical characteristics of the solutions of the differential equations of motion of celestial bodies; (3) computation of motion, i.e. the actual determination of the quantitative characteristics of motion; (4) astronomy of motion, i.e. application of mathematical solution of a problem to a specific celestial body, comparison with the results of observations, determination of initial values and parameters of motion, and checking the physical and mathematical models employed for a given problem.
Relativistic Optimized Link by KLT
NASA Astrophysics Data System (ADS)
Maccone, C.
The KLT is a way of optimizing the signal processing of a given noisy signal by projecting the noisy signal itself onto the set of orthonormal basis functions spanned by the eigenfunctions of the autocorrelation of the noisy signal. Thus, the key problem in computing the KLT of a noisy signal is the computation of the eigenvalues and eigenfunctions of the autocorrelation of the noisy signal. For the special case of the Brownian motion (i.e. the basic Gaussian noisy signal) it can be proved that the KLT eigenfunctions are just sines, i.e. the KLT is the same as the FT. Let us now bring relativity into the KLT picture (this paper is confined to special relativity; general relativity can be KLT-studied also, but the calculations are, of course, even more difficult). Also, only rectilinear motions will be considered here. So, if one considers a source in relativistic motion, then the noisy signal undergoes a time-rescaling that depends on the type of relativistic motion. In past work this author has demostrated that the eigenfunctions of the time-rescaled, relativistic Brownian motion are Bessel functions of the first kind, and their eigenvalues are the zeros of such Bessel functions. In addition, it is stated (without proofs) that explicit formulae for the KLT signal processing can be found for the particularly important cases of the noisy signals received on Earth from a relativistic spacecraft whose motion is either: 1) uniform; or 2) uniformly accelerated.
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.
BL Lac objects and relativistic beaming
NASA Technical Reports Server (NTRS)
Worrall, Diana M.
1986-01-01
General arguments for relativistic beaming in BL Lac objects are reviewed. These include overproduction of X-rays and fast time variability. Comments are made about the relationship of the X-ray continuum to that at lower frequencies, and observational evidence for and against continuum radiation being relativistically beamed is discussed. Finally, there is discussion of the influence of geometrical effects on predictions for time variability as a function of frequency in the context of inhomogeneous synchrotron self-Compton jet models.
Non-axisymmetric local magnetostatic equilibrium
Candy, Jefferey M.; Belli, Emily A.
2015-03-24
In this study, we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas. Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of the shear in the 3D shape. A spectrally-accurate method for solution of the resulting nonlinear partial differential equations is also developed. We verify the correctness of the spectral method, in the axisymmetric limit, through comparisons with an independent numerical solution. Some analytic results for the two-dimensional case are given, and the connection to Boozermore » coordinates is clarified.« less
Supersonic quasi-axisymmetric vortex breakdown
NASA Technical Reports Server (NTRS)
Kandil, Osama A.; Kandil, Hamdy A.; Liu, C. H.
1991-01-01
An extensive computational study of supersonic quasi-axisymmetric vortex breakdown in a configured circular duct is presented. The unsteady, compressible, full Navier-Stokes (NS) equations are used. The NS equations are solved for the quasi-axisymmetric flows using an implicit, upwind, flux difference splitting, finite volume scheme. The quasi-axisymmetric solutions are time accurate and are obtained by forcing the components of the flowfield vector to be equal on two axial planes, which are in close proximity of each other. The effect of Reynolds number, for laminar flows, on the evolution and persistence of vortex breakdown, is studied. Finally, the effect of swirl ration at the duct inlet is investigated.
Acoustic Bessel-like beam formation by an axisymmetric grating
NASA Astrophysics Data System (ADS)
Jiménez, N.; Romero-García, V.; Picó, R.; Cebrecos, A.; Sánchez-Morcillo, V. J.; Garcia-Raffi, L. M.; Sánchez-Pérez, J. V.; Staliunas, K.
2014-04-01
We report Bessel-like beam formation of acoustic waves by means of an axisymmetric grating of rigid tori. The results show that the generated beam pattern is similar to that of Bessel beams, characterized by elongated non-diffracting focal spots. A multiple foci structure is observed, due to the finite size of the lens. The dependence of the focal distance on the frequency is also discussed, on the basis of an extended grating theory. Experimental validation of acoustic Bessel-like beam formation is also reported for sound waves. The results can be generalized to wave beams of different nature, as optical or matter waves.
Marginally stable circular orbits in stationary axisymmetric spacetimes
NASA Astrophysics Data System (ADS)
Beheshti, Shabnam; Gasperín, Edgar
2016-07-01
We derive necessary and sufficient conditions for the existence of marginally stable circular orbits (MSCOs) of test particles in a stationary axisymmetric (SAS) spacetime which possesses a reflection symmetry with respect to the equatorial plane; photon orbits and marginally bound orbits (MBOs) are also addressed. Energy and angular momentum are shown to decouple from metric quantities, rendering a purely geometric characterization of circular orbits for this general class of metrics. The subsequent system is analyzed using resultants, providing an algorithmic approach for finding MSCO conditions. MSCOs, photon orbits and MBOs are explicitly calculated for concrete examples of physical interest.
NASA Astrophysics Data System (ADS)
Ge, Wenjun; Modest, Michael F.; Marquez, Ricardo
2015-05-01
The spherical harmonics (PN) method is a radiative transfer equation solver, which approximates the radiative intensity as a truncated series of spherical harmonics. For general 3-D configurations, N(N + 1) / 2 intensity coefficients must be solved from a system of coupled second-order elliptic PDEs. In 2-D axisymmetric applications, the number of equations and intensity coefficients reduces to (N + 1) 2 / 4 if the geometric relations of the intensity coefficients are taken into account. This paper presents the mathematical details for the transformation and its implementation on the OpenFOAM finite volume based CFD software platform. The transformation and implementation are applicable to any arbitrary axisymmetric geometry, but the examples to test the new formulation are based on a wedge grid, which is the most common axisymmetric geometry in CFD simulations, because OpenFOAM and most other platforms do not have true axisymmetric solvers. Two example problems for the new axisymmetric PN formulation are presented, and the results are verified with that of the general 3-D PN solver, a Photon Monte Carlo solver and exact solutions.
Relativistic Linear Restoring Force
ERIC Educational Resources Information Center
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Relativistic Guiding Center Equations
White, R. B.; Gobbin, M.
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
Relativistic Linear Restoring Force
ERIC Educational Resources Information Center
Clark, D.; Franklin, J.; Mann, N.
2012-01-01
We consider two different forms for a relativistic version of a linear restoring force. The pair comes from taking Hooke's law to be the force appearing on the right-hand side of the relativistic expressions: d"p"/d"t" or d"p"/d["tau"]. Either formulation recovers Hooke's law in the non-relativistic limit. In addition to these two forces, we…
Relativistic HD and MHD modelling for AGN jets
NASA Astrophysics Data System (ADS)
Keppens, R.; Porth, O.; Monceau-Baroux, R.; Walg, S.
2013-12-01
Relativistic hydro and magnetohydrodynamics (MHD) provide a continuum fluid description for plasma dynamics characterized by shock-dominated flows approaching the speed of light. Significant progress in its numerical modelling emerged in the last two decades; we highlight selected examples of modern grid-adaptive, massively parallel simulations realized by our open-source software MPI-AMRVAC (Keppens et al 2012 J. Comput. Phys. 231 718). Hydrodynamical models quantify how energy transfer from active galactic nuclei (AGN) jets to their surrounding interstellar/intergalactic medium (ISM/IGM) gets mediated through shocks and various fluid instability mechanisms (Monceau-Baroux et al 2012 Astron. Astrophys. 545 A62). With jet parameters representative for Fanaroff-Riley type-II jets with finite opening angles, we can quantify the ISM volumes affected by jet injection and distinguish the roles of mixing versus shock-heating in cocoon regions. This provides insight in energy feedback by AGN jets, usually incorporated parametrically in cosmological evolution scenarios. We discuss recent axisymmetric studies up to full 3D simulations for precessing relativistic jets, where synthetic radio maps can confront observations. While relativistic hydrodynamic models allow one to better constrain dynamical parameters like the Lorentz factor and density contrast between jets and their surroundings, the role of magnetic fields in AGN jet dynamics and propagation characteristics needs full relativistic MHD treatments. Then, we can demonstrate the collimating properties of an overal helical magnetic field backbone and study differences between poloidal versus toroidal field dominated scenarios (Keppens et al 2008 Astron. Astrophys. 486 663). Full 3D simulations allow one to consider the fate of non-axisymmetric perturbations on relativistic jet propagation from rotating magnetospheres (Porth 2013 Mon. Not. R. Astron. Soc. 429 2482). Self-stabilization mechanisms related to the detailed
Computer Aided Process Planning for Non-Axisymmetric Deep Drawing Products
NASA Astrophysics Data System (ADS)
Park, Dong Hwan; Yarlagadda, Prasad K. D. V.
2004-06-01
In general, deep drawing products have various cross-section shapes such as cylindrical, rectangular and non-axisymmetric shapes. The application of the surface area calculation to non-axisymmetric deep drawing process has not been published yet. In this research, a surface area calculation for non-axisymmetric deep drawing products with elliptical shape was constructed for a design of blank shape of deep drawing products by using an AutoLISP function of AutoCAD software. A computer-aided process planning (CAPP) system for rotationally symmetric deep drawing products has been developed. However, the application of the system to non-axisymmetric components has not been reported yet. Thus, the CAPP system for non-axisymmetric deep drawing products with elliptical shape was constructed by using process sequence design. The system developed in this work consists of four modules. The first is recognition of shape module to recognize non-axisymmetric products. The second is a three-dimensional (3-D) modeling module to calculate the surface area for non-axisymmetric products. The third is a blank design module to create an oval-shaped blank with the identical surface area. The forth is a process planning module based on the production rules that play the best important role in an expert system for manufacturing. The production rules are generated and upgraded by interviewing field engineers. Especially, the drawing coefficient, the punch and die radii for elliptical shape products are considered as main design parameters. The suitability of this system was verified by applying to a real deep drawing product. This CAPP system constructed would be very useful to reduce lead-time for manufacturing and improve an accuracy of products.
NASA Technical Reports Server (NTRS)
Schnell, W. C.
1982-01-01
The jet induced effects of several exhaust nozzle configurations (axisymmetric, and vectoring/modulating varients) on the aeropropulsive performance of a twin engine V/STOL fighter design was determined. A 1/8 scale model was tested in an 11 ft transonic tunnel at static conditions and over a range of Mach Numbers from 0.4 to 1.4. The experimental aspects of the static and wind-on programs are discussed. Jet effects test techniques in general, fow through balance calibrations and tare force corrections, ASME nozzle thrust and mass flow calibrations, test problems and solutions are emphasized.
Stability of perturbed geodesics in nD axisymmetric spacetimes
NASA Astrophysics Data System (ADS)
Coimbra-Araújo, C. H.; Anjos, R. C.
2016-09-01
The effect of self-gravity of a disk matter is evaluated by the simplest modes of oscillation frequencies for perturbed circular geodesics. We plotted the radial profiles of free oscillations of an equatorial circular geodesic perturbed within the orbital plane or in the vertical direction. The calculation is carried out to geodesics of an axisymmetric n-dimensional spacetime. The profiles are computed by examples of disks embeded in five-dimensional or six-dimensional spacetime, where we studied the motion of free test particles for three axisymmetric cases: (i) the Newtonian limit of a general proposed 5D and 6D axisymmetric spacetime; (ii) a simple Randall-Sundrum (RS) 5D spacetime; (iii) general 5D and 6D RS spacetime. The equation of motion of such particles is derived and the stability study is computed for both horizontal and vertical directions, to see how extra dimensions could affect the system. In particular, we investigate a disk constructed from Miyamoto-Nagai and Chazy-Curzon with a cut parameter to generate a disk potential. Those solutions have a simple extension for extra dimensions in case (i), and by solving vacuum Einstein field equations for a kind of RS-Weyl metric in cases (ii) and (iii). We find that it is possible to compute a range of possible solutions where such perturbed geodesics are stable. Basically, the stable solutions appear, for the radial direction, in special cases when the system has 5D and in all cases when the system has 6D and, for the axial direction, in all cases when the system has both 5D or 6D.
Particle trajectory computer program for icing analysis of axisymmetric bodies
NASA Technical Reports Server (NTRS)
Frost, Walter; Chang, Ho-Pen; Kimble, Kenneth R.
1982-01-01
General aviation aircraft and helicopters exposed to an icing environment can accumulate ice resulting in a sharp increase in drag and reduction of maximum lift causing hazardous flight conditions. NASA Lewis Research Center (LeRC) is conducting a program to examine, with the aid of high-speed computer facilities, how the trajectories of particles contribute to the ice accumulation on airfoils and engine inlets. This study, as part of the NASA/LeRC research program, develops a computer program for the calculation of icing particle trajectories and impingement limits relative to axisymmetric bodies in the leeward-windward symmetry plane. The methodology employed in the current particle trajectory calculation is to integrate the governing equations of particle motion in a flow field computed by the Douglas axisymmetric potential flow program. The three-degrees-of-freedom (horizontal, vertical, and pitch) motion of the particle is considered. The particle is assumed to be acted upon by aerodynamic lift and drag forces, gravitational forces, and for nonspherical particles, aerodynamic moments. The particle momentum equation is integrated to determine the particle trajectory. Derivation of the governing equations and the method of their solution are described in Section 2.0. General features, as well as input/output instructions for the particle trajectory computer program, are described in Section 3.0. The details of the computer program are described in Section 4.0. Examples of the calculation of particle trajectories demonstrating application of the trajectory program to given axisymmetric inlet test cases are presented in Section 5.0. For the examples presented, the particles are treated as spherical water droplets. In Section 6.0, limitations of the program relative to excessive computer time and recommendations in this regard are discussed.
Baryon Loaded Relativistic Blast Waves in Supernovae
NASA Astrophysics Data System (ADS)
Chakraborti, Sayan; Ray, Alak
2011-03-01
We provide a new analytic blast wave solution which generalizes the Blandford-McKee solution to arbitrary ejecta masses and Lorentz factors. Until recently relativistic supernovae have been discovered only through their association with long-duration gamma-ray bursts (GRBs). The blast waves of such explosions are well described by the Blandford-McKee (in the ultra-relativistic regime) and Sedov-Taylor (in the non-relativistic regime) solutions during their afterglows, as the ejecta mass is negligible in comparison to the swept-up mass. The recent discovery of the relativistic supernova SN 2009bb, without a detected GRB, opens up the possibility of highly baryon loaded, mildly relativistic outflows which remains in nearly free-expansion phase during the radio afterglow. In this work, we consider a massive, relativistic shell, launched by a Central Engine Driven EXplosion (CEDEX), decelerating adiabatically due to its collision with the pre-explosion circumstellar wind profile of the progenitor. We compute the synchrotron emission from relativistic electrons in the shock amplified magnetic field. This models the radio emission from the circumstellar interaction of a CEDEX. We show that this model explains the observed radio evolution of the prototypical SN 2009bb and demonstrate that SN 2009bb had a highly baryon loaded, mildly relativistic outflow. We discuss the effect of baryon loading on the dynamics and observational manifestations of a CEDEX. In particular, our predicted angular size of SN 2009bb is consistent with very long baseline interferometric (VLBI) upper limits on day 85, but is presently resolvable on VLBI angular scales, since the relativistic ejecta is still in the nearly free-expansion phase.
