Geometric inequalities in spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Csukás, Károly Z.
2017-07-01
In geometric inequalities ADM mass plays more fundamental role than the concept of quasi-local mass. This paper is to demonstrate that using the quasi-local mass some new insights can be acquired. In spherically symmetric spacetimes the Misner-Sharp mass and the concept of the Kodama vector field provides an ideal setting to the investigations of geometric inequalities. We applying the proposed new techniques to investigate the spacetimes containing black hole or cosmological horizons but we shall also apply them in context of normal bodies. Most of the previous investigations applied only the quasi-local charges and the area. Our main point is to include the quasi-local mass in the corresponding geometrical inequalities. This way we recover some known relations but new inequalities are also derived.
Noncommutative spherically symmetric spacetimes at semiclassical order
NASA Astrophysics Data System (ADS)
Fritz, Christopher; Majid, Shahn
2017-07-01
Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\
The inverse spatial Laplacian of spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Fernandes, Karan; Lahiri, Amitabha
2017-09-01
We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field.
Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes
Abreu, Gabriel; Visser, Matt
2010-08-15
In a general time-dependent (3+1)-dimensional spherically symmetric spacetime, the so-called Kodama vector is a naturally defined geometric quantity that is timelike outside the evolving horizon and so defines a preferred class of fiducial observers. However the Kodama vector does not by itself define any preferred notion of time. We first extract as much information as possible by invoking the 'warped product' structure of spherically symmetric spacetime to study the Kodama vector, and the associated Kodama energy flux, in a coordinate-independent manner. Using this formalism we construct a general class of conservation laws, generalizing Kodama's energy flux. We then demonstrate that a preferred time coordinate - which we shall call Kodama time - can be introduced by taking the additional step of applying the Clebsch decomposition theorem to the Kodama vector. We thus construct a geometrically preferred coordinate system for any time-dependent spherically symmetric spacetime, and explore its properties. We study the geometrically preferred fiducial observers, and demonstrate that it is possible to define and calculate a generalized notion of surface gravity that is valid throughout the entire evolving spacetime. Furthermore, by building and suitably normalizing a set of radial null geodesics, we can show that this generalized surface gravity passes several consistency tests and has a physically appropriate static limit.
Thermodynamics of spherically symmetric spacetimes in loop quantum gravity
NASA Astrophysics Data System (ADS)
Mäkelä, Jarmo
2015-06-01
The choice of the area operator in loop quantum gravity is by no means unique. In addition to the area operator commonly used in loop quantum gravity there is also an area operator introduced by Krasnov in 1998, which gives uniformly spaced area spectra for the horizons of spacetime. Using Krasnov's area operator we consider the thermodynamics of spherically symmetric spacetimes equipped with horizons in loop quantum gravity. Among other things, our approach implies, in a pretty simple manner, that every horizon of spacetime emits thermal radiation and possesses entropy which, in the natural units, is one-quarter of its area. When applied to the de Sitter spacetime loop quantum gravity provides an explanation both to the presence and the smallness of the cosmological constant.
Constrained field theories on spherically symmetric spacetimes with horizons
NASA Astrophysics Data System (ADS)
Fernandes, Karan; Lahiri, Amitabha; Ghosh, Suman
2017-02-01
We apply the Dirac-Bergmann algorithm for the analysis of constraints to gauge theories defined on spherically symmetric black hole backgrounds. We find that the constraints for a given theory are modified on such spacetimes through the presence of additional contributions from the horizon. As a concrete example, we consider the Maxwell field on a black hole background, and determine the role of the horizon contributions on the dynamics of the theory.
Maximal slicing of D-dimensional spherically symmetric vacuum spacetime
Nakao, Ken-ichi; Abe, Hiroyuki; Yoshino, Hirotaka; Shibata, Masaru
2009-10-15
We study the foliation of a D-dimensional spherically symmetric black-hole spacetime with D{>=}5 by two kinds of one-parameter families of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpetlike shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces avoid the singularity irrespective of the dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of D=5, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. These data will be useful for checking five-dimensional numerical-relativity codes based on the moving puncture approach.
Self tuning scalar fields in spherically symmetric spacetimes
Appleby, Stephen
2015-05-01
We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of 'Fab-Four' models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory—introducing the second and third Galileon terms—show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing 'John' ∼ G{sup μ}{sub ν} ∂{sub μ}φ∂{sup ν}φ and a canonical kinetic term ∼ ∂{sub α}φ ∂{sup α}φ. This behaviour was first observed in [1]. The screening mechanism, which requires redundancy of the scalar field equation in the 'vacuum', fails for the 'Paul' term in an inhomogeneous spacetime.
Relativistic electromagnetic mass models in spherically symmetric spacetime
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Chatterjee, Vikram
2016-10-01
Under the static spherically symmetric Einstein-Maxwell spacetime of embedding class one we explore possibility of constructing electromagnetic mass model where mass and other physical parameters have purely electromagnetic origin (Lorentz in Proc. Acad. Sci. Amst. 6, 1904). This work is in continuation of our earlier investigation of Maurya et al. (Eur. Phys. J. C 75:389, 2015a) where we developed an algorithm and found out three new solutions of electromagnetic mass model. In the present work we consider different metric potentials ν and λ and have analyzed them in a systematic way. It is observed that some of the previous solutions related to electromagnetic mass model are nothing but special cases of the presently obtained generalized solution set. We further verify the solution set and especially show that these are extremely applicable in the case of compact stars.
Horizons versus singularities in spherically symmetric space-times
Bronnikov, K. A.; Elizalde, E.; Odintsov, S. D.; Zaslavskii, O. B.
2008-09-15
We discuss different kinds of Killing horizons possible in static, spherically symmetric configurations and recently classified as 'usual', 'naked', and 'truly naked' ones depending on the near-horizon behavior of transverse tidal forces acting on an extended body. We obtain the necessary conditions for the metric to be extensible beyond a horizon in terms of an arbitrary radial coordinate and show that all truly naked horizons, as well as many of those previously characterized as naked and even usual ones, do not admit an extension and therefore must be considered as singularities. Some examples are given, showing which kinds of matter are able to create specific space-times with different kinds of horizons, including truly naked ones. Among them are fluids with negative pressure and scalar fields with a particular behavior of the potential. We also discuss horizons and singularities in Kantowski-Sachs spherically symmetric cosmologies and present horizon regularity conditions in terms of an arbitrary time coordinate and proper (synchronous) time. It turns out that horizons of orders 2 and higher occur in infinite proper times in the past or future, but one-way communication with regions beyond such horizons is still possible.
Charged seven-dimensional spacetimes with spherically symmetric extra dimensions
De Felice, Antonio; Ringeval, Christophe
2009-06-15
We derive exact solutions of the seven-dimensional Einstein-Maxwell equations for a spacetime exhibiting Poincare invariance along four dimensions and spherical symmetry in the extra dimensions. Such topology generically arises in the context of braneworld models. Our solutions generalize previous results on Ricci-flat spacetimes admitting the two-sphere and are shown to include wormhole configurations. A regular coordinate system suitable to describe the whole spacetime is singled out, and we discuss the physical relevance of the derived solutions.
Anisotropic stars for spherically symmetric spacetimes satisfying the Karmarkar condition
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Ratanpal, B. S.; Govender, M.
2017-07-01
A new class of solution describing an anisotropic stellar configuration satisfying Karmarkar's condition i.e. spherically symmetric metric of embedding class 1, is reported. It has been shown that the compact star model is physically well-behaved and meet all the physical requirements for a stable configuration in hydrostatic equilibrium. Our model describes compact stars like Vela X-1 and 4U1608-52 to a very good approximation.
Labeling spherically symmetric spacetimes with the Ricci tensor
NASA Astrophysics Data System (ADS)
Ferrando, Joan Josep; Sáez, Juan Antonio
2017-02-01
We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper (Ferrando and Sáez 2010 Class. Quantum Grav. 27 205024). In this approach we consider every compatible algebraic type of the Ricci tensor, and we analyze specifically the conformally flat case for perfect fluid and Einstein–Maxwell solutions. As a direct application we obtain the ideal labeling (exclusively involving explicit concomitants of the metric tensor) of the Schwarzschild interior metric and the Vaidya solution. The Stephani universes and some significative subfamilies are also characterized.
NASA Astrophysics Data System (ADS)
Montero, Pedro J.; Cordero-Carrión, Isabel
2012-06-01
Brown [Phys. Rev. DPRVDAQ1550-7998 79, 104029 (2009)] has recently introduced a covariant formulation of the BSSN equations which is well suited for curvilinear coordinate systems. This is particularly desirable as many astrophysical phenomena are symmetric with respect to the rotation axis or are such that curvilinear coordinates adapt better to their geometry. However, the singularities associated with such coordinate systems are known to lead to numerical instabilities unless special care is taken (e.g., regularization at the origin). Cordero-Carrión will present a rigorous derivation of partially implicit Runge-Kutta methods in forthcoming papers, with the aim of treating numerically the stiff source terms in wavelike equations that may appear as a result of the choice of the coordinate system. We have developed a numerical code solving the BSSN equations in spherical symmetry and the general relativistic hydrodynamic equations written in flux-conservative form. A key feature of the code is that it uses a second-order partially implicit Runge-Kutta method to integrate the evolution equations. We perform and discuss a number of tests to assess the accuracy and expected convergence of the code—namely a pure gauge wave, the evolution of a single black hole, the evolution of a spherical relativistic star in equilibrium, and the gravitational collapse of a spherical relativistic star leading to the formation of a black hole. We obtain stable evolutions of regular spacetimes without the need for any regularization algorithm at the origin.
Regularization of geodesics in static spherically symmetric Kerr-Schild spacetimes
NASA Astrophysics Data System (ADS)
Galindo, Pablo; Mars, Marc
2015-04-01
We describe a method to analyze causal geodesics in static and spherically symmetric spacetimes of Kerr-Schild form which, in particular, allows for a detailed study of the geodesics in the vicinity of the central singularity by means of a regularization procedure based on a generalization of the McGehee regularization for the motion of Newtonian point particles moving in a power-law potential. The McGehee regularization was used by Belbruno and Pretorius [1] to perform a dynamical system regularization of the central singularity of the motion of massless test particles in the Schwarzschild spacetime. Our generalization allows us to consider causal (timelike or null) geodesics in any static and spherically symmetric spacetime of Kerr-Schild form. As an example, we apply these results to causal geodesics in the Schwarzschild and Reissner-Nordstrom spacetimes.
NASA Astrophysics Data System (ADS)
Tsukamoto, Naoki
2017-03-01
Gravitational lensing by the light sphere of compact objects like black holes and wormholes will give us information on the compact objects. In this paper, we provide an improved strong deflection limit analysis in a general asymptotically flat, static, spherically symmetric spacetime. The strong deflection limit analysis also works in ultrastatic spacetimes. As an example of an ultrastatic spacetime, we reexamine the deflection angle in the strong deflection limit in an Ellis wormhole spacetime. Using the strong deflection limit, we obtain the deflection angle analytically for the Reissner-Nordström spacetime. The point of the improvement is the definition of a standard variable in the strong deflection limit analysis. We show that the choice of the variable is as important as the choice of the coordinates and we conclude that one should choose a proper variable for a given spacetime.
NASA Astrophysics Data System (ADS)
Akbar, M. M.
2017-06-01
It is well known that static spherically symmetric spacetimes can admit foliations by flat spacelike hypersurfaces, which are best described in terms of the Painlevè-Gullstrand coordinates. The uniqueness and existence of such foliations were addressed earlier. In this paper, we prove, purely geometrically, that any possible foliation of a static spherically symmetric spacetime by an arbitrary codimension-one spherical spacelike geometry, up to time translation and rotation, is unique, and we find the algebraic condition under which it exists. This leads us to what can be considered as the most natural generalization of the Painlevè-Gullstrand coordinate system for static spherically symmetric metrics, which, in turn, makes it easy to derive generic conclusions on foliation and to study specific cases as well as to easily reproduce previously obtained generalizations as special cases. In particular, we note that the existence of foliation by flat hypersurfaces guarantees the existence of foliation by hypersurfaces whose Ricci curvature tensor is everywhere non-positive (constant negative curvature is a special case). The study of uniqueness and the existence concurrently solves the question of embeddability of a spherical spacelike geometry in one-dimensional higher static spherically symmetric spacetimes, and this produces known and new results geometrically, without having to go through the momentum and Hamiltonian constraints.
Dualities and geometrical invariants for static and spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Seidel, Paola Terezinha; Cabral, Luís Antonio
2016-04-01
In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.
Tomita, Kenji
2010-03-15
On the basis of the Gerlach-Sengupta theory of gauge-invariant perturbations, a formula of the integrated Sachs-Wolfe effect for a central observer is derived on general spherically symmetric spacetimes. It will be useful for comparative studies of theoretical and observational aspects of the integrated Sachs-Wolfe effect in the Lemaitre-Tolman-Bondi cosmological models which have been noticed by explaining the apparent acceleration without cosmological constant.
Asymptotic behavior of marginally trapped tubes in spherically symmetric black hole spacetimes
NASA Astrophysics Data System (ADS)
Williams, Catherine M.
We begin by reviewing some fundamental features of general relativity, then outline the mathematical definitions of black holes, trapped surfaces, and marginally trapped tubes, first in general terms, then rigorously in the context of spherical symmetry. We describe explicitly the reduction of Einstein's equation on a spherically symmetric 4-dimensional Lorentzian manifold to a system of partial differential equations on a subset of 2-dimensional Minkowski space. We discuss the asymptotic behavior of marginally trapped tubes in the Schwarzschild, Vaidya, and Reisner-Nordstrom solutions to Einstein's equations in spherical symmetry, as well as in Einstein-Maxwell-scalar field black hole spacetimes generated by evolving certain classes of asymptotically flat initial data. Our first main result gives conditions on a general stress-energy tensor Talphabeta in a spherically symmetric black hole spacetime that are sufficient to guarantee that the black hole will contain a marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Here "general" means that the matter model is arbitrary, subject only to a certain positive energy condition. A certain matter field decay rate, known as Price law decay in the literature, is not required per se for this asymptotic result, but such decay does imply that the marginally trapped tube has finite length with respect to the induced metric. In our second main result, we give two separate applications of the first theorem to self-gravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions.
Spherically symmetric cosmological spacetimes with dust and radiation — numerical implementation
Lim, Woei Chet; Regis, Marco; Clarkson, Chris E-mail: regis@to.infn.it
2013-10-01
We present new numerical cosmological solutions of the Einstein Field Equations. The spacetime is spherically symmetric with a source of dust and radiation approximated as a perfect fluid. The dust and radiation are necessarily non-comoving due to the inhomogeneity of the spacetime. Such a model can be used to investigate non-linear general relativistic effects present during decoupling or big-bang nucleosynthesis, as well as for investigating void models of dark energy with isocurvature degrees of freedom. We describe the full evolution of the spacetime as well as the redshift and luminosity distance for a central observer. After demonstrating accuracy of the code, we consider a few example models, and demonstrate the sensitivity of the late time model to the degree of inhomogeneity of the initial radiation contrast.
Quantized massive spin 1/2 fields on static spherically symmetric wormhole spacetimes
NASA Astrophysics Data System (ADS)
Shen, Zhiyong
Traversable wormholes have become a subject of intensive studies since 1988 when Morris and Thorne published their paper which put forward the energy conditions for traversable wormholes. A number of researchers have calculated the stress-energy tensors of different fields but failed to find one that meets the requirement of the wormhole geometry. Some others find different schemes to sustain traversable wormholes but either on the Planck scale or hypothetically on a macroscopic scale. Groves has developed a method to compute the renormalized stress-energy tensor for a quantized massive spin 1/2 field in a general static spherically symmetric spacetime. Using this method, I have computed the renormalized stress-energy tensors of two quantized massive spin 1/2 fields in four static spherically symmetric wormhole spacetimes. The results of my calculation suggest that these two fields can be considered exotic. However, due to the technical difficulties in implementing this method, a series of approximations are used in the computation in order to make the problem mathematically tractable; but it is not clear under what physical circumstances these approximations could hold. Besides, the cases that I investigated turned out to involve unphysically large energy densities. Because of these reasons, no firm physical conclusions can be drawn.
Optimal choices of reference for a quasilocal energy: Spherically symmetric spacetimes
Wu, Ming-Fan; Chen, Chiang-Mei; Liu, Jian-Liang; Nester, James M.
2011-10-15
For a given timelike displacement vector, the covariant Hamiltonian quasilocal energy expression requires a proper choice of reference spacetime. We propose a program for determining the reference by embedding a neighborhood of the two-sphere boundary in the dynamic spacetime into a Minkowski reference, so that the two-sphere is embedded isometrically, and then extremizing the energy to determine the embedding variables. Applying this idea to Schwarzschild spacetime, we found that for each given future timelike displacement vector our program gives a unique energy value. The static observer measures the maximal energy. Applied to the Friedmann-Lemaitre-Robertson-Walker spacetime, we find that the maximum energy value is non-negative; the associated displacement vector is the unit dual mean curvature vector; and the expansion of the two-sphere boundary matches that of its reference image. For these spherically symmetric cases the reference determined by our program is equivalent to isometrically matching the geometry at the two-sphere boundary and taking the displacement vector to be orthogonal to the spacelike constant coordinate time hypersurface, like the timelike Killing vector of the Minkowski reference.
NASA Astrophysics Data System (ADS)
Bernard, Yann L.-H.
The goal of this dissertation is to provide a systematic treatment of the coupling of fermions to non-Abelian Yang-Mills fields with gauge groups SU(N) in a static and spherically symmetric four-dimensional Lorentzian spacetime. We begin by reviewing the basic mathematical foundations and physical notions required to develop the appropriate models describing the coupled configuration. We shall present a new way to produce a consistent ansatz for the Yang-Mills potential when quantum effects are taken into account. We show that this new constructive algorithm yields a potential with the same structure as its classical counterpart commonly found in the literature. With the help of our ansatz, we derive the full coupled systems of ordinary differential equations for an electromagnetic potential with gauge group SU(N). Various results rendering account of the differences and the similarities there exist between the case when N is even and the case when N is odd are exposed in great details. Finally, an in-depth analysis of the electromagnetic coupled equations is presented, when N is an even natural number. We demonstrate, in particular, that under relatively weak hypotheses on the metric, such coupling admits no globally normalizable black-hole solutions, thereby substantially extending two theorems of Finster, Smoller and Yau.
Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity
NASA Astrophysics Data System (ADS)
Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb
2017-03-01
A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.
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
Complete affine connection in the causal boundary: static, spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Harris, Steven (Stacey) G.
2017-02-01
The boundary at I^+, future null infinity, for a standard static, spherically symmetric spactime is examined for possible linear connections. Two independent methods are employed, one for treating I^+ as the future causal boundary, and one for treating it as a conformal boundary (the latter is subsumed in the former, which is of greater generality). Both methods provide the same result: a constellation of various possible connections, depending on an arbitrary choice of a certain function, a sort of gauge freedom in obtaining a natural connection on I^+; choosing that function to be constant (for instance) results in a complete connection. Treating I^+ as part of the future causal boundary, the method is to impute affine connections on null hypersurfaces going out to I^+, in terms of a transverse vector field on each null hypersurface (there is much gauge freedom on choice of the transverse vector fields). Treating I^+ as part of a conformal boundary, the method is to make a choice of conformal factor that makes the boundary totally geodesic in the enveloping manifold (there is much gauge freedom in choice of that conformal factor). Similar examination is made of other boundaries, such as timelike infinity and timelike and spacelike singularities. These are much simpler, as they admit a unique connection from a similar limiting process (i.e., no gauge freedom); and that connection is complete.