Mueller, Bernhard; Janka, Hans-Thomas; Marek, Andreas E-mail: thj@mpa-garching.mpg.de
2013-03-20
We present a detailed theoretical analysis of the gravitational wave (GW) signal of the post-bounce evolution of core-collapse supernovae (SNe), employing for the first time relativistic, two-dimensional explosion models with multi-group, three-flavor neutrino transport based on the ray-by-ray-plus approximation. The waveforms reflect the accelerated mass motions associated with the characteristic evolutionary stages that were also identified in previous works: a quasi-periodic modulation by prompt post-shock convection is followed by a phase of relative quiescence before growing amplitudes signal violent hydrodynamical activity due to convection and the standing accretion shock instability during the accretion period of the stalled shock. Finally, a high-frequency, low-amplitude variation from proto-neutron star (PNS) convection below the neutrinosphere appears superimposed on the low-frequency trend associated with the aspherical expansion of the SN shock after the onset of the explosion. Relativistic effects in combination with detailed neutrino transport are shown to be essential for quantitative predictions of the GW frequency evolution and energy spectrum, because they determine the structure of the PNS surface layer and its characteristic g-mode frequency. Burst-like high-frequency activity phases, correlated with sudden luminosity increase and spectral hardening of electron (anti-)neutrino emission for some 10 ms, are discovered as new features after the onset of the explosion. They correspond to intermittent episodes of anisotropic accretion by the PNS in the case of fallback SNe. We find stronger signals for more massive progenitors with large accretion rates. The typical frequencies are higher for massive PNSs, though the time-integrated spectrum also strongly depends on the model dynamics.
Relativistic theory of radiofrequency current drive
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 all 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.
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.
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.
Asymmetric and axisymmetric dynamics of tropical cyclones
NASA Astrophysics Data System (ADS)
Persing, J.; Montgomery, M. T.; McWilliams, J. C.; Smith, R. K.
2013-12-01
We present the results of idealized numerical experiments to examine the difference between tropical cyclone evolution in three-dimensional (3-D) and axisymmetric (AX) model configurations. We focus on the prototype problem for intensification, which considers the evolution of an initially unsaturated AX vortex in gradient-wind balance on an f plane. Consistent with findings of previous work, the mature intensity in the 3-D model is reduced relative to that in the AX model. In contrast with previous interpretations invoking barotropic instability and related horizontal mixing processes as a mechanism detrimental to the spin-up process, the results indicate that 3-D eddy processes associated with vortical plume structures can assist the intensification process by contributing to a radial contraction of the maximum tangential velocity and to a vertical extension of tangential winds through the depth of the troposphere. These plumes contribute significantly also to the azimuthally averaged heating rate and the corresponding azimuthal-mean overturning circulation. The comparisons show that the resolved 3-D eddy momentum fluxes above the boundary layer exhibit counter-gradient characteristics during a key spin-up period, and more generally are not solely diffusive. The effects of these eddies are thus not properly represented by the subgrid-scale parameterizations in the AX configuration. The resolved eddy fluxes act to support the contraction and intensification of the maximum tangential winds. The comparisons indicate fundamental differences between convective organization in the 3-D and AX configurations for meteorologically relevant forecast timescales. While the radial and vertical gradients of the system-scale angular rotation provide a hostile environment for deep convection in the 3-D model, with a corresponding tendency to strain the convective elements in the tangential direction, deep convection in the AX model does not suffer this tendency. Also, since
Fabrication of Submillimeter Axisymmetric Optical Components
NASA Technical Reports Server (NTRS)
Grudinin, Ivan; Savchenkov, Anatoliy; Strekalov, Dmitry
2007-01-01
It is now possible to fashion transparent crystalline materials into axisymmetric optical components having diameters ranging from hundreds down to tens of micrometers, whereas previously, the smallest attainable diameter was 500 m. A major step in the fabrication process that makes this possible can be characterized as diamond turning or computer numerically controlled machining on an ultrahigh-precision lathe.
User's manual for Axisymmetric Diffuser Duct (ADD) code. Volume 3: ADD code coordinate generator
NASA Technical Reports Server (NTRS)
Anderson, O. L.; Hankins, G. B., Jr.; Edwards, D. E.
1982-01-01
This User's Manual contains a complete description of the computer codes known as the Axisymmetric Diffuser Duct (ADD) code. It includes a list of references which describe the formulation of the ADD code and comparisons of calculation with experimental flows. The input/output and general use of the code is described in the first volume. The second volume contains a detailed description of the code including the global structure of the code, list of FORTRAN variables, and descriptions of the subroutines. The third volume contains a detailed description of the CODUCT code which generates coordinate systems for arbitrary axisymmetric ducts.
Bödeker, Dietrich; Wörmann, Mirco E-mail: mwoermann@physik.uni-bielefeld.de
2014-02-01
In many phenomenologically interesting models of thermal leptogenesis the heavy neutrinos are non-relativistic when they decay and produce the baryon asymmetry of the Universe. We propose a non-relativistic approximation for the corresponding rate equations in the non-resonant case, and a systematic way for computing relativistic corrections. We determine the leading order coefficients in these equations, and the first relativistic corrections. The non-relativistic approximation works remarkably well. It appears to be consistent with results obtained using a Boltzmann equation taking into account the momentum distribution of the heavy neutrinos, while being much simpler. We also compute radiative corrections to some of the coefficients in the rate equations. Their effect is of order 1% in the regime favored by neutrino oscillation data. We obtain the correct leading order lepton number washout rate in this regime, which leads to large ( ∼ 20%) effects compared to previous computations.
Two-soliton stationary axisymmetric sprouts from Weyl seeds
NASA Astrophysics Data System (ADS)
Zellerin, T.; Semerák, O.; Zellerin, T.
2000-12-01
The Belinskii-Zakharov inverse-scattering method is employed in its two-soliton version with a general Weyl seed, to obtain a stationary axisymmetric metric which in spheroidal coordinates of the Boyer-Lindquist type appears as a generalization of the Kerr-NUT solution. It contains several constants and two functions which can be found by integration from the seed potential (they can also be written as Legendre series). With a natural choice of parameters, the solution describes a reflectionally symmetric, asymptotically flat spacetime of a rotating black hole surrounded by a stationary axisymmetric source inherited from the seed. In a static limit, it goes over to a nonlinear superposition of the seed with a Schwarzschild black hole. A number of properties of the obtained class of solutions is given, in particular the characteristics of the horizon. For moderate angular momenta there seem to be no singularities on and outside the horizon. For a thin annular disc as the seed, the solution can represent a stationary thin annular disc around a rotating black hole.
The direct numerical simulations of the turbulent wakes of axisymmetric bodies
NASA Technical Reports Server (NTRS)
Riley, J. J.; Metcalfe, R. W.
1978-01-01
Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.
Einstein Toolkit for Relativistic Astrophysics
NASA Astrophysics Data System (ADS)
Collaborative Effort
2011-02-01
The Einstein Toolkit is a collection of software components and tools for simulating and analyzing general relativistic astrophysical systems. Such systems include gravitational wave space-times, collisions of compact objects such as black holes or neutron stars, accretion onto compact objects, core collapse supernovae and Gamma-Ray Bursts. The Einstein Toolkit builds on numerous software efforts in the numerical relativity community including CactusEinstein, Whisky, and Carpet. The Einstein Toolkit currently uses the Cactus Framework as the underlying computational infrastructure that provides large-scale parallelization, general computational components, and a model for collaborative, portable code development.
Nakajima, Yuya; Seino, Junji; Nakai, Hiromi
2016-05-10
An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.
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
Convexity and symmetrization in relativistic theories
NASA Astrophysics Data System (ADS)
Ruggeri, T.
1990-09-01
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
The relativistic geoid: redshift and acceleration potential
NASA Astrophysics Data System (ADS)
Philipp, Dennis; Lämmerzahl, Claus; Puetzfeld, Dirk; Hackmann, Eva; Perlick, Volker
2017-04-01
We construct a relativistic geoid based on a time-independent redshift potential, which foliates the spacetime into isochronometric surfaces. This relativistic potential coincides with the acceleration potential for isometric congruences. We show that the a- and u- geoid, defined in a post-Newtonian framework, coincide also in a more general setup. Known Newtonian and post-Newtonian results are recovered in the respective limits. Our approach offers a relativistic definition of the Earth's geoid as well as a description of the Earth itself (or observers on its surface) in terms of an isometric congruence. Being fully relativistic, this notion of a geoid can also be applied to other compact objects such as neutron stars. By definition, this relativistic geoid can be determined by a congruence of Killing observers equipped with standard clocks by comparing their frequencies as well as by measuring accelerations of objects that follow the congruence. The redshift potential gives the correct result also for frequency comparison through optical fiber links as long as the fiber is at rest w.r.t. the congruence. We give explicit expressions for the relativistic geoid in the Kerr spacetime and the Weyl class of spacetimes. To investigate the influence of higher order mass multipole moments we compare the results for the Schwarzschild case to those obtained for the Erez-Rosen and q-metric spacetimes.
Relabeling symmetry in relativistic fluids and plasmas
NASA Astrophysics Data System (ADS)
Kawazura, Yohei; Yoshida, Zensho; Fukumoto, Yasuhide
2014-11-01
The conservation of the recently formulated relativistic canonical helicity (Yoshida et al 2014 J. Math. Phys. 55 043101) is derived from Noether's theorem by constructing an action principle on the relativistic Lagrangian coordinates (we obtain general cross helicities that include the helicity of the canonical vorticity). The conservation law is, then, explained by the relabeling symmetry pertinent to the Lagrangian label of fluid elements. Upon Eulerianizing the Noether current, the purely spatial volume integral on the Lagrangian coordinates is mapped to a space-time mixed three-dimensional integral on the four-dimensional Eulerian coordinates. The relativistic conservation law in the Eulerian coordinates is no longer represented by any divergence-free current; hence, it is not adequate to regard the relativistic helicity (represented by the Eulerian variables) as a Noether charge, and this stands the reason why the ‘conventional helicity’ is no longer a constant of motion. We have also formulated a relativistic action principle of magnetohydrodynamics (MHD) on the Lagrangian coordinates, and have derived the relativistic MHD cross helicity.
Relativistic blast waves in two dimensions. I - The adiabatic case
NASA Technical Reports Server (NTRS)
Shapiro, P. R.
1979-01-01
Approximate solutions are presented for the dynamical evolution of strong adiabatic relativistic blast waves which result from a point explosion in an ambient gas in which the density varies both with distance from the explosion center and with polar angle in axisymmetry. Solutions are analytical or quasi-analytical for the extreme relativistic case and numerical for the arbitrarily relativistic case. Some general properties of nonplanar relativistic shocks are also discussed, including the incoherence of spherical ultrarelativistic blast-wave fronts on angular scales greater than the reciprocal of the shock Lorentz factor, as well as the conditions for producing blast-wave acceleration.
Extended Galilean symmetries of non-relativistic strings
NASA Astrophysics Data System (ADS)
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Weakly nonlinear kink-type solitary waves in a fully relativistic plasma
Tribeche, Mouloud; Boukhalfa, Soufiane; Zerguini, Taha Houssine
2010-08-15
A fully and coherent relativistic fluid model derived from the covariant formulation of relativistic fluid equations is used to study small but finite amplitude solitary waves. This approach has the characteristic to be consistent with the relativistic principle and consequently leads to a more general set of equations valid for fully relativistic plasmas with arbitrary Lorentz relativistic factor. A kink-solitary wave solution is outlined. Due to electron relativistic effect, the localized structure may experience either a spreading or a compression. This latter phenomenon (compression) becomes less effective and less noticeable as the relativistic character of the ions becomes important. Our results may be relevant to cosmic relativistic double-layers and relativistic plasma structures that involve energetic plasma flows.
Relativistic MHD simulations of extragalactic jets
NASA Astrophysics Data System (ADS)
Leismann, T.; Antón, L.; Aloy, M. A.; Müller, E.; Martí, J. M.; Miralles, J. A.; Ibáñez, J. M.
2005-06-01
We have performed a comprehensive parameter study of the morphology and dynamics of axisymmetric, magnetized, relativistic jets by means of numerical simulations. The simulations have been performed with an upgraded version of the GENESIS code which is based on a second-order accurate finite volume method involving an approximate Riemann solver suitable for relativistic ideal magnetohydrodynamic flows, and a method of lines. Starting from pure hydrodynamic models we consider the effect of a magnetic field of increasing strength (up to β ≡ |b|2/2p ≈ 3.3 times the equipartition value) and different topology (purely toroidal or poloidal). We computed several series of models investigating the dependence of the dynamics on the magnetic field in jets of different beam Lorentz factor and adiabatic index. We find that the inclusion of the magnetic field leads to diverse effects which contrary to Newtonian magnetohydrodynamics models do not always scale linearly with the (relative) strength of the magnetic field. The relativistic models show, however, some clear trends. Axisymmetric jets with toroidal magnetic fields produce a cavity which consists of two parts: an inner one surrounding the beam which is compressed by magnetic forces, and an adjacent outer part which is inflated due to the action of the magnetic field. The outer border of the outer part of the cavity is given by the bow-shock where its interaction with the external medium takes place. Toroidal magnetic fields well below equipartition (β = 0.05) combined with a value of the adiabatic index of 4/3 yield extremely smooth jet cavities and stable beams. Prominent nose cones form when jets are confined by toroidal fields and carry a high Poynting flux (σ≡ |b|2/ρ>0.01 and β≥ 1). In contrast, none of our models possessing a poloidal field develops such a nose cone. The size of the nose cone is correlated with the propagation speed of the Mach disc (the smaller the speed the larger is the size). If two
NASA Astrophysics Data System (ADS)
Vereshchagin, Gregory V.; Aksenov, Alexey G.
2017-02-01
Preface; Acknowledgements; Acronyms and definitions; Introduction; Part I. Theoretical Foundations: 1. Basic concepts; 2. Kinetic equation; 3. Averaging; 4. Conservation laws and equilibrium; 5. Relativistic BBGKY hierarchy; 6. Basic parameters in gases and plasmas; Part II. Numerical Methods: 7. The basics of computational physics; 8. Direct integration of Boltzmann equations; 9. Multidimensional hydrodynamics; Part III. Applications: 10. Wave dispersion in relativistic plasma; 11. Thermalization in relativistic plasma; 12. Kinetics of particles in strong fields; 13. Compton scattering in astrophysics and cosmology; 14. Self-gravitating systems; 15. Neutrinos, gravitational collapse and supernovae; Appendices; Bibliography; Index.
Interaction of two high Reynolds number axisymmetric turbulent wakes
NASA Astrophysics Data System (ADS)
Obligado, M.; Klein, S.; Vassilicos, J. C.
2015-11-01
With the recent discovery of non-equilibrium high Reynolds number scalings in the wake of axisymmetric plates (Nedic et al., PRL, 2013), it has become of importance to develop an experimental technique that permits to easily discriminate between different wake scalings. We propose an experimental setup that tests the presence of non-equilibrium turbulence using the streamwise variation of velocity fluctuations between two bluff bodies facing a flow. We have studied two different sets of plates (one with regular and another with irregular peripheries) with Hot-Wire Anemometry in a wind tunnel. By acquiring streamwise profiles for different plate separations and identifying the wake interaction length for each separation it is possible to estimate the streamwise evolution of the single wake width. From this evolution it is also possible to deduce the turbulence dissipation scalings. This work generalizes previous studies on the interaction of plane wakes (see Gomes-Fernandes et al., JFM, 2012) to include axisymmetric wakes. We find that the wake interaction length proposed in this cited work and a constant anisotropy assumption can be used to collapse the streamwise developments of the first three moments.
Axisymmetric nonlinear waves and structures in Hall plasmas
Islam, Tanim
2012-06-15
In this paper, a general equation for the evolution of an axisymmetric magnetic field in a Hall plasma is derived, with an integral similar to the Grad-Shafranov equation. Special solutions arising from curvature-whistler drift modes that propagate along the electron drift as a Burger's shock and nonlinear periodic and soliton-like solutions to the generalized Grad-Shafranov integral-are analyzed. We derive analytical and numerical solutions in a classical electron-ion Hall plasma, in which electrons and ions are the only species in the plasmas. Results may then be applied to the following low-ionized astrophysical plasmas: in protostellar disks, in which the ions may be coupled to the motion of gases; and in molecular clouds and protostellar jets, in which the much heavier charged dust in a dusty Hall plasma may be collisionally coupled to the gas.
Relativistic Newtonian dynamics
NASA Astrophysics Data System (ADS)
Friedman, Yaakov; Mendel Steiner, Joseph
2017-05-01
A new Relativistic Newtonian Dynamics (RND) for motion under a conservative force capable to describe non-classical behavior in astronomy is proposed. The rotor experiments using Mössbauer spectroscopy with synchrotron radiation, described in the paper, indicate the influence of non-gravitational acceleration or potential energy on time. Similarly, the observed precession of Mercury and the periastron advance of binaries can be explained by the influence of gravitational potential energy on spacetime. The proposed RND incorporates the influence of potential energy on spacetime in Newton’s dynamics. The effect of this influence on time intervals, space increments and velocities is described explicitly by the use of the concept of escape trajectory. For an attracting conservative static potential we derived the RND energy conservation and the dynamics equation for motion of objects with non-zero mass and for massless particles. These equations are subsequently simplified for motion under a central force. Without the need to curve spacetime, this model predicts accurately the four non-classical observations in astronomy used to test the General Relativity.