Holographic Spherically Symmetric Metrics
NASA Astrophysics Data System (ADS)
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
Hackmann, Eva; Laemmerzahl, Claus; Kagramanova, Valeria; Kunz, Jutta
2008-12-15
The complete analytical solutions of the geodesic equation of massive test particles in higher dimensional Schwarzschild, Schwarzschild-(anti)de Sitter, Reissner-Nordstroem and Reissner-Nordstroem-(anti)de Sitter spacetimes are presented. Using the Jacobi inversion problem restricted to the theta divisor the explicit solution is given in terms of Kleinian sigma functions. The derived orbits depend on the structure of the roots of the characteristic polynomials which depend on the particle's energy and angular momentum, on the mass and the charge of the gravitational source, and the cosmological constant. We discuss the general structure of the orbits and show that due to the specific dimension-independent form of the angular momentum and the cosmological force a rich variety of orbits can emerge only in four and five dimensions. We present explicit analytical solutions for orbits up to 11 dimensions. A particular feature of Reissner-Nordstroem spacetimes is that bound and escape orbits traverse through different universes.
Spherically symmetric canonical quantum gravity
NASA Astrophysics Data System (ADS)
Brahma, Suddhasattwa
2015-06-01
Canonical quantization of spherically symmetric space-times is carried out, using real-valued densitized triads and extrinsic curvature components, with specific factor-ordering choices ensuring in an anomaly free quantum constraint algebra. Comparison with previous work [Nucl. Phys. B399, 211 (1993)] reveals that the resulting physical Hilbert space has the same form, although the basic canonical variables are different in the two approaches. As an extension, holonomy modifications from loop quantum gravity are shown to deform the Dirac space-time algebra, while going beyond "effective" calculations.
Tortoise Coordinates and Hawking Radiation in a Dynamical Spherically Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Yang, Jian; Zhao, Zheng; Tian, Gui-Hua; Liu, Wen-Biao
2009-12-01
Hawking effect from dynamical spherical Vaidya black hole, Vaidya-Bonner black hole, and Vaidya-de Sitter black hole is investigated using the improved Damour-Ruffini method. After the new tortoise coordinate transformation in which the position r of event horizon is an undetermined function and the temperature parameter κ is an undetermined constant, the Klein-Gordon equation can be written as the standard form at the event horizon, and both r and κ can be determined automatically. Then extending the outgoing wave from outside to inside of the horizon analytically, the Hawking temperature can also be obtained automatically.
NASA Astrophysics Data System (ADS)
Harada, Tomohiro; Nakao, Ken-ichi; Iguchi, Hideo
1999-08-01
It was shown recently that the metric functions which describe a spherically symmetric spacetime with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that spacetime. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by Ricons/Journals/Common/approx" ALT="approx" ALIGN="TOP"/>2y0micons/Journals/Common/beta" ALT="beta" ALIGN="TOP"/> with (1/3)
Cylindrically symmetric dust spacetime
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.
2000-07-01
We present an explicit exact solution of Einstein's equations for an inhomogeneous dust universe with cylindrical symmetry. The spacetime is extremely simple but nonetheless it has surprising new features. The universe is `closed' in the sense that the dust expands from a big-bang singularity but recollapses to a big-crunch singularity. In fact, both singularities are connected so that the whole spacetime is `enclosed' within a single singularity of general character. The big-bang is not simultaneous for the dust, and in fact the age of the universe as measured by the dust particles depends on the spatial position, an effect due to the inhomogeneity, and their total lifetime has no non-zero lower limit. Part of the big-crunch singularity is naked. The metric depends on a parameter and contains flat spacetime as a non-singular particular case. For appropriate values of the parameter the spacetime is a small perturbation of Minkowski spacetime. This seems to indicate that flat spacetime may be unstable against some global non-vacuum perturbations.
Static cylindrically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Fjällborg, Mikael
2007-05-01
We prove the existence of static solutions to the cylindrically symmetric Einstein Vlasov system, and we show that the matter cylinder has finite extension in two of the three spatial dimensions. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered by Bicak et al (2004 Class. Quantum Grav.21 1583). We also obtain this result for the Vlasov Poisson system.
Wave equation on spherically symmetric Lorentzian metrics
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.
2011-06-15
Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2016-06-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Matching a static cylindrically symmetric elastic spacetime
NASA Astrophysics Data System (ADS)
Brito, I.; Carot, J.; Mena, F. C.; Vaz, E. G. L. R.
2012-07-01
We consider a static cylindrically symmetric spacetime with elastic matter and study the matching problem of this spacetime with a suitable exterior. For the exterior, we take the Levi-Civita spacetime and its generalization including a cosmological constant, the Linet-Tian spacetime. We show that the matching is only possible with the Linet-Tian solution.
Dynamical systems and spherically symmetric cosmological models
NASA Astrophysics Data System (ADS)
He, Yanjing
2006-06-01
In this thesis we present a study of the timelike self-similar spherically symmetric cosmological models with two scalar fields with exponential potentials. We first define precisely the timelike self-similar spherically symmetric (TSS) spacetimes. We write the TSS metric in a conformally isometric form in a coordinate system adapted to the geometry of the spacetime manifold. In this coordinate system, both the metric functions of the TSS spacetimes and the potential functions of the scalar fields can be simplified to four undetermined functions of a single coordinate. As a result, the Einstein field equations reduce to an autonomous system of first-order ODEs and polynomial constraints in terms of these undetermined functions. By introducing new bounded variables as well as a new independent variable and solving the constraints, we are able to apply the theory of dynamical systems to study the properties of the TSS solutions. By finding invariant sets and associated monotonic functions, by applying the LaSalle Invariance Principle and the Monotonicity Principle, by applying the [straight phi] t -connected property of a limit set, and using other theorems, we prove that all of the TSS trajectories are heteroclinic trajectories. In addition, we conduct numerical simulations to confirm and support the qualitative analysis. We obtain all possible types of TSS solutions, by analyzing the qualitative behavior of the original system of ODES from those of the reduced one. We obtain asymptotic expressions for the TSS solutions (e.g., the asymptotic expressions for the metric functions, the source functions and the Ricci scalar). In particular, self-similar flat Friedmann-Robertson-Walker spacetimes are examined in order to obtain insights into the issues related to the null surface in general TSS spacetimes in these coordinates. A discussion of the divergence of the spacetime Ricci scalar and the possible extension of the TSS solutions across the null boundary is presented
Massive symmetric tensor field in curved spacetime
NASA Astrophysics Data System (ADS)
Higuchi, Atsushi
1989-03-01
The condition on the background spacetime is derived for the straightforward generalization of the massive symmetric tensor field (MSTF) equation to be possible. The MSTF in spatially flat Robertson-Walker spacetimes is studied in detail. The abovementioned condition in these spacetimes is verified by calculating the Klein-Gordon inner products among the solutions of the field equation. It is shown that the MSTF theory in some spacetimes has features which are probably undesirable even if the condition on the spacetime is satisfied.
NASA Astrophysics Data System (ADS)
Shabbir, Ghulam; Mahomed, F. M.; Qureshi, M. A.
2016-11-01
A study of proper projective symmetry in the most general form of non-static spherically symmetric space-time is given using direct integration and algebraic techniques. In this study, we show that when the above space-time admits proper projective symmetry it becomes a very special class of static spherically symmetric space-times.
Scalar resonances in axially symmetric spacetimes
NASA Astrophysics Data System (ADS)
Ranea-Sandoval, Ignacio F.; Vucetich, Héctor
2015-03-01
We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that nonaxial resonant modes do not exist neither in the Lanczos dust cylinder, the extreme (2 + 1) dimensional Bañados-Taitelboim-Zanelli (BTZ) spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the r2 < 0 region of the extreme (2 + 1) dimensional BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.
Spherically symmetric conformal gravity and ``gravitational bubbles''
NASA Astrophysics Data System (ADS)
Berezin, V. A.; Dokuchaev, V. I.; Eroshenko, Yu. N.
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Spherically symmetric conformal gravity and ''gravitational bubbles''
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N. E-mail: dokuchaev@inr.ac.ru
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Conformal cylindrically symmetric spacetimes in modified gravity
NASA Astrophysics Data System (ADS)
Türkog˜lu, Murat Metehan; Dog˜ru, Melis Ulu
2015-11-01
We investigate cylindrically symmetric spacetimes in the context of f(R) gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle-Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special f(R) function convenient to Λ-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different f(R) models. Finally, geometrical and physical results of the solutions are discussed.
Pseudo-Z symmetric space-times
NASA Astrophysics Data System (ADS)
Mantica, Carlo Alberto; Suh, Young Jin
2014-04-01
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form Ak is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS)4 space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
The relativistic Boltzmann equation on a spherically symmetric gravitational field
NASA Astrophysics Data System (ADS)
Takou, Etienne; Ciake Ciake, Fidèle L.
2017-10-01
In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. We consider this equation on a spherically symmetric gravitational field spacetime. The collision kernel considered here is for the hard potentials case. We prove the existence of a unique global (in time) mild solution in a suitable weighted space.
An introduction to spherically symmetric loop quantum gravity black holes
Gambini, Rodolfo; Pullin, Jorge
2015-03-26
We review recent developments in the treatment of spherically symmetric black holes in loop quantum gravity. In particular, we discuss an exact solution to the quantum constraints that represents a black hole and is free of singularities. We show that new observables that are not present in the classical theory arise in the quantum theory. We also discuss Hawking radiation by considering the quantization of a scalar field on the quantum spacetime.
Stationary spherically symmetric one-kink model in Saez-Ballester theory of gravitation
NASA Astrophysics Data System (ADS)
Kiran, M.; Reddy, D. R. K.; Rao, V. U. M.; Bhaskara Rao, M. P. V. V.
2015-03-01
In this paper we consider stationary Spherically symmetric kink space-time in the scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) in the presence of perfect fluid distribution. It is shown that spherically symmetric kink space-time does not accommodate perfect fluid distribution in this theory. Hence a vacuum model is obtained which is asymptotically flat. This model corresponds to a one kink metric in this theory. This can be considered as an analogue of usual spherically symmetric Schwarzschild case in this theory.
Onthe static and spherically symmetric gravitational field
NASA Astrophysics Data System (ADS)
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
Inflation in spherically symmetric inhomogeneous models
Stein-Schabes, J.A.
1986-11-01
Exact analytical solutions of Einstein's equations are found for a spherically symmetric inhomogeneous metric in the presence of a massless scalar field with a flat potential. The process of isotropization and homogenization is studied in detail. It is found that the time dependence of the metric becomes de Sitter for large times. Two cases are studied. The first deals with a homogeneous scalar field, while the second with a spherically symmetric inhomogeneous scalar field. In the former case the metric is of the Robertson-Walker form, while the latter is intrinsically inhomogeneous. 16 refs.
Conformal diagrams for the gravitational collapse of a spherically symmetric dust cloud
Ortiz, Nestor; Sarbach, Olivier
2010-07-12
We present an algorithm for the construction of conformal coordinates in the interior of a spherically symmetric, collapsing matter cloud in general relativity. This algorithm is based on the numerical integration of radial null geodesics. As an application we generate conformal diagrams for collapsing spherical dust clouds and analyze the causal structure of the resulting spacetimes.
New framework for studying spherically symmetric static solutions in f(R) gravity
Nzioki, Anne Marie; Goswami, Rituparno; Carloni, Sante; Dunsby, Peter K. S.
2010-04-15
We develop a new covariant formalism to treat spherically symmetric spacetimes in metric f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general f(R) gravity. These equations are used to determine the conditions for which the Schwarzschild metric is the only vacuum solution with vanishing Ricci scalar. We also show that our general framework provides a clear way of showing that the Schwarzschild solution is not a unique static spherically symmetric solution, providing some insight into how the current form of Birkhoff's theorem breaks down for these theories.
Global structure of static spherically symmetric solutions surrounded by quintessence
NASA Astrophysics Data System (ADS)
Cruz, Miguel; Ganguly, Apratim; Gannouji, Radouane; Leon, Genly; Saridakis, Emmanuel N.
2017-06-01
We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1 + 1 + 2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible classes of solutions such as cold black holes, singular spacetimes and wormholes such as the Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.
Spherically symmetric thick branes cosmological evolution
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Cavalcanti, R. T.; da Rocha, Roldão
2015-01-01
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed et al. (JHEP 1404:061. arXiv:1312.3576 [hep-th], 2014). The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, , which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in Ahmed et al. (2014), namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on . Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in Ahmed et al. (2014).
Charge Without Charge, Regular Spherically Symmetric Solutions and the Einstein-Born-Infeld Theory
NASA Astrophysics Data System (ADS)
Cirilo Lombardo, D. J.
2009-08-01
The aim of this paper is to continue the research (J. Math. Phys. 46:042501, 2005) of regular static spherically symmetric spacetimes in Einstein-Born-Infeld theories from the point of view of the spacetime geometry and the electromagnetic structure. The energy conditions, geodesic completeness and the main features of the horizons of this spacetime are explicitly shown. A new static spherically symmetric dyonic solution in Einstein-Born-Infeld theory with similar good properties as in the regular pure electric and magnetic cases of our previous work, is presented and analyzed. Also, the circumvention of a version of “no go” theorem claiming the non existence of regular electric black holes and other electromagnetic static spherically configurations with regular center is explained by dealing with a more general statement of the problem.
Casimir densities for a spherical boundary in de Sitter spacetime
NASA Astrophysics Data System (ADS)
Milton, K. A.; Saharian, A. A.
2012-03-01
Two-point functions, mean-squared fluctuations, and the vacuum expectation value of the energy-momentum tensor operator are investigated for a massive scalar field with an arbitrary curvature coupling parameter, subject to a spherical boundary in the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the sphere. Both the interior and exterior regions are considered. For the calculation in the interior region, a mode-summation method is employed, supplemented with a variant of the generalized Abel-Plana formula. This allows us to explicitly extract the contributions to the expectation values which come from de Sitter spacetime without boundaries. We show that the vacuum energy-momentum tensor is nondiagonal, with the off-diagonal component corresponding to the energy flux along the radial direction. With dependence on the boundary condition and the mass of the field, this flux can be either positive or negative. Several limiting cases of interest are then studied. In terms of the curvature coupling parameter and the mass of the field, two very different regimes are realized, which exhibit monotonic and oscillatory behavior of the vacuum expectation values, respectively, far from the sphere. The decay of the boundary-induced expectation values at large distances from the sphere is shown to be a power-law decay (monotonic or oscillating), independent of the value of the field mass. The expressions for the Casimir densities in the exterior region are generalized for a more general class of spherically symmetric spacetimes inside the sphere.
Static spherically symmetric wormholes in f( R, T) gravity
NASA Astrophysics Data System (ADS)
Zubair, M.; Waheed, Saira; Ahmad, Yasir
2016-08-01
In this work, we explore wormhole solutions in f( R, T) theory of gravity, where R is the scalar curvature and T is the trace of stress-energy tensor of matter. To investigate this, we consider a static spherically symmetric geometry with matter contents as anisotropic, isotropic, and barotropic fluids in three separate cases. By taking into account the Starobinsky f( R) model, we analyze the behavior of energy conditions for these different kinds of fluids. It is shown that the wormhole solutions can be constructed without exotic matter in few regions of space-time. We also give the graphical illustration of the results obtained and discuss the equilibrium picture for the anisotropic case only. It is concluded that the wormhole solutions with anisotropic matter are realistic and stable in this theory of gravity.
Spherically symmetric solutions in covariant Horava-Lifshitz gravity
NASA Astrophysics Data System (ADS)
Alexandre, Jean; Pasipoularides, Pavlos
2011-04-01
We study the most general case of spherically symmetric vacuum solutions in the framework of the covariant Horava-Lifshitz gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson [P. Horava and C. M. Melby-Thompson, Phys. Rev. DPRVDAQ1550-7998 82, 064027 (2010).10.1103/PhysRevD.82.064027], according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A.
Spherically symmetric solutions in covariant Horava-Lifshitz gravity
Alexandre, Jean; Pasipoularides, Pavlos
2011-04-15
We study the most general case of spherically symmetric vacuum solutions in the framework of the covariant Horava-Lifshitz gravity, for an action that includes all possible higher order terms in curvature which are compatible with power-counting normalizability requirement. We find that solutions can be separated into two main classes: (i) solutions with nonzero radial shift function, and (ii) solutions with zero radial shift function. In the case (ii), spherically symmetric solutions are consistent with observations if we adopt the view of Horava and Melby-Tomson [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).], according to which the auxiliary field A can be considered as a part of an effective general relativistic metric, which is valid only in the IR limit. On the other hand, in the case (i), consistency with observations implies that the field A should be independent of the spacetime geometry, as the Newtonian potential arises from the nonzero radial shift function. Also, our aim in this paper is to discuss and compare these two alternative but different assumptions for the auxiliary field A.
Spherically Symmetric Solutions of Light Galileon
NASA Astrophysics Data System (ADS)
Momeni, D.; Houndjo, M. J. S.; Güdekli, E.; Rodrigues, M. E.; Alvarenga, F. G.; Myrzakulov, R.
2016-02-01
We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form {L}_{φ }= -η (partial φ )2+β G^{μ ν }partial _{μ }φ partial _{ν }φ . We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of f(R,R^{μ ν }T_{μ ν }m). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.
Central MONDian spike in spherically symmetric systems
NASA Astrophysics Data System (ADS)
Hernandez, X.
2017-08-01
Under a MONDian view, astrophysical systems are expected to follow Newtonian dynamics whenever the local acceleration is above the critical a0 = 1.2 × 10-10 m s-2, and enter a modified regime for accelerations below this critical value. Indeed, the dark matter phenomenology on galactic and subgalactic scales appears always, and only, at low accelerations. It is standard to find the a < a0 regime towards the low density outskirts of astronomical systems, where under a Newtonian interpretation, dark matter becomes conspicuous. Thus, it is standard to find, and to think, of the dense central regions of observed systems as purely Newtonian. However, under spherical symmetry in the MONDian as in the Newtonian case, the local acceleration will tend to zero as one approaches the very centre of a mass distribution. It is clear that for spherically symmetric systems, an inner a < a0 region will necessarily appear interior to a critical radius, which will depend on the details of the density profile in question. Here, we calculate analytically such a critical radius for a constant-density core, and numerically for a cored isothermal profile. Under a Newtonian interpretation, such a central MONDian region will be interpreted as extra mass, analogous to the controversial black holes sometimes inferred to lie at the centres of globular clusters, despite an absence of nuclear activity detected to date. We calculate this effect and give predictions for the 'central black hole' mass to be expected under Newtonian interpretations of low density Galactic globular clusters.
Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity
NASA Astrophysics Data System (ADS)
Amir, M. Jamil; Ali, Sarfraz
2016-04-01
This paper is devoted to investigate the gravitational collapse in the framework of Chern-Simon (CS) modified gravity. For this purpose, we assume the spherically symmetric metric as an interior region and the Schwarzchild spacetime is considered as an exterior region of the star. Junction conditions are used to match the interior and exterior spacetimes. In dynamical formulation of CS modified gravity, we take the scalar field Θ as a function of radial parameter r and obtain the solution of the field equations. There arise two cases where in one case the apparent horizon forms first and then singularity while in second case the order of the formation is reversed. It means the first case results a black hole which supports the cosmic censorship hypothesis (CCH). Obviously, the second case yields a naked singularity. Further, we use Junction conditions have to calculate the gravitational mass. In non-dynamical formulation, the canonical choice of scalar field Θ is taken and it is shown that the obtained results of CS modified gravity simply reduce to those of the general relativity (GR). It is worth mentioning here that the results of dynamical case will reduce to those of GR, available in literature, if the scalar field is taken to be constant.