Nonlinear axisymmetric flexural vibration of spherical shells
NASA Technical Reports Server (NTRS)
Kunieda, H.
1972-01-01
Axisymmetric responses are presented of a nonshallow thin-walled spherical shell on the basis of nonlinear bending theory. An ordinary differential equation with nonlinearity of quadratic as well as cubic terms associated with variable time is derived. The derivation is based on the assumption that the deflection mode is the sum of four Legendre polynomials, and the Galerkin procedure is applied. The equation is solved by asymptotic expansion, and a first approximate solution is adopted. Unstable regions of this solution are discussed.
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data are presented for chamber pressures of 300 and 1000 psia.
Axisymmetric single shear element combustion instability experiment
NASA Technical Reports Server (NTRS)
Breisacher, Kevin J.
1993-01-01
The combustion stability characteristics of a combustor consisting of a single shear element and a cylindrical chamber utilizing LOX and gaseous hydrogen as propellants are presented. The combustor geometry and the resulting longitudinal mode instability are axisymmetric. Hydrogen injection temperature and pyrotechnic pulsing were used to determine stability boundaries. Mixture ratio, fuel annulus gap, and LOX post configuration were varied. Performance and stability data were obtained for chamber pressures of 300 and 1000 psia.
Direct numerical simulation of incompressible axisymmetric flows
NASA Technical Reports Server (NTRS)
Loulou, Patrick
1994-01-01
In the present work, we propose to conduct direct numerical simulations (DNS) of incompressible turbulent axisymmetric jets and wakes. The objectives of the study are to understand the fundamental behavior of axisymmetric jets and wakes, which are perhaps the most technologically relevant free shear flows (e.g. combuster injectors, propulsion jet). Among the data to be generated are various statistical quantities of importance in turbulence modeling, like the mean velocity, turbulent stresses, and all the terms in the Reynolds-stress balance equations. In addition, we will be interested in the evolution of large-scale structures that are common in free shear flow. The axisymmetric jet or wake is also a good problem in which to try the newly developed b-spline numerical method. Using b-splines as interpolating functions in the non-periodic direction offers many advantages. B-splines have local support, which leads to sparse matrices that can be efficiently stored and solved. Also, they offer spectral-like accuracy that are C(exp O-1) continuous, where O is the order of the spline used; this means that derivatives of the velocity such as the vorticity are smoothly and accurately represented. For purposes of validation against existing results, the present code will also be able to simulate internal flows (ones that require a no-slip boundary condition). Implementation of no-slip boundary condition is trivial in the context of the b-splines.
Relativistic Length Agony Continued
NASA Astrophysics Data System (ADS)
Redzic, D. V.
2014-06-01
We made an attempt to remedy recent confusing treatments of some basic relativistic concepts and results. Following the argument presented in an earlier paper (Redzic 2008b), we discussed the misconceptions that are recurrent points in the literature devoted to teaching relativity such as: there is no change in the object in Special Relativity, illusory character of relativistic length contraction, stresses and strains induced by Lorentz contraction, and related issues. We gave several examples of the traps of everyday language that lurk in Special Relativity. To remove a possible conceptual and terminological muddle, we made a distinction between the relativistic length reduction and relativistic FitzGerald-Lorentz contraction, corresponding to a passive and an active aspect of length contraction, respectively; we pointed out that both aspects have fundamental dynamical contents. As an illustration of our considerations, we discussed briefly the Dewan-Beran-Bell spaceship paradox and the 'pole in a barn' paradox.
Weakly relativistic plasma expansion
Fermous, Rachid Djebli, Mourad
2015-04-15
Plasma expansion is an important physical process that takes place in laser interactions with solid targets. Within a self-similar model for the hydrodynamical multi-fluid equations, we investigated the expansion of both dense and under-dense plasmas. The weakly relativistic electrons are produced by ultra-intense laser pulses, while ions are supposed to be in a non-relativistic regime. Numerical investigations have shown that relativistic effects are important for under-dense plasma and are characterized by a finite ion front velocity. Dense plasma expansion is found to be governed mainly by quantum contributions in the fluid equations that originate from the degenerate pressure in addition to the nonlinear contributions from exchange and correlation potentials. The quantum degeneracy parameter profile provides clues to set the limit between under-dense and dense relativistic plasma expansions at a given density and temperature.
Relativistic spin precession in the double pulsar.
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%.
Exact Relativistic `Antigravity' Propulsion
NASA Astrophysics Data System (ADS)
Felber, Franklin S.
2006-01-01
The Schwarzschild solution is used to find the exact relativistic motion of a payload in the gravitational field of a mass moving with constant velocity. At radial approach or recession speeds faster than 3-1/2 times the speed of light, even a small mass gravitationally repels a payload. At relativistic speeds, a suitable mass can quickly propel a heavy payload from rest nearly to the speed of light with negligible stresses on the payload.
SYNCHROTRON RADIATION OF SELF-COLLIMATING RELATIVISTIC MAGNETOHYDRODYNAMIC JETS
Porth, Oliver; Fendt, Christian; Vaidya, Bhargav; Meliani, Zakaria E-mail: fendt@mpia.de
2011-08-10
The goal of this paper is to derive signatures of synchrotron radiation from state-of-the-art simulation models of collimating relativistic magnetohydrodynamic (MHD) jets featuring a large-scale helical magnetic field. We perform axisymmetric special relativistic MHD simulations of the jet acceleration region using the PLUTO code. The computational domain extends from the slow-magnetosonic launching surface of the disk up to 6000{sup 2} Schwarzschild radii allowing jets to reach highly relativistic Lorentz factors. The Poynting-dominated disk wind develops into a jet with Lorentz factors of {Gamma} {approx_equal} 8 and is collimated to 1{sup 0}. In addition to the disk jet, we evolve a thermally driven spine jet emanating from a hypothetical black hole corona. Solving the linearly polarized synchrotron radiation transport within the jet, we derive very long baseline interferometry radio and (sub-) millimeter diagnostics such as core shift, polarization structure, intensity maps, spectra, and Faraday rotation measure (RM) directly from the Stokes parameters. We also investigate depolarization and the detectability of a {lambda}{sup 2}-law RM depending on beam resolution and observing frequency. We find non-monotonic intrinsic RM profiles that could be detected at a resolution of 100 Schwarzschild radii. In our collimating jet geometry, the strict bimodality in the polarization direction (as predicted by Pariev et al.) can be circumvented. Due to relativistic aberration, asymmetries in the polarization vectors across the jet can hint at the spin direction of the central engine.
Relativistic effects in chemistry
Yatsimirskii, K.B.
1995-11-01
Relativistic effects become apparent when the velocity of the electron is arbitrarily close to the speed of light (137 au) without actually attaining it (in heavy atoms of elements at the end of Mendeleev`s Periodic Table). At the orbital level, the relativistic effect is apparent in the radial contraction of penetrating s and p shells, expansion of nonpenetrating d and f shells, and the spin-orbit splitting of p-,d-, and f-shells. The appearance of a relativistic effect is indicated in the variation in the electronic configurations of the atoms in the Periodic Table, the appearance of new types of closed electron shells (6s{sub 1/2}{sup 2}, 6p{sub 1/2}{sup 2}, 7s{sub 1/2}{sup 2}, 5d{sub 3/2}{sup 4}), the stabilization of unstable oxidation states of heavy elements, the characteristic variation in the ionization enthalpies of heavy atoms, their electron affinity, hydration energies, redox potentials, and optical electronegativities. In the spectra of coordination compounds, a relativistic effect is observed when comparing the position of the charge transfer bands in analogous compounds, the parameters characterizing the ligand field strength (10Dq), the interatomic distances and angles in compounds of heavy elements. A relativistic effect is also apparent in the ability of heavy metals to form clusters and superclusters. Relativistic corrections also affect other properties of heavy metal compounds (force constants, dipole moments, biological activity, etc.).
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…
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…
Action principle for relativistic magnetohydrodynamics
NASA Astrophysics Data System (ADS)
D'Avignon, Eric; Morrison, P. J.; Pegoraro, F.
2015-04-01
A covariant action principle for ideal relativistic magnetohydrodynamics in terms of natural Eulerian field variables is given. This is done by generalizing the covariant Poisson bracket theory of Marsden et al. [Ann. Phys. 169, 29 (1986)], which uses a noncanonical bracket to effect constrained variations of an action functional. Various implications and extensions of this action principle are also discussed. Two significant byproducts of this formalism are the introduction of a new divergence-free 4-vector variable for the magnetic field, and a new Lie-dragged form for the theory.
On the relativistic anisotropic configurations
NASA Astrophysics Data System (ADS)
Shojai, F.; Kohandel, M.; Stepanian, A.
2016-06-01
In this paper we study anisotropic spherical polytropes within the framework of general relativity. Using the anisotropic Tolman-Oppenheimer-Volkov equations, we explore the relativistic anisotropic Lane-Emden equations. We find how the anisotropic pressure affects the boundary conditions of these equations. Also we argue that the behavior of physical quantities near the center of star changes in the presence of anisotropy. For constant density, a class of exact solution is derived with the aid of a new ansatz and its physical properties are discussed.
Relativistic heavy ion facilities: worldwide
Schroeder, L.S.
1986-05-01
A review of relativistic heavy ion facilities which exist, are in a construction phase, or are on the drawing boards as proposals is presented. These facilities span the energy range from fixed target machines in the 1 to 2 GeV/nucleon regime, up to heavy ion colliders of 100 GeV/nucleon on 100 GeV/nucleon. In addition to specifying the general features of such machines, an outline of the central physics themes to be carried out at these facilities is given, along with a sampling of the detectors which will be used to extract the physics. 22 refs., 17 figs., 3 tabs.
Nonaxisymmetric viscous lower branch modes in axisymmetric supersonic flows
NASA Technical Reports Server (NTRS)
Duck, Peter W.; Hall, Philip
1988-01-01
In a previous paper, the weakly nonlinear interaction of a pair of axisymmetric lower branch Tollmien-Schlichting instabilities in cylindrical supersonic flows was considered. Here the possibility that nonaxisymmetric modes might also exist is investigated. In fact, it is found that such modes do exist and, on the basis of linear theory, it appears that these modes are the most important. The nonaxisymmetric modes are found to exist for flows around cylinders with nondimensional radius alpha less than some critical value alpha sub c. This critical value alpha sub c is found to increase monotonically with the azimuthal wavenumber nu of the disturbance and it is found that unstable modes always occur in pairs. It is also shown that, in general, instability in the form of lower branch Tollmien-Schlichting waves will occur first for nonaxisymmetric modes and that in the unstable regime the largest growth rates correspond to the latter modes.
Time and 'angular' dependent backgrounds from stationary axisymmetric solutions
Obregon, Octavio; Quevedo, Hernando; Ryan, Michael P.
2004-09-15
Backgrounds depending on time and on angular variable, namely, polarized and unpolarized S{sup 1}xS{sup 2} Gowdy models, are generated as the sector inside the horizons of the manifold corresponding to axisymmetric solutions. As is known, an analytical continuation of ordinary D-branes, iD-branes allow one to find S-brane solutions. Simple models have been constructed by means of analytic continuation of the Schwarzschild and the Kerr metrics. The possibility of studying the i-Gowdy models obtained here is outlined with an eye toward seeing if they could represent some kind of generalized S-branes depending not only on time but also on an angular variable.
Steady axisymmetric vortex flows with swirl and shear
NASA Astrophysics Data System (ADS)
Elcrat, Alan R.; Fornberg, Bengt; Miller, Kenneth G.
A general procedure is presented for computing axisymmetric swirling vortices which are steady with respect to an inviscid flow that is either uniform at infinity or includes shear. We consider cases both with and without a spherical obstacle. Choices of numerical parameters are given which yield vortex rings with swirl, attached vortices with swirl analogous to spherical vortices found by Moffatt, tubes of vorticity extending to infinity and Beltrami flows. When there is a spherical obstacle we have found multiple solutions for each set of parameters. Flows are found by numerically solving the Bragg-Hawthorne equation using a non-Newton-based iterative procedure which is robust in its dependence on an initial guess.
Large elastic deformation of nonlinear axisymmetric membranes: a variational approach
Nielan, P.E.
1982-10-01
Variational equations for determining the deformed configuration of a pressurized axisymmetric membrane undergoing constant acceleration are derived. The general formulation is similar to that of Tielking and Feng. A Mooney-Rivlin material model is used for the membrane and large deformations and strains are accounted for. A Ritz procedure reduces the governing equations to a nonlinear algebraic form. Tensile instabilities are discussed in the context of the analytical solution available for a sphere. In a forthcoming report a computer program written to solve these equations will be described. The analysis and software will be verified by comparison with existing finite elasticity solutions. Solutions to new problems will be given. Ongoing work considering the coupling between structural deformation and the thermodynamics of inflation will be described and the effects of the acceleration on the pressure loads due to the gas will be discussed.
An analysis of turbulent diffusion flame in axisymmetric jet
NASA Technical Reports Server (NTRS)
Chung, P. M.; Im, K. H.
1980-01-01
The kinetic theory of turbulent flow was employed to study the mixing limited combustion of hydrogen in axisymmetric jets. The integro-differential equations in two spatial and three velocity coordinates describing the combustion were reduced to a set of hyperbolic partial differential equations in the two spatial coordinates by a binodal approximation. The MacCormick's finite difference method was then employed for solution. The flame length was longer than that predicted by the flame-sheet analysis, and was found to be in general agreement with a recent experimental result. Increase of the turbulence energy and scale resulted in an enhancement of the combustion rate and, hence, in a shorter flame length. Details of the numerical method as well as of the physical findings are discussed.
On the existence of certain axisymmetric interior metrics
Angulo Santacruz, C.; Batic, D.; Nowakowski, M.
2010-08-15
One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this effect is, in particular, important as it removes the point singularities of Schwarzschild and Reissner-Nordstroem solutions. In this context, it seems to be of some importance to probe also into ringlike singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g., Gaussian), we derive the full set of Einstein equations that the noncommutative geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by noncommutative geometry.
Relativistic equations with fractional and pseudodifferential operators
Babusci, D.; Dattoli, G.; Quattromini, M.
2011-06-15
In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with noninteger exponents. We apply the method to equations resembling generalizations of the heat equations and discuss the possibility of extending the procedure to the relativistic Schroedinger and Dirac equations.
Bruenn, Stephen W.; Lentz, Eric J.; Hix, William Raphael; ...
2016-02-16
We present four ab initio axisymmetric core-collapse supernova simulations initiated from 12, 15, 20, and 25 M⊙ zero-age main sequence progenitors. All of the simulations yield explosions and have been evolved for at least 1.2 s after core bounce and 1 s after material first becomes unbound. These simulations were computed with our Chimera code employing RbR spectral neutrino transport, special and general relativistic transport effects, and state-of-the-art neutrino interactions. Continuing the evolution beyond 1 s after core bounce allows the explosions to develop more fully and the processes involved in powering the explosions to become more clearly evident. Wemore » compute explosion energy estimates, including the negative gravitational binding energy of the stellar envelope outside the expanding shock, of 0.34, 0.88, 0.38, and 0.70 Bethe (B ≡ 1051 erg) and increasing at 0.03, 0.15, 0.19, and 0.52 BS–1, respectively, for the 12, 15, 20, and 25 M⊙ models at the endpoint of this report. We examine the growth of the explosion energy in our models through detailed analyses of the energy sources and flows. We discuss how the explosion energies may be subject to stochastic variations as exemplfied by the effect of the explosion geometry of the 20 M⊙ model in reducing its explosion energy. We compute the proto-neutron star masses and kick velocities. In conclusion, we compare our results for the explosion energies and ejected 56Ni masses against some observational standards despite the large error bars in both models and observations.« less
Relativistic Magnetic Reconnection around rotating black holes
NASA Astrophysics Data System (ADS)
Asenjo, Felipe; Comisso, Luca
2016-10-01
In recent years, the classical Sweet-Parker and Petschek models have been extended in the special relativistic regime, both for MHD plasmas and two-fluid electron-positron plasmas. Nevertheless, there could be situations, like in the vicinity of black holes, where also general relativistic effects can become important. Here, we calculate analytically the reconnection rate and other relevant quantities in a magnetic reconnection process around a rotating black hole. A striking result is that the black hole rotation is capable to produce an enhancement of the rate at which magnetic reconnection proceeds. This work is supported by Fondecyt-Chile, Grant No. 11140025.