No-scalar-hair theorem for spherically symmetric reflecting stars
NASA Astrophysics Data System (ADS)
Hod, Shahar
2016-11-01
It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential V (ψ2) is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.
Spherically symmetric solutions in higher-derivative gravity
NASA Astrophysics Data System (ADS)
Lü, H.; Perkins, A.; Pope, C. N.; Stelle, K. S.
2015-12-01
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type "no-hair" theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to "vacuum" solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as "wormholes," which can match symmetrically onto another sheet of spacetime at finite radius.
Proper conformal Killing vectors in static plane symmetric space-times
NASA Astrophysics Data System (ADS)
Hussain, T.; Khan, S.; Bokhari, A. H.; Khan, G. A.
2017-04-01
Conformal Killing vectors (CKVs) in static plane symmetric space-times were recently studied by Saifullah and Yazdan, who concluded by remarking that static plane symmetric space-times do not admit any proper CKV except in the case where these space-times are conformally flat. We present some non-conformally flat static plane symmetric space-time metrics admitting proper CKVs. For these space-times, we also investigate a special type of CKVs, known as inheriting CKVs.
Static spherically symmetric solutions in mimetic gravity: rotation curves and wormholes
NASA Astrophysics Data System (ADS)
Myrzakulov, Ratbay; Sebastiani, Lorenzo; Vagnozzi, Sunny; Zerbini, Sergio
2016-06-01
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend previous works by considering, in addition, a potential for the mimetic field. An appropriate choice of such a potential allows for the reconstruction of a number of interesting cosmological and astrophysical scenarios. We explicitly show how to reconstruct such a potential for a general static spherically symmetric space-time. A number of applications and scenarios are then explored, among which are traversable wormholes. Finally, we analytically reconstruct potentials, which leads to solutions to the equations of motion featuring polynomial corrections to the Schwarzschild space-time. Accurate choices for such corrections could provide an explanation for the inferred flat rotation curves of spiral galaxies within the mimetic gravity framework, without the need for particle dark matter.
Influence of a plasma on the shadow of a spherically symmetric black hole
NASA Astrophysics Data System (ADS)
Perlick, Volker; Tsupko, Oleg Yu.; Bisnovatyi-Kogan, Gennady S.
2015-11-01
We analytically calculate the influence of a plasma on the shadow of a black hole (or of another compact object). We restrict to spherically symmetric and static situations, where the shadow is circular. The plasma is assumed to be nonmagnetized and pressureless. We derive the general formulas for a spherically symmetric plasma density on an unspecified spherically symmetric and static spacetime. Our main result is an analytical formula for the angular size of the shadow. As a plasma is a dispersive medium, the radius of the shadow depends on the photon frequency. The effect of the plasma is significant only in the radio regime. The formalism applies not only to black holes but also, e.g., to wormholes. As examples for the underlying spacetime model, we consider the Schwarzschild spacetime and the Ellis wormhole. In particular, we treat the case that the plasma is in radial free fall from infinity onto a Schwarzschild black hole. We find that for an observer far away from a Schwarzschild black hole, the plasma has a decreasing effect on the size of the shadow. The perspectives of actually observing the influence of a plasma on the shadows of supermassive black holes are discussed.
Killing tensors in stationary and axially symmetric space-times
NASA Astrophysics Data System (ADS)
Vollmer, Andreas
2017-05-01
We discuss the existence of Killing tensors for certain (physically motivated) stationary and axially symmetric vacuum space-times. We show nonexistence of a nontrivial Killing tensor for a Tomimatsu-Sato metric (up to valence 7), for a C-metric (up to valence 9) and for a Zipoy-Voorhees metric (up to valence 11). The results are obtained by mathematically completely rigorous, nontrivial computer algebra computations with a huge number of equations involved in the problem.
New class of locally rotationally symmetric spacetimes with simultaneous rotation and spatial twist
NASA Astrophysics Data System (ADS)
Singh, Sayuri; Ellis, George F. R.; Goswami, Rituparno; Maharaj, Sunil D.
2016-11-01
We establish the existence and find the necessary and sufficient conditions for a new class of solutions of locally rotationally symmetric spacetimes that have nonvanishing rotation and spatial twist simultaneously. We transparently show that the existence of such solutions demands nonvanishing and bounded heat flux and these solutions are self-similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. Finally we argue that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.
The spherically symmetric Standard Model with gravity
NASA Astrophysics Data System (ADS)
Balasin, H.; Böhmer, C. G.; Grumiller, D.
2005-08-01
Spherical reduction of generic four-dimensional theories is revisited. Three different notions of "spherical symmetry" are defined. The following sectors are investigated: Einstein-Cartan theory, spinors, (non-)abelian gauge fields and scalar fields. In each sector a different formalism seems to be most convenient: the Cartan formulation of gravity works best in the purely gravitational sector, the Einstein formulation is convenient for the Yang-Mills sector and for reducing scalar fields, and the Newman-Penrose formalism seems to be the most transparent one in the fermionic sector. Combining them the spherically reduced Standard Model of particle physics together with the usually omitted gravity part can be presented as a two-dimensional (dilaton gravity) theory.
Spherically symmetric brane in a bulk of f(R) and Gauss-Bonnet gravity
NASA Astrophysics Data System (ADS)
Chakraborty, Sumanta; SenGupta, Soumitra
2016-11-01
Effective gravitational field equations on a four-dimensional brane embedded in a five-dimensional bulk have been considered. Using the Einstein-Hilbert action along with the Gauss-Bonnet correction term, we have derived static spherically symmetric vacuum solution to the effective field equations, first order in the Gauss-Bonnet coupling parameter. The solution so obtained, has one part corresponding to general relativity with an additional correction term, proportional to the Gauss-Bonnet coupling parameter. The correction term modifies the spacetime structure, in particular, the location of the event horizon. Proceeding further, we have derived effective field equations for f(R) gravity with Gauss-Bonnet correction term and a static spherically symmetric solution has been obtained. In this case the Gauss-Bonnet term modifies both the event and cosmological horizon of the spacetime. There exists another way of obtaining the brane metric—expanding the bulk gravitational field equations in the ratio of bulk to brane curvature scale and assuming a separable bulk metric ansatz. It turns out that static, spherically symmetric solutions obtained from this perturbative method can be matched exactly, with the solutions derived earlier. This will hold for Einstein-Hilbert plus Gauss-Bonnet as well as for f(R) with the Gauss-Bonnet correction. Implications of these results are discussed.
Killing and Noether Symmetries of Plane Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Shamir, M. Farasat; Jhangeer, Adil; Bhatti, Akhlaq Ahmad
2013-09-01
This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub's universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).
Morris-Thorne wormholes in static pseudospherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2015-06-01
In this paper, we study classical general relativistic static wormhole configurations with pseudospherical symmetry. We show that, in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in [Phys. Rev. D 82, 044034 (2010)], there exists another wormhole class, which is a truly pseudospherical counterpart of spherical Morris-Thorne wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes, the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris-Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that a hyperbolic wormhole cannot be sustained at the throat by phantom energy and that there are pseudospherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).
Spherically symmetric black-hole entropy without brick walls
NASA Astrophysics Data System (ADS)
Ren, Zhao; Yue-Qin, Wu; Li-Chun, Zhang
2003-11-01
Properties of the thermal radiation of black holes are discussed using a new equation of state density motivated by the generalized uncertainty relation in quantum gravity. There is no burst at the last stage of emission from a spherically symmetric black hole. When the new equation of state density is used to investigate the entropy of a bosonic field and fermionic field outside the horizon of a static spherically symmetric black hole, the divergence that appears in the brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution from the vicinity of the horizon.
Cosmological and spherically symmetric solutions with intersecting p-branes
NASA Astrophysics Data System (ADS)
Ivashchuk, V. D.; Melnikov, V. N.
1999-12-01
Multidimensional model describing the cosmological evolution and/or spherically symmetric configuration with n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n ``internal'' spaces are Ricci-flat, one space M0 has a nonzero curvature, and all p-branes do not ``live'' in M0, a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically symmetric solutions (containing nonextremal p-brane black holes) is considered. Post-Newtonian parameters are calculated.
NASA Astrophysics Data System (ADS)
Gerlach, Ulrich H.; Sengupta, Uday K.
1980-09-01
The coupled Einstein-Maxwell system linearized away from an arbitrarily given spherically symmetric background space-time is reduced from its four-dimensional to a two-dimensional form expressed solely in terms of gauge-invariant geometrical perturbation objects. These objects, which besides the gravitational and electromagnetic, also include mass-energy degrees of freedom, are defined on the two-manifold spanned by the radial and time coordinates. For charged or uncharged arbitrary matter background the odd-parity perturbation equations for example, reduce to three second-order linear scalar equations driven by matter and charge inhomogeneities. These three equations describe the intercoupled gravitational, electromagnetic, and acoustic perturbational degrees of freedom. For a charged black hole in an asymptotically de Sitter space-time the gravitational and electromagnetic equations decouple into two inhomogeneous scalar wave equations.
All static spherically symmetric anisotropic solutions of Einstein's equations
Herrera, L.; Di Prisco, A.; Ospino, J.
2008-01-15
An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the knowledge of two functions (instead of one) to generate all possible solutions. To illustrate the method some known cases are recovered.
Five dimensional spherically symmetric cosmological model in Brans-Dicke theory of gravitation
NASA Astrophysics Data System (ADS)
Rao, V. U. M.; Jaysudha, V.
2015-08-01
In this paper, we consider the spherically symmetric space-time in five dimensions in Brans-Dicke (Phys. Rev. 124:925, 1961) theory of gravitation in the presence of perfect fluid distribution. A determinate solution of the highly non-linear field equations is presented using (i) relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained describes five dimensional radiating model in Brans-Dicke theory. Some physical and kinematical properties of the model are also discussed.
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Raju, P.; Sobhanbabu, K.
2016-04-01
Five dimensional spherically symmetric space-time filled with two minimally interacting fields; matter and holographic dark energy components is investigated in a scalar tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To obtain a determinate solution of the highly non-linear field equations we have used (i) a relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained represents a minimally interacting and radiating holographic dark energy model in five dimensional universe. Some physical and Kinematical properties of the model are, also, studied.
Study of striations in a spherically symmetric hydrogen discharge
NASA Astrophysics Data System (ADS)
Lowell Morgan, W.; Childs, Montgomery W.
2015-10-01
Experiments on a high power spherically symmetric positive corona discharge in molecular hydrogen are reported upon. These are collisional plasmas in the H2 pressure range of about 0.75 Torr to 3 Torr. Applied voltages ranged up to 600 V on the anode with currents ranging up to 3 A. As others have observed in prior published experiments going back to 1997, we have observed spherically symmetric striations or double layers. Others have observed such striations in O2, CO2, and in mixtures of N2 and acetone or methanol, or benzene. Like H2 all these gases, except N2 itself, readily dissociate and form negative ions by dissociative attachment with electrons. We propose that the striations are instabilities arising from copious formation of negative ions that modify the radial space charge and electric field distributions in such high aspect ratio spherical discharges.
Classification of static plane symmetric spacetime via Noether gauge symmetries
NASA Astrophysics Data System (ADS)
Jhangeer, Adil; Iftikhar, Nazish; Naz, Tayyaba
2016-07-01
In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1-4 is presented.
Propagation of Scalar Fields in a Plane Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Celestino, Juliana; Alves, Márcio E. S.; Barone, F. A.
2016-12-01
The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Grøn regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution for the scalar field in terms of the Kummer and Tricomi confluent hypergeometric functions.
Stability of Schwarzschild-AdS for the Spherically Symmetric Einstein-Klein-Gordon System
NASA Astrophysics Data System (ADS)
Holzegel, Gustav; Smulevici, Jacques
2013-01-01
In this paper, we study the global behavior of solutions to the spherically symmetric coupled Einstein-Klein-Gordon (EKG) system in the presence of a negative cosmological constant. For the Klein-Gordon mass-squared satisfying a ≥ -1 (the Breitenlohner-Freedman bound being a > -9/8), we prove that the Schwarzschild-AdS spacetimes are asymptotically stable: Small perturbations of Schwarzschild-AdS initial data again lead to regular black holes, with the metric on the black hole exterior approaching, at an exponential rate, a Schwarzschild-AdS spacetime. The main difficulties in the proof arise from the lack of monotonicity for the Hawking mass and the asymptotically AdS boundary conditions, which render even (part of) the orbital stability intricate. These issues are resolved in a bootstrap argument on the black hole exterior, with the redshift effect and weighted Hardy inequalities playing the fundamental role in the analysis. Both integrated decay and pointwise decay estimates are obtained. As a corollary of our estimates on the Klein-Gordon field, one obtains in particular exponential decay in time of spherically-symmetric solutions to the linear Klein-Gordon equation on Schwarzschild-AdS.
Spherically symmetric solutions of the λ -R model
NASA Astrophysics Data System (ADS)
Loll, R.; Pires, L.
2017-08-01
We derive spherically symmetric solutions of the classical λ -R model, a minimal, anisotropic modification of general relativity with a preferred foliation and two local degrees of freedom. Starting from a 3 +1 decomposition of the four-metric in a general spherically symmetric ansatz, we perform a phase space analysis of the reduced model. We show that its constraint algebra is consistent with that of the full λ -R model, and also yields a constant mean curvature or maximal slicing condition as a tertiary constraint. Although the solutions contain the standard Schwarzschild geometry for the general relativistic value λ =1 or for vanishing mean extrinsic curvature K , they are in general nonstatic, incompatible with asymptotic flatness, and parametrized not only by a conserved mass. We show by explicit computation that the four-dimensional Ricci scalar of the solutions is in general time dependent and nonvanishing.
Implications of the Cosmological Constant for Spherically Symmetric Mass Distributions
NASA Astrophysics Data System (ADS)
Zubairi, Omair; Weber, Fridolin
2013-04-01
In recent years, scientists have made the discovery that the expansion rate of the Universe is increasing rather than decreasing. This acceleration leads to an additional term in Albert Einstein's field equations which describe general relativity and is known as the cosmological constant. This work explores the aftermath of a non-vanishing cosmological constant for relativistic spherically symmetric mass distributions, which are susceptible to change against Einstein's field equations. We introduce a stellar structure equation known as the Tolman-Oppenhiemer-Volkoff (TOV) equation modified for a cosmological constant, which is derived from Einstein's modified field equations. We solve this modified TOV equation for these spherically symmetric mass distributions and obtain stellar properties such as mass and radius and investigate changes that may occur depending on the value of the cosmological constant.
General static spherically symmetric solutions in Horava gravity
Capasso, Dario; Polychronakos, Alexios P.
2010-04-15
We derive the equations describing a general static spherically symmetric configuration for the softly broken Horava gravity introduced by A. Kehagias and K. Sfetsos with nonzero shift field and no-projectability condition. These represent 'hedgehog' versions of black holes with radial 'hair' arising from the shift field. For the case of the standard de Witt kinetic term ({lambda}=1) there is an infinity of solutions that exhibit a deformed version of reparametrization invariance away from the general relativistic limit. Special solutions also arise in the anisotropic conformal point {lambda}=(1/3). Moreover we obtain an implicit general expression for the solutions with N{sub r}=0 and generic {lambda}. In this context we study the presence of horizons for standard matter and the related Hawking temperature, generalizing the corresponding relations in the usual static spherically symmetric case.
Elastoplastic state of spherical shells with cyclically symmetric circular holes
NASA Astrophysics Data System (ADS)
Storozhuk, E. A.; Chernyshenko, I. S.; Rudenko, I. B.
2012-09-01
The elastoplastic state of thin spherical shells with cyclically symmetric circular holes is considered. A numerical procedure for solving such nonlinear problems is proposed. The distribution of stresses, strains, and displacements over their concentration zones is studied. The stress-strain state of shells with four holes made of a plastic material and subjected to internal pressure of given intensity is analyzed. The numerical results are presented in the form of graphs and tables
Multiscale numerical modeling of the spherically symmetric cryosurgery problem
NASA Astrophysics Data System (ADS)
Kudryashov, N. A.; Shilnikov, K. E.
2017-01-01
The work is concerned with the numerical studying of the cryogenic biotissue destruction by a spherically symmetric tip. The multiscale bioheat transfer model is used for the describing of the biological solutions crystallization features. An explicit finite volume based approximation is applied for the numerical modeling of the processes taking place during the cryosurgery. The phase averaging method is applied as an computationally economic approach for the numerical modeling of the problem under study.
Gyroid phase of fluids with spherically symmetric competing interactions.
Edelmann, Markus; Roth, Roland
2016-06-01
We study the phase diagram of a fluid with spherically symmetric competing pair interactions that consist of a short-ranged attraction and a longer-ranged repulsion in addition to a hard core. To this end we perform free minimizations of three-dimensional triple periodic structures within the framework of classical density functional theory. We compare our results to those from Landau theory. Our main finding is that the double gyroid phase can exist as a thermodynamically stable phase.
NASA Astrophysics Data System (ADS)
Zhdanov, V.; Stashko, O.
2016-12-01
We study exact special solutions of the joint system of Einstein equations and scalar field equations with a non-zero self-interaction potential, which describe spherically symmetric static configurations. The space-time is asymptotically flat with a naked singularity at the center. The testbody motion is analyzed; we found conditions for existence of non-connected regions of stable circular orbits. We show the existence of static trajectories of particles that hang above the configuration.
Dzhunushaliev, Vladimir; Folomeev, Vladimir; Singleton, Douglas; Myrzakulov, Ratbay
2010-08-15
In this paper we investigate wormhole and spherically symmetric solutions in four-dimensional gravity plus a matter source consisting of a ghost scalar field with a sine-Gordon potential. For the wormhole solutions we also include the possibility of electric and/or magnetic charges. For both types of solutions we perform a linear stability analysis and show that the wormhole solutions are stable and that when one turns on the electric and/or magnetic field the solution remains stable. The linear stability analysis of the spherically symmetric solutions indicates that they can be stable or unstable depending on one of the parameters of the system. This result for the spherically symmetric solution is nontrivial since a previous investigation of four-dimensional gravity plus a ghost scalar field with a {lambda}{phi}{sup 4} interaction found only unstable spherically symmetric solutions. Both the wormhole and spherically symmetric solutions presented here asymptotically go to anti-de Sitter space-time.
All spherically symmetric charged anisotropic solutions for compact stars
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal
2017-06-01
In the present paper we develop an algorithm for all spherically symmetric anisotropic charged fluid distributions. Considering a new source function ν (r) we find a set of solutions which is physically well behaved and represents compact stellar models. A detailed study specifically shows that the models actually correspond to strange stars in terms of their mass and radius. In this connection we investigate several physical properties like energy conditions, stability, mass-radius ratio, electric charge content, anisotropic nature and surface redshift through graphical plots and mathematical calculations. All the features from these studies are in excellent agreement with the already available evidence in theory as well as observations.
Corrected Entropy of a General Spherically Symmetric Black Hole
NASA Astrophysics Data System (ADS)
He, Tang-mei; Yang, Jin-bo; Wu, Feng-jie
2012-07-01
Adopting the tortoise coordinates transformation in the advanced Eddington coordinates and applying the generalized law of thermodynamics, we discuss the corrected entropy of a general spherically symmetric black hole beyond the semi-classical limit. We give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Two examples are explicitly worked out. The conclusion is that the corrected entropy includes a logarithmically term and an inverse term to the Bekenstein-Hawking entropy, which is the same form as that of the static and the stationary black holes discussed by using the loop quantum gravity and the string theory.
Spherically symmetric solutions in modified Horava-Lifshitz gravity
Kiritsis, Elias
2010-02-15
We find spherically symmetric solutions in the modified Horava-Lifshitz gravity proposed recently by Blas, Pujolas and Sibiryakov. The nonlinear equations of the two-derivative action turn out to be similar to those stemming from the four-derivative action explored recently. We analyze the solutions and derive constraints on the relevant new coupling constant. We also analyze the case where the cosmological constant is nonzero. We derive the large-distance expansion of solutions and show that the power of the standard Newton's law is modified in the presence of a cosmological constant.
Static spherically symmetric solutions in f(G) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
2016-05-01
We investigate interior solutions for static spherically symmetric metric in the background of f(G) gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law f(G) model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter ω = -1.5. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman-Oppenheimer-Volkoff equation.
Electrostatic spherically symmetric configurations in gravitating nonlinear electrodynamics
Diaz-Alonso, J.; Rubiera-Garcia, D.
2010-03-15
We perform a study of the gravitating electrostatic spherically symmetric (G-ESS) solutions of Einstein field equations minimally coupled to generalized nonlinear Abelian gauge models in three space dimensions. These models are defined by Lagrangian densities which are general functions of the gauge field invariants, restricted by some physical conditions of admissibility. They include the class of nonlinear electrodynamics supporting electrostatic spherically symmetric (ESS) nontopological soliton solutions in absence of gravity. We establish that the qualitative structure of the G-ESS solutions of admissible models is fully characterized by the asymptotic and central-field behaviors of their ESS solutions in flat space (or, equivalently, by the behavior of the Lagrangian densities in vacuum and on the point of the boundary of their domain of definition, where the second gauge invariant vanishes). The structure of these G-ESS configurations for admissible models supporting divergent-energy ESS solutions in flat space is qualitatively the same as in the Reissner-Nordstroem case. In contrast, the G-ESS configurations of the models supporting finite-energy ESS solutions in flat space exhibit new qualitative features, which are discussed in terms of the Arnowitt-Deser-Misner mass, the charge, and the soliton energy. Most of the results concerning well-known models, such as the electrodynamics of Maxwell, Born-Infeld, and the Euler-Heisenberg effective Lagrangian of QED, minimally coupled to gravitation, are shown to be corollaries of general statements of this analysis.
String loops in the field of braneworld spherically symmetric black holes and naked singularities
Stuchlík, Z.; Kološ, M. E-mail: martin.kolos@fpf.slu.cz
2012-10-01
We study motion of current-carrying string loops in the field of braneworld spherically symmetric black holes and naked singularities. The spacetime is described by the Reissner-Nordström geometry with tidal charge b reflecting the non-local tidal effects coming from the external dimension; both positive and negative values of the spacetime parameter b are considered. We restrict attention to the axisymmetric motion of string loops when the motion can be fully governed by an appropriately defined effective potential related to the energy and angular momentum of the string loops. In dependence on these two constants of the motion, the string loops can be captured, trapped, or can escape to infinity. In close vicinity of stable equilibrium points at the centre of trapped states the motion is regular. We describe how it is transformed to chaotic motion with growing energy of the string loop. In the field of naked singularities the trapped states located off the equatorial plane of the system exist and trajectories unable to cross the equatorial plane occur, contrary to the trajectories in the field of black holes where crossing the equatorial plane is always admitted. We concentrate our attention to the so called transmutation effect when the string loops are accelerated in the deep gravitational field near the black hole or naked singularity by transforming the oscillatory energy to the energy of the transitional motion. We demonstrate that the influence of the tidal charge can be substantial especially in the naked singularity spacetimes with b > 1 where the acceleration to ultrarelativistic velocities with Lorentz factor γ ∼ 100 can be reached, being more than one order higher in comparison with those obtained in the black hole spacetimes.
Exit Time Distribution in Spherically Symmetric Two-Dimensional Domains
NASA Astrophysics Data System (ADS)
Rupprecht, J.-F.; Bénichou, O.; Grebenkov, D. S.; Voituriez, R.
2015-01-01
The distribution of exit times is computed for a Brownian particle in spherically symmetric two-dimensional domains (disks, angular sectors, annuli) and in rectangles that contain an exit on their boundary. The governing partial differential equation of Helmholtz type with mixed Dirichlet-Neumann boundary conditions is solved analytically. We propose both an exact solution relying on a matrix inversion, and an approximate explicit solution. The approximate solution is shown to be exact for an exit of vanishing size and to be accurate even for large exits. For angular sectors, we also derive exact explicit formulas for the moments of the exit time. For annuli and rectangles, the approximate expression of the mean exit time is shown to be very accurate even for large exits. The analysis is also extended to biased diffusion. Since the Helmholtz equation with mixed boundary conditions is encountered in microfluidics, heat propagation, quantum billiards, and acoutics, the developed method can find numerous applications beyond exit processes.
Winds from T Tauri stars. I - Spherically symmetric models
NASA Technical Reports Server (NTRS)
Hartmann, Lee; Avrett, Eugene H.; Loeser, Rudolf; Calvet, Nuria
1990-01-01
Line fluxes and profiles are computed for a sequence of spherically symmetric T Tauri wind models. The calculations indicate that the H-alpha emission of T Tauri stars arises in an extended and probably turbulent circumstellar envelope at temperatures above about 8000 K. The models predict that Mg II resonance line emission should be strongly correlated with H-alpha fluxes; observed Mg II/H-alpha ratios are inconsistent with the models unless extinction corrections have been underestimated. The models predict that most of the Ca II resonance line and IR triplet emission arises in dense layers close to the star rather than in the wind. H-alpha emission levels suggest mass loss rates of about 10 to the -8th solar mass/yr for most T Tauri stars, in reasonable agreement with independent analysis of forbidden emission lines. These results should be useful for interpreting observed line profiles in terms of wind densities, temperatures, and velocity fields.
Absorbed dose from traversing spherically symmetric, Gaussian radioactive clouds
Thompson, J.M. ); Poston, J.W. . Dept. of Nuclear Engineering)
1999-06-01
If a large radioactive cloud is produced, sampling may require that an airplane traverse the cloud. A method to predict the absorbed dose to the aircrew from penetrating the radioactive cloud is needed. Dose rates throughout spherically symmetric Gaussian clouds of various sizes, and the absorbed doses from traversing the clouds, were calculated. Cloud size is a dominant parameter causing dose to vary by orders of magnitude for a given dose rate measured at some distance. A method to determine cloud size, based on dose rate readings at two or more distances from the cloud center, was developed. This method, however, failed to resolve the smallest cloud sizes from measurements made at 1,000 m to 2,000 m from the cloud center.
Spherically symmetric Einstein-aether perfect fluid models
Coley, Alan A.; Latta, Joey; Leon, Genly; Sandin, Patrik E-mail: genly.leon@ucv.cl E-mail: lattaj@mathstat.dal.ca
2015-12-01
We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.
Spherically symmetric simulation of plasma liner driven magnetoinertial fusion
Samulyak, Roman; Parks, Paul; Wu Lingling
2010-09-15
Spherically symmetric simulations of the implosion of plasma liners and compression of plasma targets in the concept of the plasma jet driven magnetoinertial fusion have been performed using the method of front tracking. The cases of single deuterium and xenon liners and double layer deuterium-xenon liners compressing various deuterium-tritium targets have been investigated, optimized for maximum fusion energy gains, and compared with theoretical predictions and scaling laws of [P. Parks, Phys. Plasmas 15, 062506 (2008)]. In agreement with the theory, the fusion gain was significantly below unity for deuterium-tritium targets compressed by Mach 60 deuterium liners. The most optimal setup for a given chamber size contained a target with the initial radius of 20 cm compressed by a 10 cm thick, Mach 60 xenon liner, achieving a fusion energy gain of 10 with 10 GJ fusion yield. Simulations also showed that composite deuterium-xenon liners reduce the energy gain due to lower target compression rates. The effect of heating of targets by alpha particles on the fusion energy gain has also been investigated.
NASA Astrophysics Data System (ADS)
Alexandre, Jean; Pasipoularides, Pavlos
2011-10-01
In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton’s Law in the IR limit λ→1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. DPRVDAQ1550-7998 83, 084030 (2011).10.1103/PhysRevD.83.084030][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys.1475-7516 12 (2010) 007.10.1088/1475-7516/2010/12/007], and we assume, as in [A. M. da Silva, Classical Quantum GravityCQGRDG0264-9381 28, 055011 (2011).10.1088/0264-9381/28/5/055011], that λ is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit λ→1, unless λ does not run, and has the fixed value λ=1. Finally, we comment on the Horava and Melby-Thompson approach [P. Horava and C. M. Melby-Thompson, Phys. Rev. DPRVDAQ1550-7998 82, 064027 (2010).10.1103/PhysRevD.82.064027] in which A is assumed as a part of the space-time metric in the IR.
Alexandre, Jean; Pasipoularides, Pavlos
2011-10-15
In this note we examine whether spherically symmetric solutions in covariant Horava-Lifshitz gravity can reproduce Newton's Law in the IR limit {lambda}{yields}1. We adopt the position that the auxiliary field A is independent of the space-time metric [J. Alexandre and P. Pasipoularides, Phys. Rev. D 83, 084030 (2011).][J. Greenwald, V. H. Satheeshkumar, and A. Wang, J. Cosmol. Astropart. Phys. 12 (2010) 007.], and we assume, as in [A. M. da Silva, Classical Quantum Gravity 28, 055011 (2011).], that {lambda} is a running coupling constant. We show that under these assumptions, spherically symmetric solutions fail to restore the standard Newtonian physics in the IR limit {lambda}{yields}1, unless {lambda} does not run, and has the fixed value {lambda}=1. Finally, we comment on the Horava and Melby-Thompson approach [P. Horava and C. M. Melby-Thompson, Phys. Rev. D 82, 064027 (2010).] in which A is assumed as a part of the space-time metric in the IR.
Spherically Symmetric Space Time with Regular de Sitter Center
NASA Astrophysics Data System (ADS)
Dymnikova, Irina
We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center.
Scalar self-energy for a charged particle in global monopole spacetime with a spherical boundary
NASA Astrophysics Data System (ADS)
Bezerra de Mello, E. R.; Saharian, A. A.
2012-07-01
We analyze combined effects of the geometry produced by a global monopole and a concentric spherical boundary on the self-energy of a point-like scalar charged test particle at rest. We assume that the boundary is outside the monopole’s core with a general spherically symmetric inner structure. An important quantity to this analysis is the three-dimensional Green function associated with this system. For both Dirichlet and Neumann boundary conditions obeyed by the scalar field on the sphere, the Green function presents a structure that contains contributions due to the background geometry of the spacetime and the boundary. Consequently, the corresponding induced scalar self-energy also presents a similar structure. For points near the sphere, the boundary-induced part dominates and the self-force is repulsive/attractive with respect to the boundary for Dirichlet/Neumann boundary condition. In the region outside the sphere at large distances from it, the boundary-free part in the self-energy dominates and the corresponding self-force can be either attractive or repulsive with dependence of the curvature coupling parameter for scalar field. In particular, for the minimal coupling we show the presence of a stable equilibrium point for the Dirichlet boundary condition. In the region inside the sphere, the nature of the self-force depends on the specific model for the monopole’s core. As illustrations of the general procedure adopted, we shall consider two distinct models, namely the flower-pot and the ballpoint-pen ones.
Free boundary value problem to 3D spherically symmetric compressible Navier-Stokes-Poisson equations
NASA Astrophysics Data System (ADS)
Kong, Huihui; Li, Hai-Liang
2017-02-01
In the paper, we consider the free boundary value problem to 3D spherically symmetric compressible isentropic Navier-Stokes-Poisson equations for self-gravitating gaseous stars with γ -law pressure density function for 6/5 <γ ≤ 4/3. For stress-free boundary condition and zero flow density continuously across the free boundary, the global existence of spherically symmetric weak solutions is shown, and the regularity and long time behavior of global solution are investigated for spherically symmetric initial data with the total mass smaller than a critical mass.
Static, spherically symmetric solutions with a scalar field in Rastall gravity
NASA Astrophysics Data System (ADS)
Bronnikov, K. A.; Fabris, J. C.; Piattella, O. F.; Santos, E. C.
2016-12-01
Rastall's theory belongs to the class of non-conservative theories of gravity. In vacuum, the only non-trivial static, spherically symmetric solution is the Schwarzschild one, except for a very special case. When a canonical scalar field is coupled to the gravity sector in this theory, new exact solutions appear for some values of the Rastall parameter a. Some of these solutions describe the same space-time geometry as the recently found solutions in the k-essence theory with a power function for the kinetic term of the scalar field. There is a large class of solutions (in particular, those describing wormholes and regular black holes) whose geometry coincides with that of solutions of GR coupled to scalar fields with nontrivial self-interaction potentials; the form of these potentials, however, depends on the Rastall parameter a. We also note that all solutions of GR with a zero trace of the energy-momentum tensor, including black-hole and wormhole ones, may be re-interpreted as solutions of Rastall's theory.
Spherically Symmetric Solution of the Weyl-Dirac Theory of Gravitation and its Consequences
NASA Astrophysics Data System (ADS)
Babourova, O. V.; Frolov, B. N.; Kudlaev, P. E.; Romanova, E. V.
2016-12-01
The Poincaré and Poincaré-Weyl gauge theories of gravitation with Lagrangians quadratic on curvature and torsion in post-Riemannian spaces with the Dirac scalar field is discussed in a historical aspect. The various hypotheses concerning the models of a dark matter with the help of a scalar field are considered. The new conformal Weyl-Dirac theory of gravitation is proposed, which is a gravitational theory in Cartan-Weyl spacetime with the Dirac scalar field representing the dark matter model. A static spherically symmetric solution of the field equations in vacuum for a central compact mass is obtained as the metrics conformal to the Yilmaz-Rosen metrics. On the base of this solution one considers a radial movement of an interplanetary spacecraft starting from the Earth. Using the Newton approximation one obtains that the asymptotic line-of-sight velocity in this case depends on the parameters of the solution, and therefore one can obtain, on basis of the observable data, the values of these parameters and then the value of a rest mass of the Dirac scalar field.
Spherically symmetric thin shells in Brans-Dicke theory of gravity
Letelier, P.S.; Wang, A. )
1993-07-15
The dynamics of spherically symmetric thin shells (or bubbles) is studied in the framework of the Brans-Dicke theory of gravity, using the Newman-Penrose formalism. The Brans-Dicke (BD) gravitational field equations on the bubble wall are given explicitly in terms of the discontinuities of the metric coefficients and the BD scalar field. Consequently, once the space-time geometry outside of the wall is given, these equations, together with the equation of state of the wall, uniquely determine the motion of the bubble. Using the generalized'' Bianchi identities, the interaction of a bubble with gravitational and matter fields is investigated. In particular, it is found that a bubble does not interact with an electromagnetic field, but it does with a scalar field or a fluid. The attraction and repulsion of a bubble are also studied. Exact solutions are constructed, and it is found that some of these solutions represent wormholes. However, these wormholes are different from the ones in Einstein's theory of gravity, in the sense that the throats of the wormholes are not necessarily built with exotic'' matter.
NASA Astrophysics Data System (ADS)
Brihaye, Yves; Hartmann, Betti
2005-01-01
We construct solutions of an Einstein Yang Mills system including a cosmological constant in 4 + n spacetime dimensions, where the n-dimensional manifold associated with the extra dimensions is taken to be Ricci flat. Assuming the matter and metric fields to be independent of the n extra coordinates, a spherical symmetric ansatz for the fields leads to a set of coupled ordinary differential equations. We find that for n > 1 only solutions with either one non-zero Higgs field or with all Higgs fields constant and zero gauge field function (corresponding to a Wu Yang-type ansatz) exist. We give the analytic solutions available in this model. These are 'embedded' Abelian solutions with a diverging size of the manifold associated with the extra n dimensions. Depending on the choice of parameters, these latter solutions either represent naked singularities or they possess a single horizon. We also present solutions of the effective four-dimensional Einstein Yang Mills Higgs-dilaton model, where the higher-dimensional cosmological constant induces a Liouville-type potential. The solutions are non-Abelian solutions with diverging Higgs fields, which exist only up to a maximal value of the cosmological constant.
On all possible static spherically symmetric EYM solitons and black holes
NASA Astrophysics Data System (ADS)
Oliynyk, Todd A.; Künzle, H. P.
2002-02-01
We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for any action of the rotation group (or SU(2)) by automorphisms of a principal bundle over spacetime whose structure group is a compact semi-simple Lie group G. These actions are characterized by a vector in the Cartan subalgebra of fraktur g and are called regular if the vector lies in the interior of a Weyl chamber. In the irregular cases (the majority for larger gauge groups) the boundary value problem that results for possible asymptotically flat soliton or black hole solutions is more complicated than in the previously discussed regular cases. In particular, there is no longer a gauge choice possible in general so that the Yang-Mills potential can be given by just real-valued functions. We prove the local existence of regular solutions near the singularities of the system at the centre, the black hole horizon, and at infinity, establish the parameters that characterize these local solutions, and discuss the set of possible actions and the numerical methods necessary to search for global solutions. That some special global solutions exist is easily derived from the fact that fraktur s fraktur u (2) is a subalgebra of any compact semi-simple Lie algebra. But the set of less trivial global solutions remains to be explored.
Time-dependent spherically symmetric accretion onto compact X-ray sources
NASA Technical Reports Server (NTRS)
Cowie, L. L.; Ostriker, J. P.; Stark, A. A.
1978-01-01
Analytical arguments and a numerical hydrodynamic code are used to investigate spherically symmetric accretion onto a compact object, in an attempt to provide some insight into gas flows heated by an outgoing X-ray flux. It is shown that preheating of spherically symmetric accretion flows by energetic radiation from an X-ray source results in time-dependent behavior for a much wider range of source parameters than was determined previously and that there are two distinct types of instability. The results are compared with observations of X-ray bursters and transients as well as with theories on quasars and active galactic nuclei that involve quasi-spherically symmetric accretion onto massive black holes. Models based on spherically symmetric accretion are found to be inconsistent with observations of bursters and transients.
The Glimm scheme for perfect fluids on plane-symmetric Gowdy spacetimes
NASA Astrophysics Data System (ADS)
Barnes, A. P.; Lefloch, P. G.; Schmidt, B. G.; Stewart, J. M.
2004-11-01
We propose a new, augmented formulation of the coupled Euler Einstein equations for perfect fluids on plane-symmetric Gowdy spacetimes. The unknowns of the augmented system are the density and velocity of the fluid and the first- and second-order spacetime derivatives of the metric. We solve the Riemann problem for the augmented system, allowing propagating discontinuities in both the fluid variables and the first- and second-order derivatives of the geometry coefficients. Our main result, based on Glimm's random choice scheme, is the existence of solutions with bounded total variation of the Euler Einstein equations, up to the first time where a blow-up singularity (unbounded first-order derivatives of the geometry coefficients) occurs. We demonstrate the relevance of the augmented system for numerical relativity. We also consider general vacuum spacetimes and solve a Riemann problem, by relying on a theorem by Rendall on the characteristic value problem for the Einstein equations.