Numerical Simulation of Slinger Combustor Using 2-D Axisymmetric Computational Model
NASA Astrophysics Data System (ADS)
Lee, Semin; Park, Soo Hyung; Lee, Donghun
2010-06-01
Small-size turbojet engines have difficulties in maintaining the chemical reaction due to the limitation of chamber size. The combustion chamber is generally designed to improve the reaction efficiency by the generation of vortices in the chamber and to enhance air-fuel mixing characteristics. In the initial stage of designing the combustor, analysis of the 3-D full configuration is not practical due to the huge time consuming computation and grid generation followed by modifications of the geometry. In the present paper, an axisymmetric model maintaining geometric similarity and flow characteristic of 3-D configuration is developed. Based on numerical results from the full 3-D configuration, model reduction is achieved toward 2-D axisymmetric configuration. In the modeling process, the area and location of each hole in 3-D full configuration are considered reasonably and replaced to the 2-D axisymmetric model. By using the 2-D axisymmetric model, the factor that can affect the performance is investigated with the assumption that the flow is non-reacting and turbulent. Numerical results from the present model show a good agreement with numerical results from 3-D full configuration model such as existence of vortex pair in forward region and total pressure loss. By simplifying the complex 3-D model, computing time can be remarkably reduced and it makes easy to find effects of geometry modification.
Axisymmetric instability in a thinning electrified jet.
Dharmansh; Chokshi, Paresh
2016-04-01
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.
Axisymmetric instability in a thinning electrified jet
NASA Astrophysics Data System (ADS)
Dharmansh; Chokshi, Paresh
2016-04-01
The axisymmetric stability of an electrified jet is analyzed under electrospinning conditions using the linear stability theory. The fluid is considered Newtonian with a finite electrical conductivity, modeled as a leaky dielectric medium. While the previous studies impose axisymmetric disturbances on a cylindrical jet of uniform radius, referred to as the base state, in the present study the actual thinning jet profile, obtained as the steady-state solution of the one-dimensional slender filament model, is treated as the base state. The analysis takes into account the role of variation in the jet variables like radius, velocity, electric field, and surface charge density along the thinning jet in the stability behavior. The eigenspectrum of the axisymmetric disturbance growth rate is constructed from the linearized disturbance equations discretized using the Chebyshev collocation method. The most unstable growth rate for the thinning jet is significantly different from that for the uniform radius jet. For the same electrospinning conditions, while the uniform radius jet is predicted to be highly unstable, the thinning jet profile is found to be unstable but with a relatively very low growth rate. The stabilizing role of the thinning jet is attributed to the variation in the surface charge density as well as the extensional deformation rate in the fluid ignored in the uniform radius jet analysis. The dominant mode for the thinning jet is an oscillatory conducting mode driven by the field-charge coupling. The disturbance energy balance finds the electric force to be the dominant force responsible for the disturbance growth, potentially leading to bead formation along the fiber. The role of various material and process parameters in the stability behavior is also investigated.
Chandrasekhar-Kendall modes and Taylor relaxation in an axisymmetric torus
Tang, X.Z.; Boozer, A.H.
2005-10-01
The helicity-conserving Taylor relaxation of a plasma in a toroidal chamber to a force-free configuration, which means j=(j{sub parallel})/B)B with j{sub parallel}/B independent of position, can be generalized to include the external injection of magnetic helicity. When this is done, j{sub parallel}/B has resonant values, which can be understood using the eigenmodes of Taylor-relaxed plasmas enclosed by a perfectly conducting toroidal shell. These eigenmodes include a toroidal generalization of those found by Chandrasekhar and Kendall (CK) [Astrophys. J. 126, 457 (1957)] for a spherical chamber, which has no externally produced magnetic flux. It is shown that the CK modes in an axisymmetric torus are of three types: (1) helical modes as well as axisymmetric modes that have (2) and have no (3) net toroidal flux. Yoshida and Giga (YG) [Math. Z. 204, 235 (1990)] published a fourth class of modes: axisymmetric modes that have no net toroidal flux in the chamber due to toroidal flux produced by a net poloidal current in the shell canceling the net toroidal flux from the plasma currents. Jensen and Chu [Phys. Fluids 27, 2881 (1984)], as well as Taylor [Rev. Mod. Phys. 58, 741 (1986)], considered modes in which the vector potential was zero on the axisymmetric toroidal chamber. It is shown that these Jensen-Chu-Taylor modes include only the CK helical modes and the CK axisymmetric modes without net toroidal flux. If the toroidal chamber is perfectly conducting except for a cut that prevents a net poloidal current from flowing, resonances in j{sub parallel}/B occur at the eigenvalues of the axisymmetric CK modes. Jensen and Chu studied this type of resonance. Without the cut, so a poloidal current flows to conserve the net toroidal flux, it is shown that j{sub parallel}/B resonances occur at the eigenvalues of the CK modes that have no net toroidal flux and at the eigenvalues of the YG modes, which are upshifted from the eigenvalues of the axisymmetric CK modes that carry
Relativistic quantum information and time machines
NASA Astrophysics Data System (ADS)
Ralph, Timothy C.; Downes, Tony G.
2012-01-01
Relativistic quantum information combines the informational approach to understanding and using quantum mechanical systems - quantum information - with the relativistic view of the Universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves - effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.
Energetic particle transport in relativistic flows
NASA Technical Reports Server (NTRS)
Webb, G. M.
1992-01-01
A discussion is given of pitch angle dependent and diffusive transport equations for cosmic rays applicable for both special relativistic and general relativistic flows, derived from the relativistic Boltzmann equation. As an example of particle transport in a curved spacetime we give a pitch angle dependent transport equation appropriate for radial accretion onto a Schwarzschild black hole. The roles of fluid shear, acceleration and compression on the energy changes of particles in the diffusive transport equations are emphasized. Also discussed are special flows (e.g. rigidly rotating flows) associated with a Killing vector for which a constant of the motion of the particles can be identified, and for which simplified transport equations can be constructed.
Isodynamic axisymmetric equilibrium near the magnetic axis
NASA Astrophysics Data System (ADS)
Arsenin, V. V.
2013-08-01
Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo's configuration).
Elastic clearance change in axisymmetric shearing process
NASA Astrophysics Data System (ADS)
Yoshida, Yoshinori
2016-10-01
An axisymmetric shearing experiment is conducted for a sheet of low carbon steel and stainless steel. Elastic change in the clearance between punch and die is measured. The increase of the clearance in shearing is confirmed and the influence of sheared material's flow stress on the clearance change is shown. Finite element analysis (FEA) of shearing with Gurson-Tvergaard-Needlman model (GTN model) is conducted for shearing of the carbon steels with rigid tools as a numerical experiment. Burr height is predicted in the FEA and the result is compared with the experimental result. In addition, the influence of the clearance on stress state in the material is investigated.
Super-collimation by axisymmetric photonic crystals
Purlys, V.; Gailevičius, D.; Peckus, M.; Gadonas, R.; Maigyte, L.; Staliunas, K.
2014-06-02
We propose and experimentally show the mechanism of beam super-collimation by axisymmetric photonic crystals, specifically by periodic (in propagation direction) structure of layers of concentric rings. The physical mechanism behind the effect is an inverse scattering cascade of diffracted wave components back into on- and near-axis angular field components, resulting in substantial enhancement of intensity of these components. We explore the super-collimation by numerical calculations and prove it experimentally. We demonstrate experimentally the axial field enhancement up to 7 times in terms of field intensity.
Isodynamic axisymmetric equilibrium near the magnetic axis
Arsenin, V. V.
2013-08-15
Plasma equilibrium near the magnetic axis of an axisymmetric toroidal magnetic confinement system is described in orthogonal flux coordinates. For the case of a constant current density in the vicinity of the axis and magnetic surfaces with nearly circular cross sections, expressions for the poloidal and toroidal magnetic field components are obtained in these coordinates by using expansion in the reciprocal of the aspect ratio. These expressions allow one to easily derive relationships between quantities in an isodynamic equilibrium, in which the absolute value of the magnetic field is constant along the magnetic surface (Palumbo’s configuration)
The breaking of axisymmetric slender liquid bridges
NASA Astrophysics Data System (ADS)
Meseguer, J.
1983-05-01
Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems.
Mach disk from underexpanded axisymmetric nozzle flow
NASA Technical Reports Server (NTRS)
Chang, I.-S.; Chow, W. L.
1974-01-01
The flowfield associated with the underexpanded axisymmetric nozzle freejet flow including the appearance of a Mach disk has been studied. It is shown that the location and size of the Mach disk are governed by the appearance of a triple-point shock configuration and the condition that the central core flow will reach a state of 'choking at a throat'. It is recognized that coalescence of waves requires special attention and the reflected wave, as well as the vorticity generated from these wave interactions, have to be taken accurately into account. The theoretical results obtained agreed well with the experimental data.
Axisymmetric scrape-off plasma transport
Singer, C.E.; Langer, W.D.
1983-05-01
The two-dimensional flow of a collision dominated hydrogen scrape-off plasma in an axisymmetric tokamak is examined. This flow is described by a set of equations which contain the dominant terms in a maximal ordering appropriate to high density experimental divertors and reactor scrape-off plasmas. Comparison of the theory to estimates of scrape-off parameters in the Doublet III expanded boundary plasmas suggests that analysis of classical and neoclassical processes alone may be sufficient to predict plasma transport in high density scrape-off plasmas of practical importance.
Blair, D.G.; Buckingham, M.J. . Dept. of Physics)
1989-01-01
The Marcel Grossmann Meetings have been conceived with the aim of reviewing recent developments in gravitation and general relativity, with major emphasis on mathematical foundations and physical predictions. Their main object is to elicit contributions which deepen our understanding of spacetime structure as well as to review the status of experiments testing Einstein's theory of gravitation.
SAMPEX Relativistic Microbursts Observation
NASA Astrophysics Data System (ADS)
Liang, X.; Comess, M.; Smith, D. M.; Selesnick, R. S.; Sample, J. G.; Millan, R. M.
2012-12-01
Relativistic (>1 MeV) electron microburst precipitation is thought to account for significant relativistic electron loss. We present the statistical and spectral analysis of relativistic microbursts observed by the Proton/Electron Telescope (PET) on board the Solar Anomalous Magnetospheric Particle Explorer(SAMPEX) satellite from 1992 to 2004. Spectrally we find that microbursts are well fit by an exponential energy distribution in the 0.5-4 MeV range with a spectral e-folding energy of E0 < 375 keV. We also discuss the comparison of morning microbursts with events at midnight, which were first identified as microbursts by O'Brien et al. (2004). Finally, we compare the loss-rates due to microbursts and non-microburst precipitation during storm times and averaged over all times.
B1:. Relativistic Astrophysics
NASA Astrophysics Data System (ADS)
Friedman, John L.
2002-09-01
This review summarizes the parallel session on relativistic astrophysics at GR16. Much of the work reported here involved the structure and stability of neutron stars and the astrophysics of accretion disks around neutron stars and black holes. A large part of the recent work in relativistic astrophysics is tied to numerical investigations of binary coalescence and gravitational waves, but these topics demanded sessions of their own; gravitational waves in the present session were mentioned in connection with neutron-star instability and in a talk on coupling of gravitational waves to radio waves. Two talks involved relativistic stellar systems and cosmology. Finally, several authors outlined advances involving gravitational collapse, cosmic censorship, and baby universes.
Stacey, W. M.; Bae, C.
2015-06-15
A systematic formalism for the calculation of rotation in non-axisymmetric tokamaks with 3D magnetic fields is described. The Braginskii Ωτ-ordered viscous stress tensor formalism, generalized to accommodate non-axisymmetric 3D magnetic fields in general toroidal flux surface geometry, and the resulting fluid moment equations provide a systematic formalism for the calculation of toroidal and poloidal rotation and radial ion flow in tokamaks in the presence of various non-axisymmetric “neoclassical toroidal viscosity” mechanisms. The relation among rotation velocities, radial ion particle flux, ion orbit loss, and radial electric field is discussed, and the possibility of controlling these quantities by producing externally controllable toroidal and/or poloidal currents in the edge plasma for this purpose is suggested for future investigation.
Lucchesi, David M; Peron, Roberto
2010-12-03
The pericenter shift of a binary system represents a suitable observable to test for possible deviations from the newtonian inverse-square law in favor of new weak interactions between macroscopic objects. We analyzed 13 years of tracking data of the LAGEOS satellites with GEODYN II software but with no models for general relativity. From the fit of LAGEOS II pericenter residuals we have been able to obtain a 99.8% agreement with the predictions of Einstein's theory. This result may be considered as a 99.8% measurement in the field of the Earth of the combination of the γ and β parameters of general relativity, and it may be used to constrain possible deviations from the inverse-square law in favor of new weak interactions parametrized by a Yukawa-like potential with strength α and range λ. We obtained |α| ≲ 1 × 10(-11), a huge improvement at a range of about 1 Earth radius.
The special relativistic shock tube
NASA Technical Reports Server (NTRS)
Thompson, Kevin W.
1986-01-01
The shock-tube problem has served as a popular test for numerical hydrodynamics codes. The development of relativistic hydrodynamics codes has created a need for a similar test problem in relativistic hydrodynamics. The analytical solution to the special relativistic shock-tube problem is presented here. The relativistic shock-jump conditions and rarefaction solution which make up the shock tube are derived. The Newtonian limit of the calculations is given throughout.
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas.
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K
2010-06-01
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin- 1/2, and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin- 1/2 contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
Electromagnetic wave equations for relativistically degenerate quantum magnetoplasmas
Masood, Waqas; Eliasson, Bengt; Shukla, Padma K.
2010-06-15
A generalized set of nonlinear electromagnetic quantum hydrodynamic (QHD) equations is derived for a magnetized quantum plasma, including collisional, electron spin-(1/2), and relativistically degenerate electron pressure effects that are relevant for dense astrophysical systems, such as white dwarfs. For illustrative purposes, linear dispersion relations are derived for one-dimensional magnetoacoustic waves for a collisionless nonrelativistic degenerate gas in the presence of the electron spin-(1/2) contribution and for magnetoacoustic waves in a plasma containing relativistically degenerate electrons. It is found that both the spin and relativistic degeneracy at high densities tend to slow down the magnetoacoustic wave due to the Pauli paramagnetic effect and relativistic electron mass increase. The present study outlines the theoretical framework for the investigation of linear and nonlinear behaviors of electromagnetic waves in dense astrophysical systems. The results are applied to calculate the magnetoacoustic speeds for both the nonrelativistic and relativistic electron degeneracy cases typical for white dwarf stars.
Axisymmetric photonic structures with PT-symmetry
NASA Astrophysics Data System (ADS)
Ahmed, Waqas W.; Herrero, Ramon; Botey, Muriel; Staliunas, Kestutis
2016-09-01
PT-symmetric structures in photonic crystals, combining refractive index and gain-loss modulations is becoming a research field with increasing interest due to the light directionality induced by these particular potentials. Here, we consider PT-symmetric potentials with axial symmetry to direct light to the crystal central point obtaining a localization effect. The axial and PT-symmetric potential intrinsically generates an exceptional central point in the photonic crystal by the merge of both symmetries. This particular point in the crystal lattice causes field amplitude gradients with exponential slopes around the crystal center. The field localization strongly depends on the phase of the central point and on the complex amplitude of the PT-potential. The presented work analyzes in a first stage 1D linear PT-axisymmetric crystals and the role of the central point phase that determines the defect character, i.e. refractive index defect, gain-loss defect or a combination of both. The interplay of the directional light effect induced by the PT-symmetry and the light localization around the central point through the axial symmetry enhances localization and allows higher field concentration for certain phases. The linearity of the studied crystals introduces an exponential growth of the field that mainly depends on the complex amplitude of the potential. The work is completed by the analysis of 2D PT-axisymmetric potentials showing different spatial slopes and growth rates caused by symmetry reasons.