Exact solution for the Casimir stress in a spherically symmetric medium
Leonhardt, Ulf; Simpson, William M. R.
2011-10-15
We calculated the stress of the quantum vacuum, the Casimir stress, in a spherically symmetric medium, Maxwell's fish eye, surrounded by a perfect mirror and derived an exact analytic solution. Our solution questions the idea that the Casimir force of a spherical mirror is repulsive--we found an attractive stress in the medium that diverges at the mirror.
Dynamical singularity resolution in spherically symmetric black hole formation
Ziprick, Jonathan; Kunstatter, Gabor
2009-07-15
We study numerically the effects of loop quantum gravity motivated corrections on massless scalar field collapse in Painleve-Gullstrand coordinates. Near criticality the system exhibits Choptuik scaling with a mass gap and a new scaling relationship dependant upon the quantum length scale. Classical singularities are resolved by a radiationlike phase in the quantum collapse: the black hole consists of a compact region of spacetime bounded by a single, smooth trapping horizon. The 'evaporation' is not complete but leaves behind a small expanding shell that disperses to infinity.
Spherically symmetric inhomogeneous bianisotropic media: Wave propagation and light scattering
NASA Astrophysics Data System (ADS)
Novitsky, Andrey; Shalin, Alexander S.; Lavrinenko, Andrei V.
2017-05-01
We develop a technique for finding closed-form expressions for electromagnetic fields in radially inhomogeneous bianisotropic media, both the solutions of the Maxwell equations and material tensors being defined by the set of auxiliary two-dimensional matrices. The approach is applied to determine the scattering cross-sections by spherical particles, the fields inside which correspond to the Airy-exponential waves.
Models of spherical shells as sources of Majumdar-Papapetrou type spacetimes
NASA Astrophysics Data System (ADS)
García-Reyes, Gonzalo
2017-03-01
By starting with a seed Newtonian potential-density pair we construct relativistic thick spherical shell models for a Majumdar-Papapetrou type conformastatic spacetime. As a simple example, we considerer a family of Plummer-Hernquist type relativistic spherical shells. As a second application, these structures are then used to model a system composite by a dust disk and a halo of matter. We study the equatorial circular motion of test particles around such configurations. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. The models considered satisfying all the energy conditions.
Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves
NASA Astrophysics Data System (ADS)
Mantica, Carlo Alberto; Suh, Young Jin
2016-12-01
In this paper we present some new results about n(≥ 4)-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for n > 4 and a pp-wave space-time in n = 4. In all cases an algebraic classification for the Weyl tensor is provided for n = 4 and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson-Walker space-time. In particular we show that a conformally flat (PZS)n, n ≥ 4, space-time is conformal to the Robertson-Walker space-time.
Spherically symmetric black holes in f (R) gravity: is geometric scalar hair supported?
NASA Astrophysics Data System (ADS)
Cañate, Pedro; Jaime, Luisa G.; Salgado, Marcelo
2016-08-01
We critically discuss current research on black hole (BH) solutions in f (R) gravity and shed light on its geometrical and physical significance. We also investigate the meaning, existence or lack thereof of Birkhoff’s theorem (BT) in this kind of modified gravity. We then focus on the analysis and search for non-trivial (i.e. hairy) asymptotically flat (AF) BH solutions in static and spherically symmetric (SSS) spacetimes in vacuum having the property that the Ricci scalar does not vanish identically in the domain of outer communication. To do so, we provide and enforce regularity conditions at the horizon in order to prevent the presence of singular solutions there. Specifically, we consider several classes of f (R) models like those proposed recently for explaining the accelerated expansion in the Universe and which have been thoroughly tested in several physical scenarios. Finally, we report analytical and numerical evidence about the absence of geometric hair in AFSSSBH solutions in those f (R) models. First, we submit the models to the available no-hair theorems (NHTs), and in the cases where the theorems apply, the absence of hair is demonstrated analytically. In the cases where the theorems do not apply, we resort to a numerical analysis due to the complexity of the non-linear differential equations. With that aim, a code to solve the equations numerically was built and tested using well-known exact solutions. In a future investigation we plan to analyze the problem of hair in de Sitter and anti-de Sitter backgrounds.
Stability of spherically symmetric, charged black holes and multipole moments for stationary systems
NASA Astrophysics Data System (ADS)
Gursel, Yekta
This dissertation is written in two parts. Part I deals with the question of stability of a spherically symmetric, charged black hole against scalar, electromagnetic, and gravitational perturbations. It consists of two papers written in collaboration with Igor D. NoVikov, Vernon D. Sandberg and A. A. Starobinsky. In these papers we describe the dynamical evolution of these perturbations on the interior of a Reissner-Nordstrom black hole. The instability of the hole's Cauchy horizon is discussed in detail in terms of the energy densities of the test fields as measured by a freely falling observer approaching the Cauchy horizon. We conclude that the Cauchy horizon of the analytically extended Reissner-Nordstrom solution is highly unstable and not a physical feature of a realistic gravitational collapse. Part II of this dissertation addresses two problems closely connected with muitipole structure of stationary, asymptotically flat spacetimes. It consists of two papers written in collaboration with Kip S. Thorne despite the fact that his name does not appear on one of them. The first one (Paper III in this thesis) shows the equivalence of the moments defined by Kip S. Thorne and the moments defined by Robert Geroch and Richard Hansen. The second (Paper IV in this thesis) proves a conjecture by Kip S. Thorne: In the limit of "slow" motion, general relativistic gravity produces no changes whatsoever in the classical Euler equations of rigid body motion. We prove this conjecture by giving an algorithm for generating rigidly rotating solutions of Einstein's equations from nonrotating, static solutions.
NASA Astrophysics Data System (ADS)
Erices, Cristián; Martínez, Cristián
2015-08-01
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a nonpositive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants. Two of these essential parameters have a local meaning and characterize the gravitational field strength. The other two have a topological origin, as they define an improper coordinate transformation that provides the stationary solution from the static one. The Petrov scheme is considered to explore the effects of the scalar field on the algebraic classification of the solutions. In general, these spacetimes are of type I. However, the presence of the scalar field allows us to find a nonvacuum type O solution and a wider family of type D spacetimes, in comparison with the vacuum case. The mass and angular momentum of the solution are computed using the Regge-Teitelboim method in the case of a negative cosmological constant. In absence of a cosmological constant, the curvature singularities in the vacuum solutions can be removed by including a phantom scalar field, yielding nontrivial locally homogeneous spacetimes. These spacetimes are of particular interest, as they have all their curvature invariants constant.
Spherically Symmetric Waves of a Reaction-Diffusion Equation.
1980-02-01
sets as t +c) and ones that decay (u(x,t) - 0 uniformly as t . This suggested the existence of the unstable equilibrium. There is an interesting global... existence and supply a description of such behaviour. Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and Grant No. DAAG29-77-G...infinity". The technique is to invert this idea and deduce the existence of spherical type wave behaviour from knouir,( one-dimensional behaviour. We
Comment on "Self-gravitating spherically symmetric solutions in scalar-torsion theories"
NASA Astrophysics Data System (ADS)
Yaqin, Ainol; Gunara, Bobby Eka
2017-07-01
We find a crucial miscalculation in [G. Kofinas, E. Papantonopoulos, and E. N. Saridakis, Self-gravitating spherically symmetric solutions in scalar-torsion theories, Phys. Rev. D 91, 104034 (2015), 10.1103/PhysRevD.91.104034] which leads to the wrong master equation. This follows that there is no wormhole-like solution for hyperbolic scalar potential and the solution at large distances differs from that of [G. Kofinas, E. Papantonopoulos, and E. N. Saridakis, Self-gravitating spherically symmetric solutions in scalar-torsion theories, Phys. Rev. D 91, 104034 (2015), 10.1103/PhysRevD.91.104034].
Vlasov, A.A.; Logunov, A.A.
1986-01-01
It is shown that the external gravitational field of a nonstatic spherically symmetric body is static in the relativistic theory of gravitation. In the general theory of relativity it is shown that the graviational field exterior to a nonstatic spherically symmetric body reduces to a static gravitational field given by the Schwarzschild metric (Birkhoff's theorem). However, the Schwarzschild solution does not satisfy the equations of the relativistic theory of gravitation, and it is therefore necessary to prove the analogous theorem in the latter theory.
NASA Astrophysics Data System (ADS)
Li, Ping; Li, Xin-zhou; Xi, Ping
2016-06-01
We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\
MØLLER Energy-Momentum Prescription for a Locally Rotationally Symmetric Space-Time
NASA Astrophysics Data System (ADS)
Aydogdu, Oktay
The energy distribution in the Locally Rotationally Symmetric (LRS) Bianchi type II space-time is obtained by considering the Møller energy-momentum definition in both Einstein's theory of general relativity and teleparallel theory of relativity. The energy distribution which includes both the matter and gravitational field is found to be zero in both of these different gravitation theories. This result agrees with previous works of Cooperstock and Israelit, Rosen, Johri et al., Banerjee and Sen, Vargas, and Aydogdu and Salti. Our result — the total energy of the universe is zero — supports the view points of Albrow and Tryon.
NASA Astrophysics Data System (ADS)
She, M.; Jiang, L. P.
2014-12-01
In this paper, an oscillating dark energy model is presented in an isotropic but inhomogeneous plane symmetric space-time by considering a time periodic varying deceleration parameter. We find three different types of new solutions which describe different scenarios of oscillating universe. The first two solutions show an oscillating universe with singularities. For the third one, the universe is singularity-free during the whole evolution. Moreover, the Hubble parameter oscillates and keeps positive which explores an interesting possibility to unify the early inflation and late time acceleration of the universe.
Simulating irradiance during lunar eclipses: the spherically symmetric case.
Vollmer, Michael; Gedzelman, Stanley David
2008-12-01
Irradiance during total lunar eclipses is simulated using a pinhole model. The Moon is illuminated by direct sunlight that is refracted into the Earth's shadow as it passes through the atmosphere at the terminator but is depleted by scattering by molecules, extinction by aerosol particles, absorption by ozone, and obstruction by clouds and elevated land. On a spherical, sea-level Earth, and a cloudless, molecular atmosphere with no ozone, the eclipsed Moon appears red and calculated irradiance at the center of the umbra is reduced by a factor of about 2400 from direct moonlight. Selective absorption mainly of light around 600 nm by stratospheric ozone turns the periphery of the umbra pale blue. Typical distributions of aerosol particles, ozone, mountains, and clouds around the terminator reduce irradiance by an additional factor of the order of 100.
No nonminimally coupled massless scalar hair for spherically symmetric neutral black holes
NASA Astrophysics Data System (ADS)
Hod, Shahar
2017-08-01
We provide a remarkably compact proof that spherically symmetric neutral black holes cannot support static nonminimally coupled massless scalar fields. The theorem is based on causality restrictions imposed on the energy-momentum tensor of the fields near the regular black-hole horizon.
Sooting and disruption in spherically symmetrical combustion of decane droplets in air
NASA Technical Reports Server (NTRS)
Dryer, F. L.; Williams, F. A.; Haggard, J. B., Jr.; Shaw, B. D.
1987-01-01
The paper presents the results of experiments on the burning of individual 1-2 mm decane droplets in air at room temperature and atmospheric pressure. The NASA Lewis 2.2 s drop tower was used as well as a newly designed droplet-combustion apparatus that promotes nearly spherically symmetrical combustion. Unanticipated disruptions related to sooting behavior were encountered.
The general class of the vacuum spherically symmetric equations of the general relativity theory
Karbanovski, V. V. Sorokin, O. M.; Nesterova, M. I.; Bolotnyaya, V. A.; Markov, V. N. Kairov, T. V.; Lyash, A. A.; Tarasyuk, O. R.
2012-08-15
The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.
Brito, Irene; Mena, Filipe C
2017-08-01
We prove that, for a given spherically symmetric fluid distribution with tangential pressure on an initial space-like hypersurface with a time-like boundary, there exists a unique, local in time solution to the Einstein equations in a neighbourhood of the boundary. As an application, we consider a particular elastic fluid interior matched to a vacuum exterior.
Curvature dependence of relativistic epicyclic frequencies in static, axially symmetric spacetimes
NASA Astrophysics Data System (ADS)
Vieira, Ronaldo S. S.; Kluźniak, Włodek; Abramowicz, Marek
2017-02-01
The sum of squared epicyclic frequencies of nearly circular motion (ωr2+ωθ2 ) in axially symmetric configurations of Newtonian gravity is known to depend both on the matter density and on the angular velocity profile of circular orbits. It was recently found that this sum goes to zero at the photon orbits of Schwarzschild and Kerr spacetimes. However, these are the only relativistic configurations for which such a result exists in the literature. Here, we extend the above formalism in order to describe the analogous relation for geodesic motion in arbitrary static, axially symmetric, asymptotically flat solutions of general relativity. The sum of squared epicyclic frequencies is found to vanish at photon radii of vacuum solutions. In the presence of matter, we obtain that ωr2+ωθ2>0 for perturbed timelike circular geodesics on the equatorial plane if the strong energy condition holds for the matter-energy fluid of spacetime; in vacuum, the allowed region for timelike circular geodesic motion is characterized by the inequality above. The results presented here may be of use to shed light on general issues concerning the stability of circular orbits once they approach photon radii, mainly the ones corresponding to stable photon motion.
The double-power approach to spherically symmetric astrophysical systems
NASA Astrophysics Data System (ADS)
Lingam, Manasvi; Nguyen, Phuc H.
2014-05-01
In this paper, we present two simple approaches for deriving anisotropic distribution functions for a wide range of spherical models. The first method involves multiplying and dividing a basic augmented density with polynomials in r and constructing more complex augmented densities in the process, from which we obtain the double-power distribution functions. This procedure is applied to a specific case of the Veltmann models that is known to closely approximate the Navarro-Frenk-White (NFW) profile, and also to the Plummer and Hernquist profiles (in the appendix). The second part of the paper is concerned with obtaining hypervirial distribution functions, i.e. distribution functions that satisfy the local virial theorem, for several well-known models. In order to construct the hypervirial augmented densities and the corresponding distribution functions, we start with an appropriate ansatz for the former and proceed to determine the coefficients appearing in that ansatz by expanding the potential-density pair as a series, around r = 0 and r = ∞. By doing so, we obtain hypervirial distribution functions, valid in these two limits, that can generate the potential-density pairs of these models to an arbitrarily high degree of accuracy. This procedure is explicitly carried out for the Hénon isochrone, Jaffe, Dehnen and NFW models and the accuracy of this procedure is established. Finally, we derive some universal properties for these hypervirial distribution functions, involving the asymptotic behaviour of the anisotropy parameter and its relation to the density slope in this regime. In particular, we show that the cusp slope-central anisotropy inequality is saturated.
Fermion Chiral Anomaly and Atiyah-Patodi Index for Spherical Spacetime Boundaries.
NASA Astrophysics Data System (ADS)
Schmidt, Jeffrey Robert
We study the structure of the fermion chiral anomaly in four-dimensional Euclidean spacetime bounded by a spherical surface via the Atiyah-Patodi-Singer Index Theorem. The significance of the index theorem in physics is discussed through examples taken from high energy and solid state physics. The proof of the index theorem is then detailed in a relatively pedestrian manner. Two exactly soluble examples involving self-dual gauge fields are presented and the anomaly explicitly evaluated. These two cases consist of a fermion interacting with a U(1) electromagnetic field and an SU(2) instanton, respectively.
Sheet-like assemblies of spherical particles with point-symmetrical patches.
Mani, Ethayaraja; Sanz, Eduardo; Roy, Soumyajit; Dijkstra, Marjolein; Groenewold, Jan; Kegel, Willem K
2012-04-14
We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.
The Design and Synthesis of Highly Branched and Spherically Symmetric Fluorinated Oils and Amphiles
Jiang, Zhong-Xing; Yu, Y. Bruce
2007-01-01
A new emulsifier design principle, based on concepts borrowed from protein science, is proposed. Using this principle, a class of highly branched and spherically symmetric fluorinated oils and amphiles has been designed and synthesized, for potential applications in the construction of fluorocarbon nanoparticles. The Mitsunobu reaction was employed as the key step for introducing three perfluoro-tert-butoxyl groups into pentaerythritol derivatives with excellent yields and extremely simple isolation procedures. Due to the symmetric arrangement of the fluorine atoms, each fluorinated oil or amphile molecule gives one sharp singlet 19F NMR signal. PMID:18461118
NASA Astrophysics Data System (ADS)
Ratkiewicz, R.; Barnes, A.; Molvik, G. A.
1996-07-01
The heliospheric termination shock is expected to move in response to variation in upstream solar wind conditions. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gasdynamic model of shock motion [Barnes, 1993] to spherically symmetric [Ratkiewicz et al., 1995], to investigate the qualitative features of global behavior of shock motion. The boundary conditions of the calculation are given by the solar wind parameters as a function of time on an inner spherical boundary, and a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary.
NASA Astrophysics Data System (ADS)
Ivanovski, S. L.; Zakharov, V. V.; Della Corte, V.; Crifo, J.-F.; Rotundi, A.; Fulle, M.
2017-01-01
In-situ measurements of individual dust grain parameters in the immediate vicinity of a cometary nucleus are being carried by the Rosetta spacecraft at comet 67P/Churyumov-Gerasimenko. For the interpretations of these observational data, a model of dust grain motion as realistic as possible is requested. In particular, the results of the Stardust mission and analysis of samples of interplanetary dust have shown that these particles are highly aspherical, which should be taken into account in any credible model. The aim of the present work is to study the dynamics of ellipsoidal shape particles with various aspect ratios introduced in a spherically symmetric expanding gas flow and to reveal the possible differences in dynamics between spherical and aspherical particles. Their translational and rotational motion under influence of the gravity and of the aerodynamic force and torque is numerically integrated in a wide range of physical parameters values including those of comet 67P/Churyumov-Gerasimenko. The main distinctions of the dynamics of spherical and ellipsoidal particles are discussed. The aerodynamic characteristics of the ellipsoidal particles, and examples of their translational and rotational motion in the postulated gas flow are presented.
Maeda, Hideki
2006-05-15
We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud including the perturbative effects of quantum gravity. The n({>=}5)-dimensional action with the Gauss-Bonnet term for gravity is considered and a simple formulation of the basic equations is given for the spacetime M{approx_equal}M{sup 2}xK{sup n-2} with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with n=5 and n{>=}6. There are two families of solutions, which we call plus-branch and the minus-branch solutions. A plus-branch solution can be attached to the outside vacuum region which is asymptotically anti-de Sitter in spite of the absence of a cosmological constant. Bounce inevitably occurs in the plus-branch solution for n{>=}6, and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of n=5 must be naked. On the other hand, a minus-branch solution can be attached to the outside asymptotically flat vacuum region. We show that naked singularities are massless for n{>=}6, while massive naked singularities are possible for n=5. In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for n{>=}6, while it is ingoing-null for n=5. In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for n{>=}10 and for n=9 depending on the parameters in the initial data, while a naked singularity is always formed for 5{<=}n{<=}8. These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.
General theory of spherically symmetric boundary-value problems of the linear transport theory.
NASA Technical Reports Server (NTRS)
Kanal, M.
1972-01-01
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
Zapol, B.; Zapol, P.
2014-09-03
Closed expressions for matrix elements < lm'|A(G)|lm >, where |lm > are spherical functions and A(G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q(l) and their moments Q(lm), as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodicities and other trends in these properties are revealed.
General theory of spherically symmetric boundary-value problems of the linear transport theory.
NASA Technical Reports Server (NTRS)
Kanal, M.
1972-01-01
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
NASA Technical Reports Server (NTRS)
Jackson, G. S.; Avedisian, C. T.
1993-01-01
The effect of initial droplet diameter on the burning rate of sooting fuels (n-heptane and 1-chloro-octane) is studied experimentally at low gravity. A 1.2 s drop tower provided a low gravity environment to minimize buoyancy and achieve spherically symmetric flames for stationary droplets. Free-floating and fiber supported droplets were burned, and both methods gave matching results for droplets of similar initial diameter.
No nonminimally coupled massless scalar hair for spherically symmetric neutral reflecting stars
NASA Astrophysics Data System (ADS)
Hod, Shahar
2017-07-01
It has recently been proved that horizonless compact stars with reflecting boundary conditions cannot support spatially regular matter configurations made of minimally coupled scalar fields, vector fields, and tensor fields. In the present paper we extend this intriguing no-hair property to the physically interesting regime of scalar fields with nonminimal coupling to gravity. In particular, we prove that static spherically symmetric configurations made of nonminimally coupled massless scalar fields cannot be supported by compact reflecting stars.
SOLA-STAR: a one-dimensional ICED-ALE hydrodynamics program for spherically symmetric flows
Cloutman, L.D.
1980-07-01
This report describes a simple, general-purpose, and efficient algorithm for solving one-dimensional spherically symmetric, transient fluid-dynamics problems using a variation of the ICED-ALE technique. Included are the finite difference equations, three test problems that illustrate various capabilities of the program, and a complete code description, including a listing, sample data decks and output, a summary of important variable names, and hints for conversion to other operating systems.
Non-static spherically symmetric exact solution of the Einstein-Maxwell field equations
NASA Astrophysics Data System (ADS)
Mahmood, Ayesha; Siddiqui, Azad A.; Feroze, Tooba
2017-10-01
We present a class of exact spherically symmetric and non-static solutions of Einstein-Maxwell's field equations. We have assumed isotropic pressure distribution and have taken ansatz on two of the gravitational potentials. The solutions admit negative pressure. We show that the solutions satisfy physical boundary conditions associated with the Einstein-Maxwell exact solutions. Therefore, these solutions can model physical systems such as moving dark energy stars.
Prasanna, A.R.
1982-05-15
In this brief paper we present a complete exact solution for the external magnetic field (dipolar at infinity) of a static magnetic star on the spherically symmetric background metric solution of Rosen's bimetric theory of gravity. Unlike in general relativity the field is well behaved throughout the manifold except at r = 0, and thus allows one to consider the field for stars collapsed beyond 2m.
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin E-mail: izumi@phys.ntu.edu.tw
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
NASA Astrophysics Data System (ADS)
Ortiz, Néstor; Sarbach, Olivier
2014-04-01
A spherical dust cloud which is initially at rest and which has a monotonously decaying density profile collapses and forms a shell-focusing singularity. Provided the density profile is not too flat, meaning that its second radial derivative is negative at the centre, this singularity is visible to local, and sometimes even to global observers. According to the strong cosmic censorship conjecture, such naked singularities should be unstable under generic, non-spherical perturbations of the initial data or when more realistic matter models are considered. In an attempt to gain further insight into this stability issue, in this work we initiate the analysis of a simpler but related problem. We discuss the stability of test fields propagating in the vicinity of the Cauchy horizon associated to the naked central singularity. We first study the high-frequency limit and show that the fields undergo a blueshift as they approach the Cauchy horizon. However, in contrast to what occurs at inner horizons of black holes, we show that the blueshift is uniformly bounded along incoming and outgoing null rays. Motivated by this boundedness result, we take a step beyond the geometric optics approximation and consider the Cauchy evolution of spherically symmetric test scalar fields. We prove that under reasonable conditions on the initial data a suitable rescaled field can be continuously extended to the Cauchy horizon. In particular, this result implies that the physical field is everywhere finite on the Cauchy horizon away from the central singularity.
NASA Astrophysics Data System (ADS)
Hod, Shahar
2016-12-01
The physical properties of bound-state charged massive scalar field configurations linearly coupled to a spherically symmetric charged reflecting shell are studied analytically. To that end, we solve the Klein-Gordon wave equation for a static scalar field of proper mass μ, charge coupling constant q, and spherical harmonic index l in the background of a charged shell of radius R and electric charge Q. It is proved that the dimensionless inequality μR <√{(qQ) 2 -(l + 1 / 2) 2 } provides an upper bound on the regime of existence of the composed charged-spherical-shell-charged-massive-scalar-field configurations. Interestingly, we explicitly show that the discrete spectrum of shell radii {Rn(μ,qQ,l)}n = 0 n = ∞ which can support the static bound-state charged massive scalar field configurations can be determined analytically. We confirm our analytical results by numerical computations.
Casimir effect of the electromagnetic field in D-dimensional spherically symmetric cavities
Teo, L. P.
2010-10-15
Eigenmodes of the electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE modes and one polarization for TM modes, giving rise to a total of (D-1) polarizations. In case of a D-dimensional ball, the eigenfrequencies of the electromagnetic field with perfectly conducting boundary condition coincides with the eigenfrequencies of gauge 1-forms with relative boundary condition; whereas the eigenfrequencies of the electromagnetic field with infinitely permeable boundary condition coincides with the eigenfrequencies of gauge 1-forms with absolute boundary condition. Casimir energies of single and concentric spherical shells in D-dimensions are computed. The Casimir energy of concentric spherical shells can be written as a sum of the single spherical shell contributions and an interacting term, and the latter is free of divergence. The interacting term always gives rise to an attractive force between the two spherical shells. Its leading term is the Casimir force acting between two parallel plates of the same area, as expected by proximity force approximation.
NASA Astrophysics Data System (ADS)
Sen, K. K., Wilson, S. J.
The advancement of observational techniques over the years has led to the discovery of a large number of stars exhibiting complex spectral structures, thus necessitating the search for new techniques and methods to study radiative transfer in such stars with moving envelopes. This led to the introduction of the concept of "photon escape probability" and the wisdom of expressing the transfer equations in "comoving frames" (CMF). Radiative transfer problems in spherically moving media form a branch of mathematical physics which uses mathematics of a very distinctive kind. Radiative Transfer in Moving Media records the basic mathematical methodologies, both analytical and numerical, developed for solving radiation transfer problems in spherically symmetric moving media, in the consideration of macroscopic velocity fields only. Part I contains the basic notions of radiation-matter interaction in participating media and constructs the relevant transfer equations to be solved in the subsequent chapters. Part II considers the basic mathematical methods for solving the transfer problems in extensive moving atmospheres when it is observed in the lab frame. Part III introduces the analytical and numerical methods for solving radiative transfer problems in spherically symmetric moving atmospheres when expressed in the comoving frame. This book is addressed to graduate students and researchers in Astrophysics, in particular to those studying radiative transfer in stellar atmospheres.
Beyond Extreme Ultra Violet (BEUV) Radiation from Spherically symmetrical High-Z plasmas
NASA Astrophysics Data System (ADS)
Yoshida, Kensuke; Fujioka, Shinsuke; Higashiguchi, Takeshi; Ugomori, Teruyuki; Tanaka, Nozomi; Kawasaki, Masato; Suzuki, Yuhei; Suzuki, Chihiro; Tomita, Kentaro; Hirose, Ryouichi; Eshima, Takeo; Ohashi, Hayato; Nishikino, Masaharu; Scally, Enda; Nshimura, Hiroaki; Azechi, Hiroshi; O'Sullivan, Gerard
2016-03-01
Photo-lithography is a key technology for volume manufacture of high performance and compact semiconductor devices. Smaller and more complex structures can be fabricated by using shorter wavelength light in the photolithography. One of the most critical issues in development of the next generation photo-lithography is to increase energy conversion efficiency (CE) from laser to shorter wavelength light. Experimental database of beyond extreme ultraviolet (BEUV) radiation was obtained by using spherically symmetrical high-Z plasmas generated with spherically allocated laser beams. Absolute energy and spectra of BEUV light emitted from Tb, Gd, and Mo plasmas were measured with a absolutely calibrated BEUV calorimeter and a transmission grating spectrometer. 1.0 x 1012 W/cm2 is the optimal laser intensity to produced efficient BEUV light source plasmas with Tb and Gd targets. Maximum CE is achieved at 0.8% that is two times higher than the published CEs obtained with planar targets.
NASA Astrophysics Data System (ADS)
Jafari, Ghadir; Setare, Mohammad R.; Bakhtiarizadeh, Hamid R.
2017-10-01
This article is devoted to static spherically symmetric black hole solutions of dRGT (de Rham-Gabadadze-Tolley) massive gravity in the presence of cosmological constant. The unitary and non-unitary gauges are used to find the solutions in three, four and five dimensions. We show that there are two general classes of solutions. In one of them, the effect of massive potential is appeared as the effective cosmological constant. By investigating these solutions in different dimensions, we find an expression for effective cosmological constant in arbitrary dimensions.
Complete synthetic seismograms up to 2 Hz for transversely isotropic spherically symmetric media
NASA Astrophysics Data System (ADS)
Kawai, Kenji; Takeuchi, Nozomu; Geller, Robert J.
2006-02-01
We use the direct solution method (DSM) with optimally accurate numerical operators to calculate complete (including both body and surface waves) three-component synthetic seismograms for transversely isotropic (TI), spherically symmetric media, up to 2 Hz. We present examples of calculations for both deep (600 km) and shallow (5 km) sources. Such synthetics should be useful in forward and inverse studies of earth structure. In order to make these calculations accurately and efficiently the vertical grid spacing, maximum angular order, and cut-off depth must be carefully and systematically chosen.
Axi-symmetric patterns of active polar filaments on spherical and composite surfaces
NASA Astrophysics Data System (ADS)
Srivastava, Pragya; Rao, Madan
2014-03-01
Experiments performed on Fission Yeast cells of cylindrical and spherical shapes, rod-shaped bacteria and reconstituted cylindrical liposomes suggest the influence of cell geometry on patterning of cortical actin. A theoretical model based on active hydrodynamic description of cortical actin that includes curvature-orientation coupling predicts spontaneous formation of acto-myosin rings, cables and nodes on cylindrical and spherical geometries [P. Srivastava et al, PRL 110, 168104(2013)]. Stability and dynamics of these patterns is also affected by the cellular shape and has been observed in experiments performed on Fission Yeast cells of spherical shape. Motivated by this, we study the stability and dynamics of axi-symmetric patterns of active polar filaments on the surfaces of spherical, saddle shaped and conical geometry and classify the stable steady state patterns on these surfaces. Based on the analysis of the fluorescence images of Myosin-II during ring slippage we propose a simple mechanical model for ring-sliding based on force balance and make quantitative comparison with the experiments performed on Fission Yeast cells. NSF Grant DMR-1004789 and Syracuse Soft Matter Program.
Spherically symmetric vacuum in covariant F (T )=T +α/2 T2+O (Tγ) gravity theory
NASA Astrophysics Data System (ADS)
DeBenedictis, Andrew; Ilijić, Saša
2016-12-01
Recently, a fully covariant version of the theory of F (T ) torsion gravity has been introduced by M. Kršśák and E. Saridakis [Classical Quantum Gravity 33, 115009 (2016)]. In covariant F (T ) gravity, the Schwarzschild solution is not a vacuum solution for F (T )≠T , and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework, we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with F (T )=T +(α /2 )T2 , representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this, we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, α , which governs deviations from general relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the Solar System or greater universe could be attributable to nonlinear torsion.
Mimoso, Jose P.; Le Delliou, Morgan; Mena, Filipe C.
2010-06-15
We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell, and we argue that cosmological initial conditions should allow its global validity. We analyze the particular cases of the Lemaitre-Tolman-Bondi dust models with a cosmological constant as an example of a cold dark matter model with a cosmological constant ({Lambda}-CDM model) and its generalization to contain a central perfect-fluid core. These models provide simple but physically interesting illustrations of our results.
Nonlinear vibration of moderately thick anti-symmetric angle-ply shallow spherical shell
NASA Astrophysics Data System (ADS)
Chia, C. Y.; Chia, D. S.
1992-08-01
Equations of motion for the large-amplitude flexural vibration of an anti-symmetrically laminated angle-ply shallow spherical shell with rectangular planform are derived by use of Hamilton's principle. The effects of transverse shear and rotatory inertia are included in this study. A solution is formulated in the form of generalized double Fourier series with time-dependent coefficients and satisfies the five boundary conditions along each of simply supported edges. The Galerkin procedure furnishes an infinite system of ordinary differential equations for the time-dependent coefficients. These equations can be truncated to obtain any desired degree of accuracy. The method of harmonic balance is used for a solution. Numerical results for nonlinear free vibrations of isotropic, orthotropic and laminated shallow shells are presented graphically for various shell parameters and lamination geometries. The transverse shear effect on the shell frequency of vibration is discussed in some detail.
Compton and synchrotron processes in spherically-symmetric non-thermal sources
NASA Technical Reports Server (NTRS)
Gould, R. J.
1979-01-01
A framework is developed for the accurate calculation of Compton and synchrotron processes in a special class of spherically-symmetric sources. The models considered take a distribution in magnetic field values and high-energy electron density that varies smoothly from central values to values at the outer boundary of the source. Further, the assumption is made that the magnetic field has local disorder (isotropy) and the high-energy electron distribution has local isotropy. Then, in terms of parameters of the source, the synchrotron brightness distribution, total synchrotron flux, Compton-synchrotron flux, and synchrotron self-absorption turnover are all computed accurately. Results are given with a view toward application to the analysis of compact non-thermal sources.
Kawakami, Hayato; Mitsuda, Eiji; Nambu, Yasusada; Tomimatsu, Akira
2009-07-15
In considering the gravitational collapse of matter, it is an important problem to clarify what kind of conditions leads to the formation of naked singularity. For this purpose, we apply the 1+3 orthonormal frame formalism introduced by Uggla et al. to the spherically symmetric gravitational collapse of a perfect fluid. This formalism allows us to construct an autonomous system of evolution and constraint equations for scale-invariant dynamical variables normalized by the volume expansion rate of the timelike orthonormal frame vector. We investigate the asymptotic evolution of such dynamical variables towards the formation of a central singularity and present a conjecture that the steep spatial gradient for the normalized density function is a characteristic of the naked singularity formation.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-15
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Transfer of X-rays through a spherically symmetric gas cloud
NASA Technical Reports Server (NTRS)
Hatchett, S.; Buff, J.; Mccray, R.
1976-01-01
Approximate solutions are presented for the transfer of radiation through spherically symmetric gas clouds surrounding a point source of X-rays. The approach is similar to that of Tarter and Salpeter (1969) except that heating by Compton scattering and the Auger effect is included. The temperature and ionization structure are sensitive to the source spectrum, and the solutions are not unique if soft X-rays are deficient. The emergent spectrum is rich in optical, ultraviolet, and X-ray emission lines. The radiation force due to photoelectric absorption of X-rays may exceed the force due to Compton scattering by a factor of order 10 for the radiation fields and densities likely to be encountered in galactic binary X-ray sources.
A new model for spherically symmetric charged compact stars of embedding class 1
NASA Astrophysics Data System (ADS)
Maurya, S. K.; Gupta, Y. K.; Ray, Saibal; Deb, Debabrata
2017-01-01
In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant A=0, which shows that our solutions represent the so-called `electromagnetic mass model' [17], and, secondly, the metric function ν (r), for the limit n tending to infinity, converts to ν (r)=C{r}2+ ln B, which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence.
Collisionless relaxation of self-gravitating systems with spherically symmetric dynamics
NASA Astrophysics Data System (ADS)
Ziegler, Harald J.; Wiechen, Heinz
1990-10-01
A recent theory of the collisionless relaxation of self-gravitating matter is applied to systems with spherically symmetric dynamics. Therefore consideration is given to additional constants of motion of the exact dynamics, which arise from the given symmetry, i.e. conservation of phase-space density and conservation of single particle angular momentum of the exact dynamics as well as total energy conservation and the mixing character of collisionless relaxation are considered. The strength of the relaxation process is governed by the amount of nonequilibrium energy of a given initial state. As can be expected by heuristic arguments the resulting final equilibrium states on macroscopic scales show a stronger dependence on the initial states compared with systems having an arbitrarily (more violent) dynamical evolution.
Dynamical systems approach to relativistic spherically symmetric static perfect fluid models
NASA Astrophysics Data System (ADS)
Heinzle, J. Mark; Röhr, Niklas; Uggla, Claes
2003-11-01
We investigate relativistic spherically symmetric static perfect fluid models with barotropic equations of state that are asymptotically polytropic and linear at low and high pressures, respectively. We generalize standard work on Newtonian polytropes to a relativistic setting and to a much larger class of equations of state. This is accomplished by introducing dimensionless variables that are asymptotically homology invariant in the low pressure regime, which yields a reformulation of the field equations into a regular dynamical system on a three-dimensional compact state space. A global picture of the solution space is thus obtained which makes it possible to derive qualitative features and to prove theorems about mass radius properties. Moreover, the framework is also suited for numerical computations, as illustrated by several numerical examples, e.g., the ideal neutron gas and examples that involve phase transitions.
Heliospheric termination shock motion in response to LISM variations: Spherically symmetric model
NASA Astrophysics Data System (ADS)
Ratkiewicz, R.; Barnes, A.; Spreiter, J. R.
The unsteady spherically symmetric one-dimensional gasdynamic model appears to be a powerful tool in the investigation of the termination shock motion. Such a model has previously been used to examine the response of the heliospheric termination shock to variations in upstream solar wind conditions [Ratkiewicz et al., 1996]. In the current paper we apply the same model to study response of the shock to variations in the interstellar medium. The initial-boundary conditions for the unsteady calculations are given by the pressure as a function of time on an outer boundary either alone or with the density as a function of time on an inner boundary. The motion of the termination shock is caused by fluctuations in both solar wind and interstellar plasma parameters and has a rather complicated behavior, characterized by a sequence of perturbations that hit the termination shock and are reflected from the outer boundary.
Most general spherically symmetric M2-branes and type-IIB strings
Wang Zhaolong; Lue, H.
2009-09-15
We obtain the most general spherically symmetric M2-branes and type-IIB strings, with R{sup 1,2}xSO(8) and R{sup 1,1}xSO(8) isometries, respectively. We find that there are 12 different classes of M2-branes, and we study their curvature properties. In particular, we obtain new smooth M2-brane wormholes that connect two asymptotic regions: one is flat and the other can be either flat or AdS{sub 4}xS{sup 7}. We find that these wormholes are traversable with certain timelike trajectories. We also obtain the most general Ricci-flat solutions in five dimensions with R{sup 1,1}xSO(3) isometries.
NASA Astrophysics Data System (ADS)
Miyakawa, Takahiko; Nakamura, Shin; Yabu, Hiroyuki
2017-03-01
We study the ground state of a two-component dipolar Fermi gas in a spherically symmetric harmonic trap at zero temperature. On the basis of the Thomas-Fermi-von Weizsäcker approximation, we obtain a phase diagram of the system with equal but opposite values of the magnetic moment. We find that a phase-separated state, which spontaneously breaks the spherical symmetry of the system, emerges.