Linear lateral vibration of axisymmetric liquid briges
NASA Astrophysics Data System (ADS)
Ferrera, C.; Montanero, J. M.; Cabezas, M. G.
A liquid bridge is a mass of liquid sustained by the action of the surface tension force between two parallel supporting disks Apart from their basic scientific interest a liquid bridge can be considered as the simplest idealization of the configuration appearing in the floating zone technique used for crystal growth and purification of high melting point materials footnote Messeguer et al emph Crystal Growth Res bf 5 27 1999 This has conferred considerable interest on the study of liquid bridges not only in fluid mechanics but also in the field of material engineering The axisymmetric dynamics of an isothermal liquid bridge has been frequently analysed over the past years The studies have considered different phenomena such as free oscillations footnote Montanero emph E J Mech B Fluids bf 22 169 2003 footnote Acero and Montanero emph Phys Fluids bf 17 078105 2005 forced vibrations footnote Perales and Messeguer emph Phys Fluids A bf 4 1110 1992 g-jitter effects footnote Messeguer and Perales emph Phys Fluids A bf 3 2332 1991 extensional deformation footnote Zhang et al emph J Fluid Mech bf 329 207 1996 and breakup process footnote Espino et al emph Phys Fluids bf 14 3710 2002 among others Works considering the nonaxisymmetric dynamical behaviour of a liquid bridge has been far less common footnote Sanz and Diez emph J Fluid Mech bf 205 503 1989 In the present study the linear vibration of an axisymmetric liquid
CLASSIFICATION OF STELLAR ORBITS IN AXISYMMETRIC GALAXIES
Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood E-mail: k.holley@vanderbilt.edu
2015-09-20
It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.
MATRIX ANALYSIS OF AXISYMMETRIC SHELLS UNDER GENERAL LOADING.
Displacement Method. The structures are idealized by truncated conical shell elements and circular flat plate elements, joined together at nodal circles. Loads...represented by a combination of Fourier series are applied to the nodal circles, and the behavior is calculated in terms of the displacements and
ERIC Educational Resources Information Center
Antippa, Adel F.
2009-01-01
We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…
Radiation from Relativistic Jets
NASA Technical Reports Server (NTRS)
Nishikawa, K.-I.; Mizuno, Y.; Hardee, P.; Sol, H.; Medvedev, M.; Zhang, B.; Nordlund, A.; Frederiksen, J. T.; Fishman, G. J.; Preece, R.
2008-01-01
Nonthermal radiation observed from astrophysical systems containing relativistic jets and shocks, e.g., gamma-ray bursts (GRBs), active galactic nuclei (AGNs), and Galactic microquasar systems usually have power-law emission spectra. Recent PIC simulations of relativistic electron-ion (electron-positron) jets injected into a stationary medium show that particle acceleration occurs within the downstream jet. In the presence of relativistic jets, instabilities such as the Buneman instability, other two-streaming instability, and the Weibel (filamentation) instability create collisionless shocks, which are responsible for particle (electron, positron, and ion) acceleration. The simulation results show that the Weibel instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields. These magnetic fields contribute to the electron's transverse deflection behind the jet head. The 'jitter' radiation from deflected electrons in small-scale magnetic fields has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation, a case of diffusive synchrotron radiation, may be important to understand the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.
Relativistic impulse dynamics.
Swanson, Stanley M
2011-08-01
Classical electrodynamics has some annoying rough edges. The self-energy of charges is infinite without a cutoff. The calculation of relativistic trajectories is difficult because of retardation and an average radiation reaction term. By reconceptuallizing electrodynamics in terms of exchanges of impulses rather than describing it by forces and potentials, we eliminate these problems. A fully relativistic theory using photonlike null impulses is developed. Numerical calculations for a two-body, one-impulse-in-transit model are discussed. A simple relationship between center-of-mass scattering angle and angular momentum was found. It reproduces the Rutherford cross section at low velocities and agrees with the leading term of relativistic distinguishable-particle quantum cross sections (Møller, Mott) when the distance of closest approach is larger than the Compton wavelength of the particle. Magnetism emerges as a consequence of viewing retarded and advanced interactions from the vantage point of an instantaneous radius vector. Radiation reaction becomes the local conservation of energy-momentum between the radiating particle and the emitted impulse. A net action is defined that could be used in developing quantum dynamics without potentials. A reinterpretation of Newton's laws extends them to relativistic motion.
ERIC Educational Resources Information Center
Antippa, Adel F.
2009-01-01
We solve the problem of the relativistic rocket by making use of the relation between Lorentzian and Galilean velocities, as well as the laws of superposition of successive collinear Lorentz boosts in the limit of infinitesimal boosts. The solution is conceptually simple, and technically straightforward, and provides an example of a powerful…
Relativistic effects on plasma expansion
Benkhelifa, El-Amine; Djebli, Mourad
2014-07-15
The expansion of electron-ion plasma is studied through a fully relativistic multi-fluids plasma model which includes thermal pressure, ambipolar electrostatic potential, and internal energy conversion. Numerical investigation, based on quasi-neutral assumption, is performed for three different regimes: nonrelativistic, weakly relativistic, and relativistic. Ions' front in weakly relativistic regime exhibits spiky structure associated with a break-down of quasi-neutrality at the expanding front. In the relativistic regime, ion velocity is found to reach a saturation limit which occurs at earlier stages of the expansion. This limit is enhanced by higher electron velocity.
Single electron relativistic clock interferometer
NASA Astrophysics Data System (ADS)
Bushev, P. A.; Cole, J. H.; Sholokhov, D.; Kukharchyk, N.; Zych, M.
2016-09-01
Although time is one of the fundamental notions in physics, it does not have a unique description. In quantum theory time is a parameter ordering the succession of the probability amplitudes of a quantum system, while according to relativity theory each system experiences in general a different proper time, depending on the system's world line, due to time dilation. It is therefore of fundamental interest to test the notion of time in the regime where both quantum and relativistic effects play a role, for example, when different amplitudes of a single quantum clock experience different magnitudes of time dilation. Here we propose a realization of such an experiment with a single electron in a Penning trap. The clock can be implemented in the electronic spin precession and its time dilation then depends on the radial (cyclotron) state of the electron. We show that coherent manipulation and detection of the electron can be achieved already with present day technology. A single electron in a Penning trap is a technologically ready platform where the notion of time can be probed in a hitherto untested regime, where it requires a relativistic as well as quantum description.
NASA Technical Reports Server (NTRS)
Goldstein, M. E.; Rosenbaum, B. M.
1972-01-01
A model, based on Lighthill's theory, for predicting aerodynamic noise from a turbulent shear flow is developed. This model is a generalization of the one developed by Ribner. Unlike Ribner's model, it does not require that the turbulent correlations factor into space and time-dependent parts. It replaces his assumption of isotropic. turbulence by the more realistic one of axisymmetric turbulence. The implications of the model for jet noise are discussed.
NOVA: a nonvariational code for solving MHD stability of axisymmetric toroidal plasmas
Cheng, C.Z.; Chance, M.S.
1986-04-01
A nonvariational approach for determining the ideal MHD stability of axisymmetric toroidal confinement systems is presented. The code (NOVA) employs cubic B-spline finite elements and Fourier expansion in a general flux coordinate (psi, theta, zeta) system. Better accuracy and faster convergence were obtained in comparison with the variational PEST and ERATO codes. The nonvariational approach can be extended to problems having non-Hermitian eigenmode equations where variational energy principles cannot be obtained.
Nonlinear Stability of a Viscous Axisymmetric Jet.
NASA Astrophysics Data System (ADS)
Horwitz, Judith Ann
The nonlinear temporal stability of a viscous axisymmetric jet using a hyperbolic tangent approximation to the actual mean flow is studied with respect to axisymmetric and helical disturbances. For the case of axisymmetric disturbances the weakly nonlinear Stuart-Watson perturbation expansion is used to study the self interaction of the fundamental in a neighborhood of the critical Reynolds number (R_{c}). The Landau constant is positive indicating there is a supercritical Hopf bifurcation. In order to extend these results past R ~ R_ {c}, a severely truncated Fourier model expansion using the Stuart-Watson functions to represent the r dependence, exponentials in z and unknown amplitudes in time is substituted into the Navier-Stokes equation. A projection onto an appropriate subspace leads to a low dimensional (five) system of amplitude equations for the disturbance of the fundamental, harmonic and distortion to the mean flow. The bifurcation package AUTO and Fourier spectrum are used to characterize the nature of the solutions for various values of R. Numerical results show that the periodic solution is stable for 55.3 < R < 72.3. There is a secondary bifurcation at R = 72.3 to a quasiperiodic solution with 2 incommensurate frequencies (Q_2) f_1 and f_2. Each peak in the Fourier spectrum can be indexed according to f = f_1 + nf_2 for n = 0,+/-1, +/-2,.... As R increases past R = 78 there is a transition through another periodic regime and then finally a transition to intermittency for 100 < R < 1000. In the case of helical disturbances the ten dimensional system of amplitude equations has a stable periodic solution for 21.75 < R < 33.2. For 33.2 < R < 37, there is a Q_2 solution. The Fourier spectrum contains two families of peaks: q _{n} = nf_1 - (n - 1)f_2 for n = 0,1,2, ... and w_{n} = nf_1 - (n + 1)f_2 for n = 1,2,3,.... As R increases f_2/f _1 increases and the limiting frequency w_1 --> 0 as f_2/f_1 -->.5 indicating a possible homoclinic orbit. No bounded
NASA Astrophysics Data System (ADS)
Szmytkowski, Radosław; Łukasik, Grzegorz
2016-06-01
The ground state of the Dirac one-electron atom, placed in a weak, static electric field of definite 2L polarity, is studied within the framework of the first-order perturbation theory. The Sturmian expansion of the generalized Dirac-Coulomb Green function [R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 825 (1997), 10.1088/0953-4075/30/4/007; erratum R. Szmytkowski, J. Phys. B: At. Mol. Opt. Phys. 30, 2747 (1997), 10.1088/0953-4075/30/11/023] is used to derive closed-form analytical expressions for various far-field and near-nucleus static electric multipole susceptibilities of the atom. The far-field multipole susceptibilities—the polarizabilities αL, the electric-to-magnetic cross susceptibilities αE L →M (L ∓1 ), and the electric-to-toroidal-magnetic cross susceptibilities αE L →T L —are found to be expressible in terms of one or two nonterminating generalized hypergeometric functions F2 with the unit argument. Counterpart formulas for the near-nucleus multipole susceptibilities—the electric nuclear shielding constants σEL→E L, the near-nucleus electric-to-magnetic cross susceptibilities σE L →M (L ∓1 ), and the near-nucleus electric-to-toroidal-magnetic cross susceptibilities σE L →T L —involve one or two terminating F2(1 ) series and for each L may be rewritten in terms of elementary functions. Numerical values of the far-field dipole, quadrupole, octupole, and hexadecapole susceptibilities are provided for selected hydrogenic ions. The effect of a declared uncertainty in the CODATA 2014 recommended value of the fine-structure constant α on the accuracy of numerical results is investigated. Analytical quasirelativistic approximations, valid to the second order in α Z , where Z is the nuclear charge number, are also derived for all types of the far-field and near-nucleus susceptibilities considered in the paper.
NASA Astrophysics Data System (ADS)
Schuecker, P.; Caldwell, R. R.; Böhringer, H.; Collins, C. A.; Guzzo, L.; Weinberg, N. N.
2003-04-01
New observational constraints on the cosmic matter density Omegam and an effectively redshift-independent equation of state parameter wx of the dark energy are obtained while simultaneously testing the strong and null energy conditions of general relativity on macroscopic scales. The combination of REFLEX X-ray cluster and type-Ia supernova data shows that for a flat Universe the strong energy condition might presently be violated whereas the null energy condition seems to be fulfilled. This provides another observational argument for the present accelerated cosmic expansion and the absence of exotic physical phenomena related to a broken null energy condition. The marginalization of the likelihood distributions is performed in a manner to include a large fraction of the recently discussed possible systematic errors involved in the application of X-ray clusters as cosmological probes. This yields for a flat Universe, Omegam =0.29+0.08-0.12 and wx=-0.95+0.30-0.35 (1sigma errors without cosmic variance). The scatter in the different analyses indicates a quite robust result around wx=-1, leaving little room for the introduction of new energy components described by quintessence-like models or phantom energy. The most natural interpretation of the data is a positive cosmological constant with wx=-1 or something like it.
A solvable model of axisymmetric and non-axisymmetric droplet bouncing.
Andrew, Matthew; Yeomans, Julia M; Pushkin, Dmitri O
2017-02-07
We introduce a solvable Lagrangian model for droplet bouncing. The model predicts that, for an axisymmetric drop, the contact time decreases to a constant value with increasing Weber number, in qualitative agreement with experiments, because the system is well approximated as a simple harmonic oscillator. We introduce asymmetries in the velocity, initial droplet shape, and contact line drag acting on the droplet and show that asymmetry can often lead to a reduced contact time and lift-off in an elongated shape. The model allows us to explain the mechanisms behind non-axisymmetric bouncing in terms of surface tension forces. Once the drop has an elliptical footprint the surface tension force acting on the longer sides is greater. Therefore the shorter axis retracts faster and, due to the incompressibility constraints, pumps fluid along the more extended droplet axis. This leads to a positive feedback, allowing the drop to jump in an elongated configuration, and more quickly.
Axisymmetric Column Collapse in a Rotating System
NASA Astrophysics Data System (ADS)
Warnett, Jay; Thomas, Peter; Dennisenko, Petr
2012-11-01
We discuss experimental and computational results of a study investigating the collapse of an initially axisymmetric cylindrical column of granular material within a rotating environment of air or liquids. In industry this type of granular column collapse that is subject to background rotation is encountered, for instance, in the context of the spreading of powders and fertilizers. In comparison to its non-rotating counterpart the physical characteristics of the column collapse in a rotating system are expected to be modified by effects arising from centrifugal forces and Coriolis forces. We compare our new results for the rotating flow to data available in the literature for the collapse of granular columns in non-rotating systems to highlight the differences observed.
Turbulence characteristics of an axisymmetric reacting flow
NASA Technical Reports Server (NTRS)
Gould, R. D.; Stevenson, W. H.; Thompson, H. D.
1984-01-01
Turbulent sudden expansion flows are of significant theoretical and practical importance. Such flows have been the subject of extensive analytical and experimental study for decades, but many issues are still unresolved. Detailed information on reacting sudden expansion flows is very limited, since suitable measurement techniques have only been available in recent years. The present study of reacting flow in an axisymmetric sudden expansion was initiated under NASA support in December 1983. It is an extension of a reacting flow program which has been carried out with Air Force support under Contract F33615-81-K-2003. Since the present effort has just begun, results are not yet available. Therefore a brief overview of results from the Air Force program will be presented to indicate the basis for the work to be carried out.
Prediction of an axisymmetric combusting flow
NASA Technical Reports Server (NTRS)
Correa, S. M.
1983-01-01
A numerical model for turbulent, recirculating combusting flow is developed and applied to a research combustor. The model is based on the time-averaged Navier-Stokes equations with k-epsilon turbulence closure and the compositional fluctuations at each point are given probabilistically in terms of the mixture fraction. The probability density function is derived from transport equations for its first two moments along with an assumption regarding its shape. The resulting equations are solved using a standard line relaxation algorithm. It is found that the predictions of the model are in good agreement with data from an axisymmetric, bluff-body stabilized research combustor, while the major discrepancies are similar to those found in isothermal flow comparisons. The peculiar features of this flow which contribute to the errors are examined. The agreement between the theory and data deteriorates as the central jet velocity is increased which indicates an enhanced role for unsteady effects.
Compact neutron imaging system using axisymmetric mirrors
Khaykovich, Boris; Moncton, David E; Gubarev, Mikhail V; Ramsey, Brian D; Engelhaupt, Darell E
2014-05-27
A dispersed release of neutrons is generated from a source. A portion of this dispersed neutron release is reflected by surfaces of a plurality of nested, axisymmetric mirrors in at least an inner mirror layer and an outer mirror layer, wherein the neutrons reflected by the inner mirror layer are incident on at least one mirror surface of the inner mirror layer N times, wherein N is an integer, and wherein neutrons reflected by the outer mirror are incident on a plurality of mirror surfaces of the outer layer N+i times, where i is a positive integer, to redirect the neutrons toward a target. The mirrors can be formed by a periodically reversed pulsed-plating process.
Axisymmetric Drop Shape Analysis (ADSA): An Outline.
Saad, Sameh M I; Neumann, A Wilhelm
2016-12-01
Drop shape techniques for the measurement of interfacial tension are powerful, versatile and flexible. The shape of the drop/bubble depends on the balance between surface tension and external forces, e.g. gravity. This balance is reflected mathematically in the Laplace equation of capillarity. Axisymmetric Drop Shape Analysis (ADSA) is a commonly used drop shape technique. A streamlined version of the development of ADSA over the past several decades is presented to illustrate its validity and range of utility. Several configurations of interest will be considered and presented systematically. Shape and surface tension will be linked to a shape parameter based on proper concepts of differential geometry. The resulting shape parameter will be shown to allow determination of the range of applicability of such a drop shape method.
Ideal ballooning modes in axisymmetric mirror machines
Baldwin, D.E.; McNamara, B.; Willmann, P.
1980-12-15
A simple code is described that finds marginally stable (..omega../sup 2/ = 0) ballooning-type MHD modes, localized about a field line in an axisymmetric, open-ended, plasma confinement device. The equations are based on a lower bound for the perturbed energy delta W, derived by W. Newcomb from the ideal MHD energy principle, and are cast in the form of a Ricatti equation for the first derivative of the eigenfunction, with the open boundary conditions that this derivative vanish at the plasma boundary down each field line. The input to the code is the two-dimensional shape of a field line, the field strength B(s), and parameters to define pressure profiles throughout the system. The objective is to find the highest plasma pressures for which the given line is MHD-stable.
Direct numerical simulation of axisymmetric turbulence
NASA Astrophysics Data System (ADS)
Qu, Bo; Bos, Wouter J. T.; Naso, Aurore
2017-09-01
The dynamics of decaying, strictly axisymmetric, incompressible turbulence is investigated using direct numerical simulations. It is found that the angular momentum is a robust invariant of the system. It is further shown that long-lived coherent structures are generated by the flow. These structures can be associated with stationary solutions of the Euler equations. The structures obey relations in agreement with predictions from selective decay principles, compatible with the decay laws of the system. Two different types of decay scenarios are highlighted. The first case results in a quasi-two-dimensional flow with a dynamical behavior in the poloidal plane similar to freely decaying two-dimensional turbulence. In a second regime, the long-time dynamics is dominated by a single three-dimensional mode.
Axisymmetric collapse of rotating, isothermal clouds
NASA Technical Reports Server (NTRS)
Boss, A. P.; Haber, J. G.
1982-01-01
The results of over 50 new models of the axisymmetric collapse of rotating, isothermal clouds are presented, with the following objectives: (1) to fully explore the initial conditions necessary for collapse from uniform density and uniform rotation, subject to constant volume and constant pressure boundary conditions; (2) to catalog the possible end states for cloud collapse from these initial conditions; and (3) to determine if there is a critical value of rotational energy/gravitational energy associated with ring formation, as appears to be the case for adiabatic clouds. Three end states are obtained: Bonnor-Ebert spheroids, rings and collapsing disks. The rings are formed with values of the ratio of rotational energy to the absolute value of the gravitational energy typically less than the Maclaurin spheroid value for dynamic instability to ring formation.
Nonlinear axisymmetric liquid currents in spherical annuli
NASA Technical Reports Server (NTRS)
Astafyeva, N. M.; Vvedenskaya, N. D.; Yavorskaya, I. M.
1978-01-01
A numerical analysis of non-linear axisymmetric viscous flows in spherical annuli of different gap sizes is presented. Only inner sphere was supposed to rotate at a constant angular velocity. The streamlines, lines of constant angular velocity, kinetic energy spectra, and spectra of velocity components are obtained. A total kinetic energy and torque needed to rotate the inner sphere are calculated as functions of Re for different gap sizes. In small-gap annulus nonuniqueness of steady solutions of Navier-Stokes equations is established and regions of different flow regime existences are found. Numerical solutions in a wide-gap annulus and experimental results are used in conclusions about flow stability in the considered range of Re. The comparison of experimental and numerical results shows close qualitative and quantitative agreement.
DYNAMICS OF STRONGLY TWISTED RELATIVISTIC MAGNETOSPHERES
Parfrey, Kyle; Beloborodov, Andrei M.; Hui, Lam
2013-09-10
Magnetar magnetospheres are believed to be strongly twisted due to shearing of the stellar crust by internal magnetic stresses. We present time-dependent axisymmetric simulations showing in detail the evolution of relativistic force-free magnetospheres subjected to slow twisting through large angles. When the twist amplitude is small, the magnetosphere moves quasi-statically through a sequence of equilibria of increasing free energy. At some twist amplitude the magnetosphere becomes tearing-mode unstable to forming a resistive current sheet, initiating large-scale magnetic reconnection in which a significant fraction of the magnetic free energy can be dissipated. This ''critical'' twist angle is insensitive to the resistive length scale. Rapid shearing temporarily stabilizes the magnetosphere beyond the critical angle, allowing the magnetosphere of a rapidly differentially rotating star to store and dissipate more free energy. In addition to these effects, shearing the surface of a rotating star increases the spindown torque applied to the star. If shearing is much slower than rotation, the resulting spikes in spindown rate can occur on timescales anywhere from the long twisting timescale to the stellar spin period or shorter, depending both on the stellar shear distribution and the existing distribution of magnetospheric twists. A model in which energy is stored in the magnetosphere and released by a magnetospheric instability therefore predicts large changes in the measured spindown rate before soft gamma repeater giant flares.
Efficient acceleration of relativistic magnetohydrodynamic jets
NASA Astrophysics Data System (ADS)
Toma, Kenji; Takahara, Fumio
2013-08-01
Relativistic jets in active galactic nuclei, galactic microquasars, and gamma-ray bursts are widely considered to be magnetohydrodynamically driven by black hole accretion systems, although the conversion mechanism from the Poynting into the particle kinetic energy flux is still open. Recent detailed numerical and analytical studies of global structures of steady, axisymmetric magnetohydrodynamic (MHD) flows with specific boundary conditions have not reproduced as rapid an energy conversion as required by observations. In order to find more suitable boundary conditions, we focus on the flow along a poloidal magnetic field line just inside the external boundary, without treating the transfield force balance in detail. We find some examples of the poloidal field structure and corresponding external pressure profile for an efficient and rapid energy conversion as required by observations, and that the rapid acceleration requires a rapid decrease of the external pressure above the accretion disk. We also clarify the differences between the fast magnetosonic point of the MHD flow and the sonic point of the de Laval nozzle.
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.
Time-dependent closure relations for relativistic collisionless fluid equations.
Bendib-Kalache, K; Bendib, A; El Hadj, K Mohammed
2010-11-01
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space (ω,k), where ω and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter ω/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc²/T , where m is the particle rest mass and T, the plasma temperature in energy units.
Time-dependent closure relations for relativistic collisionless fluid equations
Bendib-Kalache, K.; Bendib, A.; El Hadj, K. Mohammed
2010-11-15
Linear fluid equations for relativistic and collisionless plasmas are derived. Closure relations for the fluid equations are analytically computed from the relativistic Vlasov equation in the Fourier space ({omega},k), where {omega} and k are the conjugate variables of time t and space x variables, respectively. The mathematical method used is based on the projection operator techniques and the continued fraction mathematical tools. The generalized heat flux and stress tensor are calculated for arbitrary parameter {omega}/kc where c is the speed of light, and for arbitrary relativistic parameter z=mc{sup 2}/T, where m is the particle rest mass and T, the plasma temperature in energy units.
Criterion for stability of a special relativistically covariant dynamical system
NASA Astrophysics Data System (ADS)
Horwitz, L. P.; Zucker, D.
2017-03-01
We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the geometric method (GEM) developed for the analysis of nonrelativistic Hamiltonian systems to study the local stability of a relativistic Duffing oscillator. Poincaré plots of the simulated motion are consistent with the RGEM. We find a threshold for the external driving force required for chaotic behavior in the Minkowski spacetime.
Axisymmetric Plume Simulations with NASA's DSMC Analysis Code
NASA Technical Reports Server (NTRS)
Stewart, B. D.; Lumpkin, F. E., III
2012-01-01
A comparison of axisymmetric Direct Simulation Monte Carlo (DSMC) Analysis Code (DAC) results to analytic and Computational Fluid Dynamics (CFD) solutions in the near continuum regime and to 3D DAC solutions in the rarefied regime for expansion plumes into a vacuum is performed to investigate the validity of the newest DAC axisymmetric implementation. This new implementation, based on the standard DSMC axisymmetric approach where the representative molecules are allowed to move in all three dimensions but are rotated back to the plane of symmetry by the end of the move step, has been fully integrated into the 3D-based DAC code and therefore retains all of DAC s features, such as being able to compute flow over complex geometries and to model chemistry. Axisymmetric DAC results for a spherically symmetric isentropic expansion are in very good agreement with a source flow analytic solution in the continuum regime and show departure from equilibrium downstream of the estimated breakdown location. Axisymmetric density contours also compare favorably against CFD results for the R1E thruster while temperature contours depart from equilibrium very rapidly away from the estimated breakdown surface. Finally, axisymmetric and 3D DAC results are in very good agreement over the entire plume region and, as expected, this new axisymmetric implementation shows a significant reduction in computer resources required to achieve accurate simulations for this problem over the 3D simulations.
Relativistic electrons in space.
NASA Technical Reports Server (NTRS)
Simnett, G. M.
1972-01-01
This paper reviews the current state of knowledge concerning relativistic electrons, above 0.3 MeV, in interplanetary space, as measured by detectors on board satellites operating beyond the influence of the magnetosphere. The electrons have a galactic component, which at the lower energies is subject both to solar modulation and to spasmodic 'quiet time' increases and a direct solar component correlated with flare activity. The recent measurements have established the form of the differential energy spectrum of solar flare electrons. Electrons have been detected from flares behind the visible solar disk. Relativistic electrons do not appear to leave the sun at the time of the flash phase of the flare, although there are several signatures of electron acceleration at this time. The delay is interpreted as taking place during the transport of the electrons through the lower corona.
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
Simulations of Dynamic Relativistic Magnetospheres
NASA Astrophysics Data System (ADS)
Parfrey, Kyle Patrick
Neutron stars and black holes are generally surrounded by magnetospheres of highly conducting plasma in which the magnetic flux density is so high that hydrodynamic forces are irrelevant. In this vanishing-inertia—or ultra-relativistic—limit, magnetohydrodynamics becomes force-free electrodynamics, a system of equations comprising only the magnetic and electric fields, and in which the plasma response is effected by a nonlinear current density term. In this dissertation I describe a new pseudospectral simulation code, designed for studying the dynamic magnetospheres of compact objects. A detailed description of the code and several numerical test problems are given. I first apply the code to the aligned rotator problem, in which a star with a dipole magnetic field is set rotating about its magnetic axis. The solution evolves to a steady state, which is nearly ideal and dissipationless everywhere except in a current sheet, or magnetic field discontinuity, at the equator, into which electromagnetic energy flows and is dissipated. Magnetars are believed to have twisted magnetospheres, due to internal magnetic evolution which deforms the crust, dragging the footpoints of external magnetic field lines. This twisting may be able to explain both magnetars' persistent hard X-ray emission and their energetic bursts and flares. Using the new code, I simulate the evolution of relativistic magnetospheres subjected to slow twisting through large angles. The field lines expand outward, forming a strong current layer; eventually the configuration loses equilibrium and a dynamic rearrangement occurs, involving large-scale rapid magnetic reconnection and dissipation of the free energy of the twisted magnetic field. When the star is rotating, the magnetospheric twisting leads to a large increase in the stellar spin-down rate, which may take place on the long twisting timescale or in brief explosive events, depending on where the twisting is applied and the history of the system
Relativistic statistical arbitrage
NASA Astrophysics Data System (ADS)
Wissner-Gross, Alexander; Freer, Cameron
2011-03-01
Recent advances in high-frequency financial trading have made light propagation delays between geographically separated exchanges relevant. Here we show that there exist optimal locations from which to coordinate the statistical arbitrage of pairs of spacelike separated securities, and calculate a representative map of such locations on Earth. Furthermore, trading local securities along chains of such intermediate locations results in a novel econophysical effect, in which the relativistic propagation of tradable information is effectively slowed or stopped by arbitrage.
Relativistic statistical arbitrage
NASA Astrophysics Data System (ADS)
Wissner-Gross, A. D.; Freer, C. E.
2010-11-01
Recent advances in high-frequency financial trading have made light propagation delays between geographically separated exchanges relevant. Here we show that there exist optimal locations from which to coordinate the statistical arbitrage of pairs of spacelike separated securities, and calculate a representative map of such locations on Earth. Furthermore, trading local securities along chains of such intermediate locations results in a novel econophysical effect, in which the relativistic propagation of tradable information is effectively slowed or stopped by arbitrage.
Local relativistic exact decoupling
NASA Astrophysics Data System (ADS)
Peng, Daoling; Reiher, Markus
2012-06-01
We present a systematic hierarchy of approximations for local exact decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a unitary transformation of only the atomic block-diagonal part of the Hamiltonian. Systematically, off-diagonal Hamiltonian matrix blocks can be subjected to a unitary transformation to yield relativistically corrected matrix elements. The full hierarchy is investigated with respect to the accuracy reached for the electronic energy and for selected molecular properties on a balanced test molecule set that comprises molecules with heavy elements in different bonding situations. Our atomic (local) assembly of the unitary exact-decoupling transformation—called local approximation to the unitary decoupling transformation (DLU)—provides an excellent local approximation for any relativistic exact-decoupling approach. Its order-N2 scaling can be further reduced to linear scaling by employing a neighboring-atomic-blocks approximation. Therefore, DLU is an efficient relativistic method well suited for relativistic calculations on large molecules. If a large molecule contains many light atoms (typically hydrogen atoms), the computational costs can be further reduced by employing a well-defined nonrelativistic approximation for these light atoms without significant loss of accuracy. We also demonstrate that the standard and straightforward transformation of only the atomic block-diagonal entries in the Hamiltonian—denoted diagonal local approximation to the Hamiltonian (DLH) in this paper—introduces an error that is on the order of the error of second-order Douglas-Kroll-Hess (i.e., DKH2) when compared with exact-decoupling results. Hence, the local DLH approximation would be pointless in an exact-decoupling framework, but can be efficiently employed in combination with the fast to evaluate DKH2 Hamiltonian in order to speed up calculations
Gravitationally confined relativistic neutrinos
NASA Astrophysics Data System (ADS)
Vayenas, C. G.; Fokas, A. S.; Grigoriou, D.
2017-09-01
Combining special relativity, the equivalence principle, and Newton’s universal gravitational law with gravitational rather than rest masses, one finds that gravitational interactions between relativistic neutrinos with kinetic energies above 50 MeV are very strong and can lead to the formation of gravitationally confined composite structures with the mass and other properties of hadrons. One may model such structures by considering three neutrinos moving symmetrically on a circular orbit under the influence of their gravitational attraction, and by assuming quantization of their angular momentum, as in the Bohr model of the H atom. The model contains no adjustable parameters and its solution, using a neutrino rest mass of 0.05 eV/c2, leads to composite state radii close to 1 fm and composite state masses close to 1 GeV/c2. Similar models of relativistic rotating electron - neutrino pairs give a mass of 81 GeV/c2, close to that of W bosons. This novel mechanism of generating mass suggests that the Higgs mass generation mechanism can be modeled as a latent gravitational field which gets activated by relativistic neutrinos.