NASA Astrophysics Data System (ADS)
Huang, Xiangdi
2017-02-01
One of the most influential fundamental tools in harmonic analysis is the Riesz transforms. It maps Lp functions to Lp functions for any p ∈ (1 , ∞) which plays an important role in singular operators. As an application in fluid dynamics, the norm equivalence between ‖∇u‖Lp and ‖ div u ‖ Lp +‖ curl u ‖ Lp is well established for p ∈ (1 , ∞). However, since Riesz operators sent bounded functions only to BMO functions, there is no hope to bound ‖∇u‖L∞ in terms of ‖ div u ‖ L∞ +‖ curl u ‖ L∞. As pointed out by Hoff (2006) [11], this is the main obstacle to obtain uniqueness of weak solutions for isentropic compressible flows. Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞ ≤ (2 + 1 / N)‖ div u ‖ L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.
NASA Technical Reports Server (NTRS)
Ratkiewicz, R.; Barnes, A.; Molvik, G. A.; Spreiter, J. R.; Stahara, S. S.; Cuzzi, Jeffery N. (Technical Monitor)
1995-01-01
Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.
NASA Astrophysics Data System (ADS)
Cariñena, J. F.; Perelomov, A. M.
1997-08-01
The integral representation of the orthogonal groups for zonal spherical functions of the symmetric space 0305-4470/30/15/003/img2 is used to obtain a generating function for such functions. For the case N = 3 the three-dimensional integral representation reduces to a one-dimensional one.
NASA Astrophysics Data System (ADS)
Aktosun, Tuncay; Papanicolaou, Vassilis G.
2013-06-01
The unique reconstruction of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, then v is uniquely reconstructed from the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the multiplicity is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique reconstruction is presented when the data set contains one additional piece of information. Some similar results are presented for the unique reconstruction of the potential from the transmission eigenvalues with multiplicities for a related Schrödinger equation.
NASA Astrophysics Data System (ADS)
Aktosun, Tuncay; Gintides, Drossos; Papanicolaou, Vassilis G.
2011-11-01
The recovery of a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from the set of the corresponding transmission eigenvalues for which the corresponding eigenfunctions are also spherically symmetric. If the integral of 1/v on the interval [0, b] is less than b, assuming that there exists at least one v corresponding to the data, it is shown that v is uniquely determined by the data consisting of such transmission eigenvalues and their ‘multiplicities’, where the ‘multiplicity’ is defined as the multiplicity of the transmission eigenvalue as a zero of a key quantity. When that integral is equal to b, the unique recovery is obtained when the data contain one additional piece of information. Some similar results are presented for the unique determination of the potential from the transmission eigenvalues with ‘multiplicities’ for a related Schrödinger equation.
Trampert, Patrick; Vogelgesang, Jonas; Schorr, Christian; Maisl, Michael; Bogachev, Sviatoslav; Marniok, Nico; Louis, Alfred; Dahmen, Tim; Slusallek, Philipp
2017-03-21
Laminography is a tomographic technique that allows three-dimensional imaging of flat and elongated objects that stretch beyond the extent of a reconstruction volume. Laminography images can be reconstructed using iterative algorithms based on the Kaczmarz method. This study aims to develop and demonstrate a new reconstruction algorithm that may provide superior image reconstruction quality for this challenged imaging application. The images are initially represented using the coefficients over basis functions, which are typically piecewise constant functions (voxels). By replacing voxels with spherically symmetric volume elements (blobs) based on the generalized Kaiser-Bessel window functions, the images are reconstructed using this new adapted version of the algebraic image reconstruction technique. Band-limiting properties of blob functions are beneficial particular in the case of noisy projections and with only a limited number of available projections. Study showed that using blob basis functions improved full-width-at-half-maximum resolution from 10.2±1.0 to 9.9±0.9 (p < 0.001). Signal-to-noise ratio also improved from 16.1 to 31.0. The increased computational demand per iteration was compensated by using a faster convergence rate, such that the overall performance is approximately identical for blobs and voxels. Despite the higher complexity, tomographic reconstruction from computed laminography data should be implemented using blob basis functions, especially if noisy data is expected.
Ziegler, Andy; Köhler, Thomas; Nielsen, Tim; Proksa, Roland
2006-12-01
In cone-beam transmission tomography the measurements are performed with a divergent beam of x-rays. The reconstruction with iterative methods is an approach that offers the possibility to reconstruct the corresponding images directly from these measurements. Another approach based on spherically symmetric basis functions (blobs) has been reported with results demonstrating a better image quality for iterative reconstruction algorithms. When combining the two approaches (i.e., using blobs in iterative cone-beam reconstruction of divergent rays) the problem of blob sampling without introducing aliasing must be addressed. One solution to this problem is to select a blob size large enough to ensure a sufficient sampling, but this prevents a high resolution reconstruction, which is not desired. Another solution is a heuristic low-pass filtering, which removes this aliasing, but neglects the different contributions of blobs to the absorption depending on the spatial position in the volume and, therefore, cannot achieve the best image quality. This article presents a model of sampling the blobs which is motivated by the beam geometry. It can be used for high resolution reconstruction and can be implementedefficiently.
NASA Astrophysics Data System (ADS)
Satin, Seema; Malafarina, Daniele; Joshi, Pankaj S.
2016-12-01
We study the complete gravitational collapse of a class of spherically symmetric inhomogeneous perfect fluid models obtained by introducing small radial perturbations in an otherwise homogeneous matter cloud. Our aim here is to study the genericity and stability of the formation of black holes and locally naked singularities in collapse. While the occurrence of naked singularities is known for many models of collapse, the key issue now in focus is genericity and stability of these outcomes. Towards this purpose, we study how the introduction of a somewhat general class of small inhomogeneities in homogeneous collapse leading to a black hole can change the final outcome to a naked singularity. The key feature that we assume for the perturbation profile is that of a mass profile that is separable in radial and temporal coordinates. The known models of dust and homogeneous perfect fluid collapse can be obtained from this choice of the mass profile as special cases. This choice is very general and physically well motivated and we show that this class of collapse models leads to the formation of a naked singularity as the final state.
NASA Astrophysics Data System (ADS)
Xu, Limei; Buldyrev, Sergey V.; Angell, C. Austen; Stanley, H. Eugene
2006-09-01
Using molecular dynamics simulations, we study the Jagla model of a liquid which consists of particles interacting via a spherically symmetric two-scale potential with both repulsive and attractive ramps. This potential displays anomalies similar to those found in liquid water, namely expansion upon cooling and an increase of diffusivity upon compression, as well as a liquid-liquid (LL) phase transition in the region of the phase diagram accessible to simulations. The LL coexistence line, unlike in tetrahedrally coordinated liquids, has a positive slope, because of the Clapeyron relation, corresponding to the fact that the high density phase (HDL) is more ordered than low density phase (LDL). When we cool the system at constant pressure above the critical pressure, the thermodynamic properties rapidly change from those of LDL-like to those of HDL-like upon crossing the Widom line. The temperature dependence of the diffusivity also changes rapidly in the vicinity of the Widom line, namely the slope of the Arrhenius plot sharply increases upon entering the HDL domain. The properties of the glass transition are different in the two phases, suggesting that the less ordered phase is fragile, while the more ordered phase is strong, which is consistent with the behavior of tetrahedrally coordinated liquids such as water silica, silicon, and BeF2 .
On global properties of static spherically symmetric EYM fields with compact gauge groups
NASA Astrophysics Data System (ADS)
Oliynyk, Todd A.; Künzle, H. P.
2003-11-01
The set of all possible spherically symmetric magnetic static Einstein Yang Mills field equations for an arbitrary compact semisimple gauge group G was classified in two previous papers. Local analytic solutions near the centre and a black-hole horizon as well as those that are analytic and bounded near infinity were shown to exist. Some globally bounded solutions are also known to exist because they can be obtained by embedding solutions for the G = SU(2) case which is well understood. However, more general global solutions for more complicated (so-called irregular) actions for larger gauge groups are very difficult to find numerically since they are very unstable. Here we derive rigorously some asymptotic properties of an arbitrary global solution, namely one that exists locally near a radial value r0 (in Schwarzschild-type coordinates), has positive mass m(r) at r0 and is defined for all r > r0. The set of asymptotic values of the Yang Mills potential (in a suitable well-defined gauge) is shown to be finite in the so-called regular case, but may form a more complicated real variety for models obtained from irregular rotation group actions.
NASA Astrophysics Data System (ADS)
Coughlin, Eric R.
2017-01-01
We present the exact solutions for the collapse of a spherically symmetric cold (i.e., pressureless) cloud under its own self-gravity, valid for arbitrary initial density profiles and not restricted to the realm of self-similarity. These solutions exhibit a number of remarkable features, including the self-consistent formation of and subsequent accretion onto a central point mass. A number of specific examples are provided, and we show that Penston’s solution of pressureless self-similar collapse is recovered for polytropic density profiles; importantly, however, we demonstrate that the time over which this solution holds is fleetingly short, implying that much of the collapse proceeds non-self-similarly. We show that our solutions can naturally incorporate turbulent pressure support, and we investigate the evolution of overdensities—potentially generated by such turbulence—as the collapse proceeds. Finally, we analyze the evolution of the angular velocity and magnetic fields in the limit that their dynamical influence is small, and we recover exact solutions for these quantities. Our results may provide important constraints on numerical models that attempt to elucidate the details of protostellar collapse when the initial conditions are far less idealized.
Geodesic completeness in a wormhole spacetime with horizons
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.
2015-08-01
The geometry of a spacetime containing a wormhole generated by a spherically symmetric electric field is investigated in detail. These solutions arise in high-energy extensions of general relativity formulated within the Palatini approach and coupled to Maxwell electrodynamics. Even though curvature divergences generically arise at the wormhole throat, we find that these spacetimes are geodesically complete. This provides an explicit example where curvature divergences do not imply spacetime singularities.
Shendeleva, Margarita L; Molloy, John A
2006-09-20
We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.
Two scenarios of the radial orbit instability in spherically symmetric collisionless stellar systems
NASA Astrophysics Data System (ADS)
Polyachenko, V. L.; Polyachenko, E. V.; Shukhman, I. G.
2015-01-01
The stability of a two-parameter family of radially anisotropic models with a nonsingular central density distribution is considered. Instability takes place at a sufficiently strong radial anisotropy (the so-called radial orbit instability, ROI). We show that the character of instability depends not only on the anisotropy but also on the energy distribution of stars. If this distribution is such that the highly eccentric orbits responsible for the instability are "trapped" in the radial direction near the center, then the instability develops with a characteristic growth time that exceeds considerably the Jeans and dynamical times of the trapped particles. In this case, the instability takes place only for even spherical harmonics and is aperiodic. If, however, almost all of the elongated orbits reach the outer radius of the sphere, then both even and odd harmonics turn out to be unstable. The unstable modes corresponding to odd harmonics are oscillatory in nature with characteristic frequencies of the order of the dynamical ones. The unstable perturbations corresponding to even harmonics contain only one aperiodic mode and several oscillatory modes, with the aperiodic mode being always the most unstable one. Two main interpretations of the ROI available in the literature have been analyzed: the "classical" Jeans instability related to an insufficient stellar velocity dispersion in the transversal direction and the "orbital" approach relying heavily on the analogous Lynden-Bell bar formation mechanism in disk galaxies. The assumptions that the perturbations are slow (compared to the orbital frequency of stars) and that the shape of the perturbed potential is symmetric are inherent integral conditions for the applicability of the latter. Our solutions show that the orbital approach cannot be considered as a universal one.
Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests
NASA Astrophysics Data System (ADS)
Zilhão, Miguel; Witek, Helvi; Sperhake, Ulrich; Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Nerozzi, Andrea
2010-04-01
The numerical evolution of Einstein’s field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. Brill-Lindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
NASA Astrophysics Data System (ADS)
Mostert, Wouter; Wheatley, Vincent; Pullin, Dale; Samtaney, Ravi
2015-11-01
We present results of ideal magnetohydrodynamics simulations investigating the Richtmyer-Meshkov instability in near-spherical implosions in the presence of an octahedrally symmetric seed magnetic field. The problem is motivated by the desire to maintain a symmetrical collapse of the primary shock wave, minimally distorted by the effect of the seed magnetic field, while retaining the seed-field-induced suppression of the Richtmyer-Meshkov instability. The field is generated by a set of six current loops arranged around the target as on the faces of a cube. The instability is generated on a perturbed spherical density interface that is accelerated from the outside by imploding magnetohydrodynamic shocks, which are in turn generated by a spherical Riemann problem. The perturbation on the density interface is formed with a single-dominant-mode spherical harmonics expansion. We investigate the evolution of the interface and the transport of baroclinic vorticity near the interface, and examine the extent of the distortion to the primary magnetohydrodynamic shock system induced by the seed field. This work was partially supported by the KAUST Office of Sponsored Research under Award URF/1/2162-01.
Keeton, Charles R.; Petters, A.O.
2005-11-15
We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit. In this paper we present the formalism for computing corrections to lensing observables for static, spherically symmetric gravity theories in which the corrections to the weak-deflection limit can be expanded as a Taylor series in one parameter, namely, the gravitational radius of the lens object. We take care to derive coordinate-independent expressions and compute quantities that are directly observable. We compute series expansions for the observables that are accurate to second order in the ratio {epsilon}={theta} /{theta}{sub E} of the angle subtended by the lens's gravitational radius to the weak-deflection Einstein radius, which scales with mass as {epsilon}{proportional_to}M {sup 1/2}. The positions, magnifications, and time delays of the individual images have corrections at both first and second order in {epsilon}, as does the differential time delay between the two images. Interestingly, we find that the first-order corrections to the total magnification and centroid position vanish in all gravity theories that agree with general relativity in the weak-deflection limit, but they can remain nonzero in modified theories that disagree with general relativity in the weak-deflection limit. For the Reissner-Nordstroem metric and a related metric from heterotic string theory, our formalism reveals an intriguing connection between lensing observables and the condition for having a naked singularity, which could provide an observational method for testing the existence of such objects. We apply our formalism to the galactic black hole and predict that the corrections to the image positions are at the level of 10 {mu}arc s (microarcseconds), while the correction to the time delay is a few hundredths of a second. These corrections would be measurable today if a pulsar were
Microlensing on extended structures having a spherically-symmetric mass distribution
NASA Astrophysics Data System (ADS)
Zhdanov, V.; Alexandrov, A.; Stashko, O.
2016-06-01
Different dark matter (DM) models predict various clustering properties, i.e. the possibility of DM to form massive objects on different scales. The lower mass limit of these objects according to [1, 2]. may be of the order of planetary masses. The gravitational microlensing can be used to confirm or to reject the existence of such structures and therefore to argue in favor or against concrete DM theories. There are observational programs (OGLE, EROS etc) yielding the light curves of a remote objects in high amplification events (HAE) due to microlensing on foreground masses of the Galaxy. In case when the foreground mass is an extended one, then the light curve in HAE must differ from the light curve due to ordinary microlensing on a point mass. However the question is: what is the value of this difference and is it possible to register this difference with modern observational facilities. This question has been studied elsewhere [3–5] by means of special model lens mappings. In this paper we study this problem starting directly from mass distribution of the extended structure. Namely, we consider microlensing on an extended DM clump with the cored spherically-symmetric mass profile (without a singularity in the center). We present examples of the amplification curves in both cases. Then we generate the amplification curves in case of the extended clump model for different values R, γ when the clump moves uniformly with respect to the line of sight with some impact parameter p and velocity V. These curves are then fitted with the point microlens model (with free parameters p and V) and we estimate the difference between the curves. The general outcome is that the amplification curves in case of the extended clumps are very similar to those in case of the point microlens (with appropriately chosen parameters p and V that cannot be derived from observations independently), and it would be difficult to distinguish them on the basis of observations if we deal with
The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas
NASA Astrophysics Data System (ADS)
Shariff, Karim; Cuzzi, Jeffrey N.
2015-05-01
In the subject of planetesimal formation, several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Fully nonlinear simulations using the two-fluid model are carried out (almost) up to the time when a central density singularity forms. We refer to this as the collapse time. The end result of the study is a parametrization of the collapse time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject in a particular situation. An important effect that determines the collapse time is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure, which retards particle collapse and can lead to oscillation in the size and density of the clump. In the limit of particles perfectly coupled to the gas, the characteristic ratio of gravitational force to gas pressure becomes relevant and defines a two-phase Jeans parameter, {{J}t}, which is the classical Jeans parameter with the speed of sound replaced by an effective wave speed in the coupled two-fluid medium. The parameter {{J}t} remains useful even away from the perfect coupling limit because it makes the simulation results insensitive to the initial density ratio of particles to gas (Φ0) as a separate parameter. A simple ordinary differential equation model is developed. It takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit {{J}t}\\to 0, collapse time equals the self-sedimentation time, which is inversely proportional to the Stokes number. As {{J}t} increases, the collapse time decreases with {{J}t} and eventually becomes approximately equal to the dynamical time. Values of collapse
NASA Technical Reports Server (NTRS)
Wang, Tongjiang; Davila, Joseph M.
2014-01-01
Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 solar radius as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066).We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50 deg. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.
NASA Astrophysics Data System (ADS)
Liang, Jun; Zhang, Fang-Hui; Zhang, Wei; Zhang, Jing
2014-01-01
By utilizing the improved Damour-Ruffini method with a new tortoise transformation, we study the Hawking radiation of Dirac particles from a general dynamical spherically symmetric black hole. In the improved Damour-Ruffini method, the position of the event horizon of the black hole is an undetermined function, and the temperature parameter κ is an undetermined constant. By requiring the Dirac equation to be the standard wave equation near the event horizon of the black hole, κ can be determined automatically. Therefore, the Hawking temperature can be obtained. The result is consistent with that of the Hawking radiation of scalar particles.
NASA Astrophysics Data System (ADS)
Kiess, Thomas E.
We resolve a metric singularity at large r that is due to the introduction of the cosmological constant Λ in simple static spherically symmetric systems in classical general relativity for a mass bounded within a radius r0. For the metric to be nonsingular, we find that ordinary matter must exist beyond r0, and that mass densities and Λ must have spatial ranges. These features can be developed covariantly and can ameliorate discrepancies between theoretical values of Λ and those derived from astronomical observations. Requiring a nonsingular metric in classical general relativistic modeling of this and other physical systems has the potential to offer suggestive insights into cosmological parameters.
Black holes in loop quantum gravity: the complete space-time.
Gambini, Rodolfo; Pullin, Jorge
2008-10-17
We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.
(n+1)-dimensional spherically symmetric expanding structures in R2-gravity
NASA Astrophysics Data System (ADS)
Ebrahimi, Esmaeil
2015-05-01
In this work, we consider higher-dimensional structures in R2-gravity in an expanding background. We assume a Ricci scalar constant background and use this assumption as the basic constraint to find solutions. Two classes of solutions are presented in which every one includes naked singularity and wormhole geometries. Both classes of solutions show inflationary phase of expansion favored by recent acceleration of the universe. Traversability of the wormhole solutions is discussed. The possibility of satisfying or violating the weak energy condition (WEC) for wormholes is explored. For one class of solutions, particular choices of constants result in wormholes which satisfy the WEC all over the spacetime.