Relativistic tidal disruption events
NASA Astrophysics Data System (ADS)
Levan, A.
2012-12-01
In March 2011 Swift detected an extremely luminous and long-lived outburst from the nucleus of an otherwise quiescent, low luminosity (LMC-like) galaxy. Named Swift J1644+57, its combination of high-energy luminosity (1048 ergs s-1 at peak), rapid X-ray variability (factors of >100 on timescales of 100 seconds) and luminous, rising radio emission suggested that we were witnessing the birth of a moderately relativistic jet (Γ ˜ 2 - 5), created when a star is tidally disrupted by the supermassive black hole in the centre of the galaxy. A second event, Swift J2058+0516, detected two months later, with broadly similar properties lends further weight to this interpretation. Taken together this suggests that a fraction of tidal disruption events do indeed create relativistic outflows, demonstrates their detectability, and also implies that low mass galaxies can host massive black holes. Here, I briefly outline the observational properties of these relativistic tidal flares observed last year, and their evolution over the first year since their discovery.
Point form relativistic quantum mechanics and relativistic SU(6)
NASA Technical Reports Server (NTRS)
Klink, W. H.
1993-01-01
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
Relativistic Astrophysics in Active Galactic Nuclei
NASA Astrophysics Data System (ADS)
Reynolds, C.
2014-07-01
X-ray spectroscopy and timing with XMM-Newton have given us an unprecedented view of general relativistic physics in the immediate vicinity of accreting supermassive black holes. In addition to firmly establishing the existence of black holes and allowing us to constrain their spin, we are now detecting reverberation effects from the innermost disk that will ultimately allow us to map the location of the enigmatic X-ray source. In this review talk, I shall begin by describing current status of black hole spin measurements and the tantalizing evidence for a mass dependence to the spin distribution. Building on from the previous talk, I shall then describe the general relativistic modeling of the detected reverberation delays as a means to map out the geometry of both the X-ray source and the inner accretion disk. I shall conclude by discussing the promise of ATHENA for these studies.
Parametrized relativistic dynamical framework for neutrino oscillations
NASA Astrophysics Data System (ADS)
Fanchi, John R.
2017-05-01
Mass state transitions are a key feature of parametrized relativistic dynamics (PRD). PRD is a manifestly covariant quantum theory with invariant evolution parameter. The theory has been applied to neutrino flavor oscillations between two mass states. It is generalized to transitions between three mass states and applied to the survival of electron neutrinos. The analysis shows that significant differences exist between theoretical results of the conventional model and the PRD model.
Relativistic electron beam acceleration by Compton scattering of extraordinary waves
Sugaya, R.
2006-05-15
Relativistic transport equations, which demonstrate that relativistic and nonrelativistic particle acceleration along and across a magnetic field and the generation of an electric field transverse to the magnetic field, are induced by nonlinear wave-particle scattering (nonlinear Landau and cyclotron damping) of almost perpendicularly propagating electromagnetic waves in a relativistic magnetized plasma were derived from the relativistic Vlasov-Maxwell equations. The relativistic transport equations show that electromagnetic waves can accelerate particles in the k{sup ''} direction (k{sup ''}=k-k{sup '}). Simultaneously, an intense cross-field electric field, E{sub 0}=B{sub 0}xv{sub d}/c, is generated via the dynamo effect owing to perpendicular particle drift to satisfy the generalized Ohm's law, which means that this cross-field particle drift is identical to the ExB drift. On the basis of these equations, acceleration and heating of a relativistic electron beam due to nonlinear wave-particle scattering of electromagnetic waves in a magnetized plasma were investigated theoretically and numerically. Two electromagnetic waves interact nonlinearly with the relativistic electron beam, satisfying the resonance condition of {omega}{sub k}-{omega}{sub k{sup '}}-(k{sub perpendicular}-k{sub perpendicula=} r{sup '})v{sub d}-(k{sub parallel}-k{sub parallel}{sup '})v{sub b}{approx_equal}m{omega}{sub ce}, where v{sub b} and v{sub d} are the parallel and perpendicular velocities of the relativistic electron beam, respectively, and {omega}{sub ce} is the relativistic electron cyclotron frequency. The relativistic transport equations using the relativistic drifted Maxwellian momentum distribution function of the relativistic electron beam were derived and analyzed. It was verified numerically that extraordinary waves can accelerate the highly relativistic electron beam efficiently with {beta}m{sub e}c{sup 2} < or approx. 1 GeV, where {beta}=(1-v{sub b}{sup 2}/c{sup 2}){sup -1/2}.
Axisymmetric Magnetic Mirror Fusion-Fission Hybrid
Moir, R. W.; Martovetsky, N. N.; Molvik, A. W.; Ryutov, D. D.; Simonen, T. C.
2011-05-13
The achieved performance of the gas dynamic trap version of magnetic mirrors and today’s technology we believe are sufficient with modest further efforts for a neutron source for material testing (Q=P_{fusion}/P_{input}~0.1). The performance needed for commercial power production requires considerable further advances to achieve the necessary high Q>>10. An early application of the mirror, requiring intermediate performance and intermediate values of Q~1 are the hybrid applications. The Axisymmetric Mirror has a number of attractive features as a driver for a fusion-fission hybrid system: geometrical simplicity, inherently steady-state operation, and the presence of the natural divertors in the form of end tanks. This level of physics performance has the virtue of low risk and only modest R&D needed and its simplicity promises economy advantages. Operation at Q~1 allows for relatively low electron temperatures, in the range of 4 keV, for the DT injection energy ~ 80 keV. A simple mirror with the plasma diameter of 1 m and mirror-to-mirror length of 35 m is discussed. Simple circular superconducting coils are based on today’s technology. The positive ion neutral beams are similar to existing units but designed for steady state. A brief qualitative discussion of three groups of physics issues is presented: axial heat loss, MHD stability in the axisymmetric geometry, microstability of sloshing ions. Burning fission reactor wastes by fissioning actinides (transuranics: Pu, Np, Am, Cm, .. or just minor actinides: Np, Am, Cm, …) in the hybrid will multiply fusion’s energy by a factor of ~10 or more and diminish the Q needed to less than 1 to overcome the cost of recirculating power for good economics. The economic value of destroying actinides by fissioning is rather low based on either the cost of long-term storage or even deep geologic disposal so most of the revenues of hybrids will come from electrical power. Hybrids that obtain revenues from
Relativistic Modeling Capabilities in PERSEUS Extended MHD Simulation Code for HED Plasmas
NASA Astrophysics Data System (ADS)
Hamlin, Nathaniel; Seyler, Charles
2014-10-01
We discuss the incorporation of relativistic modeling capabilities into the PERSEUS extended MHD simulation code for high-energy-density (HED) plasmas, and present the latest simulation results. The use of fully relativistic equations enables the model to remain self-consistent in simulations of such relativistic phenomena as hybrid X-pinches and laser-plasma interactions. A major challenge of a relativistic fluid implementation is the recovery of primitive variables (density, velocity, pressure) from conserved quantities at each time step of a simulation. This recovery, which reduces to straightforward algebra in non-relativistic simulations, becomes more complicated when the equations are made relativistic, and has thus far been a major impediment to two-fluid simulations of relativistic HED plasmas. By suitable formulation of the relativistic generalized Ohm's law as an evolution equation, we have reduced the central part of the primitive variable recovery problem to a straightforward algebraic computation, which enables efficient and accurate relativistic two-fluid simulations. Our code recovers expected non-relativistic results and reveals new physics in the relativistic regime. Work supported by the National Nuclear Security Administration stewardship sciences academic program under Department of Energy cooperative Agreement DE-NA0001836.
Relativistic effects in local inertial frames
NASA Technical Reports Server (NTRS)
Ashby, Neil; Bertotti, Bruno
1986-01-01
The concept of a generalized Fermi frame is introduced with the aim of describing the relativistic effects due to a third, distant body (such as the sun) upon the motion of an earth satellite. This extends Fermi's construction of a local inertial frame to the case in which there are local gravitating masses. This is done in the slow-motion, weak-field approximation by splitting the metric into an external part and a local part; Fermi's construction of local inertial coordinates defined with respect to the external metric is then used to transform the complete metric. The results show that the main relativistic effects on an earth satellite are due to the nonlinear correction in the earth's own Schwarzschild field. There are much smaller relativistic corrections in the tidal field of the sun, and an earth-sun interaction term. The spatial axes of the local frame also undergo geodetic precession. Particular care must be taken with respect to the definition of the time coordinate in the generalized Fermi frame in order that the unit of time be consistent with readings of reasonable physical clocks on earth's surface. Also discussed more rigorously is the generalized Fermi frame for a system of two bodies revolving in circular orbits around a common barycenter.
Efficient material treatment by axi-symmetrically polarized laser radiation
NASA Astrophysics Data System (ADS)
Makin, V. S.; Pestov, Yu I.; Makin, R. S.
2016-08-01
Recent years the increased interest is to the problem of interaction of nontraditionally polarized laser radiation with condensed media. The experiments with axisymmetrical polarization attract more attention. The peculiarities of interaction of axisymmetrical laser radiation with condensed matter are considered in framework of universal polariton model. It is shown that more effective is interaction of radially polarized laser radiation with surface active media. The optical schemes for efficient material treatment by radially polarized radiation are sketched.
Characteristics of an axisymmetric sudden expansion flow
NASA Technical Reports Server (NTRS)
Stevenson, W. H.; Thompson, H. D.
1985-01-01
A two-color, two component Laser Doppler Velocimeter (LDV) system operating in forward scatter has been developed in order to make simultaneous measurements of the axial and radial velocity components in an axisymmetric sudden expansion flow with and without combustion. The LDV system includes Bragg cell modulators in the four beam paths to allow a net frequency shift of 5MHz in both the green and blue beams. This permits an unambiguous measurement of negative velocities and also eliminates incomplete signal bias. The green beam probe volume has a waist diameter of 0.200 mm and is approximately 2mm long. The blue beam has a probe volume waist of 0.250 mm and is approximately 1 mm long. The scattered light from the probe volume is separated so that approximately 80% of each color passes to its respective photomultiplier tube by using a dichroic filter. Narrow bandpass filters are used to further filter unwanted signals before they are detected. A schematic diagram of the LDV system is shown.
Control of Thermoacoustic Axisymmetric and Helical Instabilities
NASA Astrophysics Data System (ADS)
Gutmark, Ephraim; Paschereit, Christian Oliver; Weisenstein, Wolfgang
1998-11-01
Unstable thermoacoustic modes were investigated and controlled in an experimental low-emission swirl stabilized combustor, in which the acoustic boundary conditions were modified to obtain combustion instability. Several axisymmetric and helical unstable modes were identified for fully premixed conditions. These unstable modes were associated with flow instabilities related to the recirculating wake-like region near the combustor axis and shear layer instabilities at the sudden expansion (dump plane). Open and closed loop active control systems were used to suppress the thermoacoustic pressure oscillations and to reduce undesired emissions of pollutants during premixed combustion. Pressure transducers and OH emission detection sensors monitored the combustion process and provide input to the processor of the control system. The actuators were high frequency valves, which were employed to superimpose modulations in the fuel stream. Symmetric and antisymmetric fuel injection schemes were tested. Suppression levels of up to 24 dB in the pressure oscillations were obtained. In some of the cases tested, concomitant reductions of NOx and CO emissions were achieved. The effect of the various pulsed fuel injection methods on the combustion structure was investigated.
Longitudinal wakefield for an axisymmetric collimator
Blednykh A.; Krinsky, S.
2012-05-25
We consider the longitudinal point-charge wakefield, w(s), for an axisymmetric collimator having inner radius b, outer radius d, inner length g, and taper length L. The taper angle {alpha} is defined by tan {alpha} = (d-b)/L. Using the electromagnetic simulation code ECHO, we explore the dependence of the wakefield on a collimator's geometric parameters over a wide range of profiles: from small-angle tapers to step-function transitions. The point-charge wakefield is determined using an approximation introduced by Podobedov and Stupakov. We have found it useful to exhibit the wakefield as a function of the scaled variable s/d{alpha}. For small taper angles, our results illustrate the satisfaction of the longitudinal scaling found by Stupakov, Bane, and Zagorodnov; and for larger taper angles, the breaking of this longitudinal scaling is clearly depicted. The use of the scaled variable s/d{alpha} turns out to be especially well suited to describing the wakefield for a collimator with step-function profile ({alpha} = {pi}/2).
Magnetic surfaces in an axisymmetric torus
Skovoroda, A. A.
2013-04-15
A method is developed for specifying the boundary equilibrium magnetic surface in an axially symmetric torus by using the absolute values of the magnetic field B = B{sub s}({theta}) and the gradient of the poloidal flux vertical bar vertical bar {nabla}{Psi} vertical bar = vertical bar {nabla}{Psi} vertical bar {sub s}({theta}) in a special flux coordinate system. By setting two surface constants (e.g., the safety factor q and dp/d{Psi}) and matching the absolute values of the magnetic field and the flux gradient on a closed magnetic surface, it is possible to find all equilibrium magnetic functions (including n {center_dot} {nabla} ln B and the local shear s) and all constants (including the toroidal current J and the shear d{mu}/d{Psi}) on this surface. Such a non-traditional formulation of the boundary conditions in solving the stability problem in an axisymmetric torus allows one to impose intentional conditions on plasma confinement and MHD stability at the periphery of the system.
Design of a Quasi-Axisymmetric Stellarator
NASA Astrophysics Data System (ADS)
Reiman, A.; Ku, L.-P.; Boozer, A.; Brooks, A.; Goldston, R.; Johnson, J.; Monticello, D.; Mynick, H.; Nazikian, R.; Neilson, G. H.; Redi, M.; Sheffield, G.; Zarnstorff, M.
1997-11-01
We have been pursuing the design of a stellarator with the following properties: 1) magnetic field sufficiently close to quasi-axisymmetric that the neoclassical transport is small compared to the turbulent transport; 2) adequate ideal MHD stability β limit; 3) good equilibrium flux surfaces at β values of interest; 4) aspect ratio comparable to that of tokamaks. For our equilibrium and stability β limits, the goal is to exceed 5%. Equilibrium flux surfaces and magnetic island widths are evaluated using the PIES 3D equilibrium code. The assumed current profile corresponds to the self-consistent bootstrap current. Analytic estimates suggest that neoclassical currents will have a large effect on island widths, leading to the requirement that the ι profile be monotonically increasing. One option being considered for construction of the stellarator would be to use the present PBX toroidal field coils and vacuum vessel, building additional coils inside the vacuum vessel. Fifteen MW of neutral beam power are available, allowing a test of the β limit.
Transient, hypervelocity flow in an axisymmetric nozzle
NASA Technical Reports Server (NTRS)
Jacobs, P. A.
1991-01-01
The performance of an axisymmetric nozzle was examined which was designed to produce uniform, parallel flow with a nominal Mach number of 8. A free-piston driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzle and, over the range of operating conditions examined, the nozzle produced satisfactory test flows. However, there were flow disturbances that persisted for significant times after flow initiation. The detailed starting process of the nozzle was also investigated by performing numerical simulations at several nominal test conditions. The classical description of the starting process, based on a quasi-one-dimensional model, provided a reasonable approximation and was used to demonstrate that the starting process could consume a significant fraction of the otherwise usable test gas. This was especially important at high operating enthalpies where nozzle supply conditions were maintained for shorter times. Multidimensional simulations illustrated a mechanism by which the starting process in the actual nozzle could take longer than that predicted by the quasi-one-dimensional analysis. However, the cause of the persistent disturbances observed in the experimental calibration was not identified.
Axisymmetric inlet minimum weight design method
NASA Technical Reports Server (NTRS)
Nadell, Shari-Beth
1995-01-01
An analytical method for determining the minimum weight design of an axisymmetric supersonic inlet has been developed. The goal of this method development project was to improve the ability to predict the weight of high-speed inlets in conceptual and preliminary design. The initial model was developed using information that was available from inlet conceptual design tools (e.g., the inlet internal and external geometries and pressure distributions). Stiffened shell construction was assumed. Mass properties were computed by analyzing a parametric cubic curve representation of the inlet geometry. Design loads and stresses were developed at analysis stations along the length of the inlet. The equivalent minimum structural thicknesses for both shell and frame structures required to support the maximum loads produced by various load conditions were then determined. Preliminary results indicated that inlet hammershock pressures produced the critical design load condition for a significant portion of the inlet. By improving the accuracy of inlet weight predictions, the method will improve the fidelity of propulsion and vehicle design studies and increase the accuracy of weight versus cost studies.
Stress Analysis of Laminated Composite Cylinders Under Non-Axisymmetric Loading
Starbuck, J.M.
1999-10-26
The use of thick-walled composite cylinders in structural applications has seen tremendous growth over the last decade. Applications include pressure vessels, flywheels, drive shafts, spoolable tubing, and production risers. In these applications, the geometry of a composite cylinder is axisymmetric but in many cases the applied loads are non-axisymmetric and more rigorous analytical tools are required for an accurate stress analysis. A closed-form solution is presented for determining the layer-by-layer stresses, strains, and displacements and first-ply failure in laminated composite cylinders subjected to non-axisymmetric loads. The applied loads include internal and external pressure, axial force, torque, axial bending moment, uniform temperature change, rotational velocity, and interference fits. The formulation is based on the theory of anisotropic elasticity and a state of generalized plane deformation along the axis of the composite cylinder. Parametric design trade studies can be easily and quickly computed using this closed-form solution. A computer program that was developed for performing the numerical calculations is described and results from specific case studies are presented.
Orientational dynamics of weakly inertial axisymmetric particles in steady viscous flows
NASA Astrophysics Data System (ADS)
Einarsson, J.; Angilella, J. R.; Mehlig, B.
2014-06-01
The orientational dynamics of weakly inertial axisymmetric particles in a steady flow is investigated. We derive an asymptotic equation of motion for the unit axial vector along the particle symmetry axis, valid for small Stokes number St, and for any axisymmetric particle in any steady linear viscous flow. This reduced dynamics is analysed in two ways, both pertain to the case of a simple shear flow. In this case inertia induces a coupling between precession and nutation. This coupling affects the dynamics of the particle, breaks the degeneracy of the Jeffery orbits, and creates two limiting periodic orbits. We calculate the leading-order Floquet exponents of the limiting periodic orbits and show analytically that prolate objects tend to a tumbling orbit, while oblate objects tend to a log-rolling orbit, in agreement with previous analytical and numerical results. Second, we analyse the role of the limiting orbits when rotational noise is present. We formulate the Fokker-Planck equation describing the orientational distribution of an axisymmetric particle, valid for small St and general Péclet number Pe. Numerical solutions of the Fokker-Planck equation, obtained by means of expansion in spherical harmonics, show that stationary orientational distributions are close to the inertia-free case when Pe St≪1, whereas they are determined by inertial effects, though small, when Pe≫1/St≫1.
Venkatesh, Suresh; Schurig, David
2016-12-12
We describe and provide a systematic procedure for computationally fast propagation of arbitrary vector electromagnetic (EM) fields through an axially symmetric medium. A cylindrical harmonic field propagator is chosen for this purpose and in most cases, this is the best and the obvious choice. Firstly, we describe the cylindrical harmonic decomposition technique in terms of both scalar and vector basis for a given input excitation field. Then we formulate a generalized discrete Fourier-Hankel transform to achieve efficient vector basis decomposition. We allow a slower, pre-computation step, that finds a representation of the axi-symmetric medium as a transfer matrix in a discrete, cylindrical-harmonic basis. We find this matrix from a series of axi-symmetric (2D) finite element simulations (also known as the 2.5D technique). This transfer matrix approach significantly reduces the computational load when the transverse size or range exceeds about 30 wavelengths. This matrix is independent of the input excitation field for a given space-bandwidth product and hence makes it reusable for different excitation fields. We numerically validate the above approaches for different axi-symmetric EM scattering media which include a hemispherical gradient-index Maxwell's fish-eye lens, a transformation optics designed spherical invisibility cloak, a thin aspheric lens, and a cylindrical perfect lens.
Relativistic Quantum Communication
NASA Astrophysics Data System (ADS)
Hosler, Dominic
In this Ph.D. thesis, I investigate the communication abilities of non-inertial observers and the precision to which they can measure parametrized states. I introduce relativistic quantum field theory with field quantisation, and the definition and transformations of mode functions in Minkowski, Schwarzschild and Rindler spaces. I introduce information theory by discussing the nature of information, defining the entropic information measures, and highlighting the differences between classical and quantum information. I review the field of relativistic quantum information. We investigate the communication abilities of an inertial observer to a relativistic observer hovering above a Schwarzschild black hole, using the Rindler approximation. We compare both classical communication and quantum entanglement generation of the state merging protocol, for both the single and dual rail encodings. We find that while classical communication remains finite right up to the horizon, the quantum entanglement generation tends to zero. We investigate the observers' abilities to precisely measure the parameter of a state that is communicated between Alice and Rob. This parameter was encoded to either the amplitudes of a single excitation state or the phase of a NOON state. With NOON states the dual rail encoding provided greater precision, which is different to the results for the other situations. The precision was maximum for a particular number of excitations in the NOON state. We calculated the bipartite communication for Alice-Rob and Alice-AntiRob beyond the single mode approximation. Rob and AntiRob are causally disconnected counter-accelerating observers. We found that Alice must choose in advance with whom, Rob or AntiRob she wants to create entanglement using a particular setup. She could communicate classically to both.
Effect of azimuthal flow fluctuations on flow and flame dynamics of axisymmetric swirling flames
NASA Astrophysics Data System (ADS)
Acharya, Vishal; Lieuwen, Timothy
2015-10-01
Recent studies have clearly shown the important role of swirl fluctuations (or, more precisely, fluctuations in axial vorticity) in the response of premixed flames to flow oscillations. An important implication of this mechanism is that the axial location of the swirler plays a key role in the phase between the acoustic flow excitation source and the resulting axial vorticity fluctuation at the flame. Similar to the previously well recognized role of azimuthal vorticity fluctuations, these swirl fluctuations are vortical and convect at the mean flow velocity, unlike the acoustic flow fluctuations. However, there is a fundamental difference between axial and azimuthal vorticity disturbances in terms of the flow oscillations they induce on the flame. Specifically, azimuthal vorticity disturbances excite radial and axial flow disturbances, while axial vorticity oscillations, in general induce both radial and azimuthal flow fluctuations, but in the axisymmetric case, they only directly excite azimuthal flow fluctuations. The axial vorticity fluctuations do, however, indirectly excite axial and radial velocity fluctuations when the axial vortex tube is tilted off-axis, such as at locations of area expansion. This difference is significant because axisymmetric flames are disturbed only by the velocity component normal to it, which stem from axial and radial velocity components only. This implies that axisymmetric mean flames are not directly affected by azimuthal flow fluctuations, since they are tangential to it. Thus, it is the extent to which the axial vorticity is tilted and rotated that controls the strength of the flow oscillations normal to the flame and, in turn, lead to heat release oscillations. This coupling process is not easily amenable to analytical calculations and, as such, we report here a computational study of the role of these different flow fluctuations on the flame response in an axisymmetric framework. The results indicate that the swirl
Modeling relativistic nuclear collisions.
Anderlik, C.; Magas, V.; Strottman, D.; Csernai, L. P.
2001-01-01
Modeling Ultra-Relativistic Heavy Ion Collisioiis at RHIC and LHC energies using a Multi Module Model is presented. The first Module is the Effective String Rope Model for the calculation of the initial stages of the reaction; the output of this module is used as the initial state for the subsequent one-fluid hydrodynainical calculation module. It is shown that such an initial state leads to the creation of the third flow component. The hydrodynamical evolution of the energy density distribution is presented for RHIC energies. The final module describing the Freeze Out; and Hadronization is also discussed.
Rössler, O E; Matsuno, K
1998-04-01
The two mindsets of absolutism and relativism are juxtaposed, and the relational or relativist stance is vindicated. The only 'absolute' entity which undeniably exists, consciousness has the reality of a dream. The escape hatch from this prison is relational, as Descartes and Levinas found out: Unfalsified relational consistency implies exteriority. Exteriority implies infinite power which in turn makes compassion inevitable. Aside from ethics as a royal way to enlightenment, a new technology called 'deep technology' may be accessible. It changes the whole world in a demonstrable fashion by manipulation of the micro frame--that is, the observer-world interface.
Relativistic quantum cryptography
NASA Astrophysics Data System (ADS)
Kaniewski, Jedrzej
Special relativity states that information cannot travel faster than the speed of light, which means that communication between agents occupying distinct locations incurs some minimal delay. Alternatively, we can see it as temporary communication constraints between distinct agents and such constraints turn out to be useful for cryptographic purposes. In relativistic cryptography we consider protocols in which interactions occur at distinct locations at well-defined times and we investigate why such a setting allows to implement primitives which would not be possible otherwise. (Abstract shortened by UMI.).
Ultrabaric relativistic superfluids
NASA Astrophysics Data System (ADS)
Papini, G.; Weiss, M.
1985-09-01
Ultrabaric superfluid solutions are obtained for Einstein's equations to examine the possibility of the existence of superluminal sound speeds. The discussion is restricted only by requiring the energy-momentum tensor and the equation of state of matter to be represented by full relativistic equations. Only a few universes are known to satisfy the conditions, and those exhibit tension and are inflationary. Superluminal sound velocities are shown, therefore, to be possible for the interior Schwarzchild metric, which has been used to explain the red shift of quasars, and the Stephiani solution (1967). The latter indicates repeated transitions between superluminal and subliminal sound velocities in the hyperbaric superfluid of the early universe.
Causal dissipation for the relativistic dynamics of ideal gases.
Freistühler, Heinrich; Temple, Blake
2017-05-01
We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.
Causal dissipation for the relativistic dynamics of ideal gases
NASA Astrophysics Data System (ADS)
Freistühler, Heinrich; Temple, Blake
2017-05-01
We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.
Relativistic differential-difference momentum operators and noncommutative differential calculus
Mir-Kasimov, R. M.
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 irreps 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.
NASA Astrophysics Data System (ADS)
Fendt, C.
1997-07-01
Highly collimated jets are observed in various astronomical objects, as active galactic nuclei, galactic high energy sources, and also young stellar objects. There is observational indication that these jets originate in accretion disks, and that magnetic fields play an important role for the jet collimation and plasma acceleration. The rapid disk rotation close to the central object leads to relativistic rotational velocities of the magnetic field lines. The structure of these axisymmetric magnetic flux surfaces follows from the trans-field force-balance described by the Grad-Schlueter-Shafranov equation. In this paper, we investigate the asymptotic field structure of differentially rotating magnetic jets, widening the study by Appl & Camenzind (1993A&A...270...71A, 1993A&A...274..699A). In general, our results show that, with the same current distribution, differentially rotating jets are collimated to smaller jet radii as compared with jets with rigidly rotating field. Differentially rotating jets need a stronger net poloidal current in order to collimate to the same asymptotic radius. Current-free solutions are not possible for differentially rotating disk-jet magnetospheres with cylindrical asymptotics. We present a simple analytical relation between the poloidal current distribution and magnetic field rotation law. A general relation is derived for the current strength for jets with maximum differential rotation and minimum differential rotation. Analytical solutions are also given in the case of a field rotation leading to a degeneration of the light cylinder. By linking the asymptotic solution to a Keplerian accretion disk, 'total expansion rates' for the jets, and also the flux distribution at the foot points of the flux surfaces are derived. Large poloidal currents imply a strong opening of flux surfaces, a stronger gradient of field rotation leads to smaller expansion rates. There is indication that AGN jet expansion rates are less than in the case of
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
NASA Astrophysics Data System (ADS)
Li, Yi; Wu, Congjun
2012-02-01
The usual Landau level quantization, as demonstrated in the 2D quantum Hall effect, is crucially based on the planar structure. In this talk, we explore its 3D counterpart possessing the full 3D rotational symmetry as well as the time reversal symmetry. We construct the Landau level Hamiltonians in 3 and higher dimensional flat space for both relativistic and non-relativistic fermions. The 3D cases with integer fillings are Z2 topological insulators. The non-relativistic version describes spin-1/2 fermions coupling to the Aharonov-Casher SU(2) gauge field. This system exhibits flat Landau levels in which the orbital angular momentum and the spin are coupled with a fixed helicity. Each filled Landau level contributes one 2D helical Dirac Fermi surface at an open boundary, which demonstrates the Z2 topological nature. A natural generalization to Dirac fermions is found as a square root problem of the above non-relativistic version, which can also be viewed as the Dirac equation defined on the phase space. All these Landau level problems can be generalized to arbitrary high dimensions systematically. [4pt] [1] Yi Li and Congjun Wu, arXiv:1103.5422.[0pt] [2] Yi Li, Ken Intriligator, Yue Yu and Congjun Wu, arXiv:1108.5650.
Transonic analysis and design of axisymmetric bodies in nonuniform flow
NASA Technical Reports Server (NTRS)
Chang, Jen-Fu; Lan, C. Edward
1987-01-01
An inviscid nonuniform axisymmetric transonic code was developed for applications in analysis and design. Propfan slipstream effect on pressure distribution for a body with and without sting was investigated. Results show that nonuniformity causes pressure coefficient to be more negative and shock strength to be stronger and more rearward. Sting attached to a body reduced the pressure peak and moves the rear shock forward. Extent and Mach profile shapes of the nonuniformity region appeared to have little effect on the pressure distribution. Increasing nonuniformity magnitude made pressure coefficient more negative and moved the shock rearward. Design study was conducted with the CONMIN optimizer for an ellipsoid and a body with the NACA-0012 counter. For the ellipsoid, the general trend showed that to reduce the pressure drag, the front portion of the body should be thinner and the contour of the rear portion should be flatter than the ellipsoid. For the design of a body with a sharp trailing edge in transonic flow with an initial shape given by the NACA-0012 contour, the pressure drag was reduced by decreasing the nose radius and increasing the thickness in the aft portion. Drag reduction percentages are given.
Refraction and Shielding of Noise in Non-Axisymmetric Jets
NASA Technical Reports Server (NTRS)
Khavaran, Abbas
1996-01-01
This paper examines the shielding effect of the mean flow and refraction of sound in non-axisymmetric jets. A general three-dimensional ray-acoustic approach is applied. The methodology is independent of the exit geometry and may account for jet spreading and transverse as well as streamwise flow gradients. We assume that noise is dominated by small-scale turbulence. The source correlation terms, as described by the acoustic analogy approach, are simplified and a model is proposed that relates the source strength to 7/2 power of turbulence kinetic energy. Local characteristics of the source such as its strength, time- or length-scale, convection velocity and characteristic frequency are inferred from the mean flow considerations. Compressible Navier Stokes equations are solved with a k-e turbulence model. Numerical predictions are presented for a Mach 1.5, aspect ratio 2:1 elliptic jet. The predicted sound pressure level directivity demonstrates favorable agreement with reported data, indicating a relative quiet zone on the side of the major axis of the elliptic jet.
Turbulent contributions to Ohm's law in axisymmetric magnetized plasmas
NASA Astrophysics Data System (ADS)
Chavdarovski, I.; Gatto, R.
2017-07-01
The effect of magnetic turbulence in shaping the current density in axisymmetric magnetized plasmas is analyzed using a turbulent extension of Ohm's law derived from the self-consistent action-angle transport theory. Besides the well-known hyper-resistive (helicity-conserving) contribution, the generalized Ohm's law contains an anomalous resistivity term and a turbulent bootstrap-like term proportional to the current density derivative. The numerical solution of the equation for equilibrium and turbulence profiles characteristic of conventional and advanced scenarios shows that, through the "turbulent bootstrap" effect and anomalous resistivity, power and parallel current can be generated which are a sizable portion (about 20%-25%) of the corresponding effects associated with the neoclassical bootstrap effect. The degree of alignment of the turbulence peak and the pressure gradient plays an important role in defining the steady-state regime. In a fully bootstrapped tokamak, the hyper-resistivity is essential in overcoming the intrinsic limitation of the hollow current profile.
Axisymmetric curvature-driven instability in a model divertor geometry
Farmer, W. A.; Ryutov, D. D.
2013-09-15
A model problem is presented which qualitatively describes a pressure-driven instability which can occur near the null-point in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Line-tying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, non-separable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.