NASA Astrophysics Data System (ADS)
Yao, Yuqi; Wang, Yao; Barbour, Randall L.; Graber, Harry L.; Chang, Jenghwa
1996-02-01
We present analytic expressions for the amplitude and phase of photon-density waves in strongly scattering, spherically symmetric, two-layer media containing a spherical object. This layered structure is a crude model of multilayered tissues whose absorption and scattering coefficients lie within a range reported in the literature for most tissue types. The embedded object simulates a pathology, such as a tumor. The normal-mode-series method is employed to solve the inhomogeneous Helmholtz equation in spherical coordinates, with suitable boundary conditions. By comparing the total field at points in the outer layer at a fixed distance from the origin when the object is present and when it is absent, we evaluate the potential sensitivity of an optical imaging system to inhomogeneities in absorption and scattering. For four types of background media with different absorption and scattering properties, we determine the modulation frequency that achieves an optimal compromise between signal-detection reliability and sensitivity to the presence of an object, the minimum detectable object radius, and the smallest detectable change in the absorption and scattering coefficients for a fixed object size. Our results indicate that (1) enhanced sensitivity to the object is achieved when the outer layer is more absorbing or scattering than the inner layer; (2) sensitivity to the object increases with the modulation frequency, except when the outer layer is the more absorbing; (3) amplitude measurements are proportionally more sensitive to a change in absorption, phase measurements are proportionally more sensitive to a change in scattering, and phase measurements exhibit a much greater capacity for distinguishing an absorption perturbation from a scattering perturbation.
NASA Astrophysics Data System (ADS)
Lee, Kuo-Wei
2016-09-01
We prove the existence and uniqueness of the Dirichlet problem for the spacelike, spherically symmetric, constant mean curvature equation with symmetric boundary data in the extended Schwarzschild spacetime. As an application, we completely solve the CMC foliation conjecture which is proposed by Malec and Murchadha (2003 Phys. Rev. D 68 124019).
NASA Astrophysics Data System (ADS)
Momeni, Davood; Chattopadhyay, Surajit; Myrzakulov, Ratbay
2015-05-01
In this paper, we study the Ehlers' transformation (sometimes called gravitational duality rotation) for reciprocal static metrics. First, we introduce the concept of reciprocal metric. We prove a theorem which shows how we can construct a certain new static solution of Einstein field equations using a seed metric. Later, we investigate the family of stationary spacetimes of such reciprocal metrics. The key here is a theorem from Ehlers', which relates any static vacuum solution to a unique stationary metric. The stationary metric has a magnetic charge. The spacetime represents Newman-Unti-Tamburino (NUT) solutions. Since any stationary spacetime can be decomposed into a 1 + 3 time-space decomposition, Einstein field equations for any stationary spacetime can be written in the form of Maxwell's equations for gravitoelectromagnetic fields. Further, we show that this set of equations is invariant under reciprocal transformations. An additional point is that the NUT charge changes the sign. As an instructive example, by starting from the reciprocal Schwarzschild as a spherically symmetric solution and reciprocal Morgan-Morgan disk model as seed metrics we find their corresponding stationary spacetimes. Starting from any static seed metric, performing the reciprocal transformation and by applying an additional Ehlers' transformation we obtain a family of NUT spaces with negative NUT factor (reciprocal NUT factors).
Foliation dependence of black hole apparent horizons in spherical symmetry
NASA Astrophysics Data System (ADS)
Faraoni, Valerio; Ellis, George F. R.; Firouzjaee, Javad T.; Helou, Alexis; Musco, Ilia
2017-01-01
Numerical studies of gravitational collapse to black holes make use of apparent horizons, which are intrinsically foliation dependent. We expose the problem and discuss possible solutions using the Hawking-Hayward quasilocal mass. In spherical symmetry, we present a physically sensible approach to the problem by restricting to spherically symmetric spacetime slicings. In spherical symmetry, the apparent horizons enjoy a restricted gauge independence in any spherically symmetric foliation, but physical quantities associated with them, such as surface gravity and temperature, are fully gauge dependent. The widely used comoving and Kodama foliations, which are of particular interest, are discussed in detail as examples.
New half-range differential approximation for spherically-symmetric radiative transfer.
NASA Technical Reports Server (NTRS)
Moreno, J. B.; Greber, I.
1971-01-01
A new half-range differential approximation for radiative transfer with spherical symmetry is presented. The development is motivated by the various failures of existing differential approximations in determining emissive-power distributions and heat transfer for concentric-spheres problems. The new approach represents a modification of the four-moment double spherical-harmonics method, to which it reduces in the planar limit. The difference is effected by relocating the discontinuity of the assumed directional distribution of radiation intensity. The shift takes the discontinuity from precisely on the division between radially inward and radially outward, to just within the radially-outward directional half range. The method is tested on a variety of concentric spheres problems with and without internal heat sources, reproducing all the important features of the exact results.
Casimir Densities for Two Concentric Spherical Shells in the Global Monopole Space-Time
NASA Astrophysics Data System (ADS)
Saharian, A. A.; Setare, M. R.
The quantum vacuum effects are investigated for a massive scalar field with general curvature coupling and obeying the Robin boundary conditions given on two concentric spherical shells with radii a and b in the (D+1)-dimensional global monopole background. The expressions are derived for the Wightman function, the vacuum expectation values of the field square, the vacuum energy density, radial and azimuthal stress components in the region between the shells. A regularization procedure is carried out by making use of the generalized Abel-Plana formula for the series over zeros of combinations of the cylinder functions. This formula allows us to extract from the vacuum expectation values the parts due to a single sphere on background of the global monopole gravitational field, and to present the "interference" parts in terms of exponentially convergent integrals, useful, in particular, for numerical evaluations. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction terms. The first one contains well-known surface divergences and needs a further regularization. The interaction forces between the spheres are finite for all values a
Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory
NASA Astrophysics Data System (ADS)
Greenwald, Jared; Lenells, Jonatan; Lu, J. X.; Satheeshkumar, V. H.; Wang, Anzhong
2011-10-01
We systematically study black holes in the Horava-Lifshitz theory by following the kinematic approach, in which a horizon is defined as the surface at which massless test particles are infinitely redshifted. Because of the nonrelativistic dispersion relations, the speed of light is unlimited, and test particles do not follow geodesics. As a result, there are significant differences in causal structures and black holes between general relativity (GR) and the Horava-Lifshitz theory. In particular, the horizon radii generically depend on the energies of test particles. Applying them to the spherical static vacuum solutions found recently in the nonrelativistic general covariant theory of gravity, we find that, for test particles with sufficiently high energy, the radius of the horizon can be made as small as desired, although the singularities can be seen, in principle, only by observers with infinitely high energy. In these studies, we pay particular attention to the global structure of the solutions, and find that, because of the foliation-preserving-diffeomorphism symmetry, Diff(M,F), they are quite different from the corresponding ones given in GR, even though the solutions are the same. In particular, the Diff(M,F) does not allow Penrose diagrams. Among the vacuum solutions, some give rise to the structure of the Einstein-Rosen bridge, in which two asymptotically flat regions are connected by a throat with a finite nonzero radius. We also study slowly rotating solutions in such a setup, and obtain all the solutions characterized by an arbitrary function A0(r). The case A0=0 reduces to the slowly rotating Kerr solution obtained in GR.
Black holes and global structures of spherical spacetimes in Horava-Lifshitz theory
Greenwald, Jared; Satheeshkumar, V. H.; Lenells, Jonatan; Lu, J. X.; Wang Anzhong
2011-10-15
We systematically study black holes in the Horava-Lifshitz theory by following the kinematic approach, in which a horizon is defined as the surface at which massless test particles are infinitely redshifted. Because of the nonrelativistic dispersion relations, the speed of light is unlimited, and test particles do not follow geodesics. As a result, there are significant differences in causal structures and black holes between general relativity (GR) and the Horava-Lifshitz theory. In particular, the horizon radii generically depend on the energies of test particles. Applying them to the spherical static vacuum solutions found recently in the nonrelativistic general covariant theory of gravity, we find that, for test particles with sufficiently high energy, the radius of the horizon can be made as small as desired, although the singularities can be seen, in principle, only by observers with infinitely high energy. In these studies, we pay particular attention to the global structure of the solutions, and find that, because of the foliation-preserving-diffeomorphism symmetry, Diff(M,F), they are quite different from the corresponding ones given in GR, even though the solutions are the same. In particular, the Diff(M,F) does not allow Penrose diagrams. Among the vacuum solutions, some give rise to the structure of the Einstein-Rosen bridge, in which two asymptotically flat regions are connected by a throat with a finite nonzero radius. We also study slowly rotating solutions in such a setup, and obtain all the solutions characterized by an arbitrary function A{sub 0}(r). The case A{sub 0}=0 reduces to the slowly rotating Kerr solution obtained in GR.
Cioslowski, Jerzy; Albin, Joanna
2013-09-14
Energies E(N) of assemblies of equicharged particles subject to spherically symmetric power-law confining potentials vary in a convoluted fashion with the particle totalities N. Accurate rigorous upper bounds to these energies, which are amenable to detailed mathematical analysis, are found to comprise terms with smooth, oscillatory, and fluctuating dependences on N. The smooth energy component is obtained as a power series in N(-2/3) with the first two terms corresponding to the bulk and Madelung energies. The oscillatory component possesses the large-N asymptotics given by a product of N(1/(λ + 1)), where λ is the power-law exponent, and a function periodic in N(1/3). The amplitude of the fluctuating component, which originates mostly from the irregular dependence of the Thomson energy E(Th)(n) on n, also scales like N(1/(λ + 1)).
NASA Astrophysics Data System (ADS)
Berberian, John Edwin
1999-01-01
A new framework is presented for analysing the spherically symmetric Einstein field equations for a zero-mass scalar field. The framework consists of a coordinate system (p, q), where the coordinate p is the scalar field, and q is a coordinate chosen to be orthogonal to p. This idea allows for a reduction of the field equations into a system of two first order partial differential equations for the areal metric function gqq and a mass function m . The metric coefficients in this coordinate system then take on values which are simply related to the scalars of the problem: 1->f˙1 ->f,gq q and-via the field equations-the scalar curvature R as well. The scalar field coordinate system is shown to have many advantages. Many of the known exact solutions (e.g. static, Roberts) are represented simply, and new self- similar solutions are derived. The framework is then applied to the problem of matching spherically symmetric scalar-tensor vacuum solutions to a homogeneous and isotropic dust solution (e.g. scalar- tensor Einstein-Straus swiss cheese solutions, scalar- tensor Oppenheimer-Snyder dust ball collapse). Scalar field coordinates are shown to be ideal for such an application. We derive the necessary matching conditions in scalar field coordinates, and show how they imply a natural extension of the Schücking condition for spherically symmetric vacuum in general relativity. The problem of finding a vacuum solution which matches a given homogeneous and isotropic solution is examined. It is found that the matching conditions are sufficient to guarantee local existence and uniqueness of the vacuum solution if it is assumed that the scalar field has neither maxima nor minima on the matching interface. In order to find explicit matched solutions, criteria are developed to screen known exact vacuum solutions for matchability, and procedures are given for determining the details of the homogeneous and isotropic solution (curvature constant, comoving radial coordinate of the
NASA Astrophysics Data System (ADS)
Zeng, Huihui
2017-10-01
For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.
NASA Astrophysics Data System (ADS)
Pfister, Herbert
2011-04-01
In comparison to previous existence proofs for static and spherically symmetric perfect fluid stars in general relativity the new proof applies to a more general class of equations of state. In the star's interior we allow for piecewise Lipschitz continuous functions, including in this way the physically important case of phase transitions. Near the star's surface we allow for even more general functions, thereby including a large class of polytropic equations of state. Furthermore, the proof technique proceeds along standard techniques of functional analysis (Banach's fixed point theorem), and therefore applies in a similar manner to static stars in Newtonian gravity, and perhaps to rotating Newtonian and Einsteinian stars. In detail, the Einstein field equations for static perfect fluid stars are transformed to a system of coupled nonlinear integral equations being valid equally in the matter region and in the vacuum exterior. These integral equations are interpreted as a mapping in a Banach space. With the standard iteration technique, beginning with appropriate start functions, it is proven that the mapping has a unique fixed point, and that the solutions have appropriate regularity properties determined by the properties of the equation of state. The introduction gives an overview of earlier work on such systems, on the question of sphericity of static fluid stars, and on possible extensions of the above methods to rotating Newtonian and Einsteinian stars. An outlook addresses the question whether our proof method may be extensible to piecewise Hölder continuous equations of state.
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.
Electrodynamics and spacetime geometry: Astrophysical applications
NASA Astrophysics Data System (ADS)
Cabral, Francisco; Lobo, Francisco S. N.
2017-07-01
After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws, where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena, such as the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.
NASA Astrophysics Data System (ADS)
Macías-Díaz, J. E.; Medina-Ramírez, I. E.; Puri, A.
2009-09-01
In the present work, the connection of the generalized Fisher-KPP equation to physical and biological fields is noted. Radially symmetric solutions to the generalized Fisher-KPP equation are considered, and analytical results for the positivity and asymptotic stability of solutions to the corresponding time-independent elliptic differential equation are quoted. An energy analysis of the generalized theory is carried out with further physical applications in mind, and a numerical method that consistently approximates the energy of the system and its rate of change is presented. The method is thoroughly tested against analytical and numerical results on the classical Fisher-KPP equation, the Heaviside equation, and the generalized Fisher-KPP equation with logistic nonlinearity and Heaviside initial profile, obtaining as a result that our method is highly stable and accurate, even in the presence of discontinuities. As an application, we establish numerically that, under the presence of suitable initial conditions, there exists a threshold for the relaxation time with the property that solutions to the problems considered are nonnegative if and only if the relaxation time is below a critical value. An analytical prediction is provided for the Heaviside equation, against which we verify the validity of our computational code, and numerical approximations are provided for several generalized Fisher-KPP problems.
Fractal boundary basins in spherically symmetric {phi}{sup 4} theory
Honda, Ethan
2010-07-15
Results are presented from numerical simulations of the flat-space nonlinear Klein-Gordon equation with an asymmetric double-well potential in spherical symmetry. Exit criteria are defined for the simulations that are used to help understand the boundaries of the basins of attraction for Gaussian 'bubble' initial data. The first exit criterion, based on the immediate collapse or expansion of bubble radius, is used to observe the departure of the scalar field from a static intermediate attractor solution. The boundary separating these two behaviors in parameter space is smooth and demonstrates a time-scaling law with an exponent that depends on the asymmetry of the potential. The second exit criterion differentiates between the creation of an expanding true-vacuum bubble and dispersion of the field leaving the false vacuum; the boundary separating these basins of attraction is shown to demonstrate fractal behavior. The basins are defined by the number of bounces that the field undergoes before inducing a phase transition. A third, hybrid exit criterion is used to determine the location of the boundary to arbitrary precision and to characterize the threshold behavior. The possible effects this behavior might have on cosmological phase transitions are briefly discussed.
Qian, Shizhi; Joo, Sang W; Hou, Wen-Sheng; Zhao, Xuxin
2008-05-20
The electrophoretic motion of a spherical nanoparticle, subject to an axial electric field in a nanotube filled with an electrolyte solution, has been investigated using a continuum theory, which consists of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. In particular, the effects of nonuniform surface charge distributions around the nanoparticle on its axial electrophoretic motion are examined with changes in the bulk electrolyte concentration and the surface charge of the tube's wall. A particle with a nonuniform charge distribution is shown to induce a corresponding complex ionic concentration field, which in turn influences the electric field and the fluid motion surrounding the particle and thus its electrophoretic velocity. As a result, contrary to the relatively simple dynamics of a particle with a uniform surface charge, dominated by the irradiating electrostatic force, that with a nonuniform surface charge distribution shows various intriguing behaviors due to the additional interplay of the nonuniform electro-osmotic effects.
Sound wave generation by a spherically symmetric outburst and AGN feedback in galaxy clusters
NASA Astrophysics Data System (ADS)
Tang, Xiaping; Churazov, Eugene
2017-07-01
We consider the evolution of an outburst in a uniform medium under spherical symmetry, having in mind active galactic nucleus feedback in the intracluster medium. For a given density and pressure of the medium, the spatial structure and energy partition at a given time tage (since the onset of the outburst) are fully determined by the total injected energy Einj and the duration tb of the outburst. We are particularly interested in the late phase evolution when the strong shock transforms into a sound wave. We studied the energy partition during such transition with different combinations of Einj and tb. For an instantaneous outburst with tb → 0, which corresponds to the extension of classic Sedov-Taylor solution with counter-pressure, the fraction of energy that can be carried away by sound waves is ≲12 per cent of Einj. As tb increases, the solution approaches the 'slow piston' limit, with the fraction of energy in sound waves approaching zero. We then repeat the simulations using radial density and temperature profiles measured in Perseus and M87/Virgo clusters. We find that the results with a uniform medium broadly reproduce an outburst in more realistic conditions once proper scaling is applied. We also develop techniques to map intrinsic properties of an outburst (Einj, tb and tage) to the observables like the Mach number of the shock and radii of the shock and ejecta. For the Perseus cluster and M87, the estimated (Einj, tb and tage) agree with numerical simulations tailored for these objects with 20-30 per cent accuracy.
Perturbative spacetimes from Yang-Mills theory
NASA Astrophysics Data System (ADS)
Luna, Andrés; Monteiro, Ricardo; Nicholson, Isobel; Ochirov, Alexander; O'Connell, Donal; Westerberg, Niclas; White, Chris D.
2017-04-01
The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.
Chang Yiren; Hsu Long; Chi Sien
2006-06-01
Since their invention in 1986, optical tweezers have become a popular manipulation and force measurement tool in cellular and molecular biology. However, until recently there has not been a sophisticated model for optical tweezers on trapping cells in the ray-optics regime. We present a model for optical tweezers to calculate the optical force upon a spherically symmetric multilayer sphere representing a common biological cell. A numerical simulation of this model shows that not only is the magnitude of the optical force upon a Chinese hamster ovary cell significantly three times smaller than that upon a polystyrene bead of the same size, but the distribution of the optical force upon a cell is also much different from that upon a uniform particle, and there is a 30% difference in the optical trapping stiffness of these two cases. Furthermore, under a small variant condition for the refractive indices of any adjacent layers of the sphere, this model provides a simple approximation to calculate the optical force and the stiffness of an optical tweezers system.
NASA Astrophysics Data System (ADS)
Bradford, R. A. W.
2015-10-01
Stationary, static, spherically symmetric solutions of the Maxwell-Dirac system, treated as classical fields, have been found which are localised and normalisable. The solutions apply to any bound energy eigenvalue in the range 0 < E < m, where m is the bare mass in the Dirac equation. A point charge of any magnitude and either sign may be placed at the origin and the solutions remain well behaved and bound. However, no such central charge is necessary to result in a bound solution. As found previously by Radford, the magnetic flux density is equal to that of a monopole at the origin. However, no monopole is present, the magnetic flux being a result of the dipole moment distribution of the Dirac field. The Dirac field magnetic dipole moment is aligned with the magnetic flux density and so the resulting magnetic self-energy is negative. It is this which results in the states being bound (E < m). The case which omits any central point charge is therefore a self-sustaining bound state solution of the Maxwell-Dirac system which is localised, normalisable, and requires no arbitrarily added "external" features (i.e., it is a soliton). As far as the author is aware, this is the first time that such an exact solution with a positive energy eigenvalue has been reported. However, the solution is not unique since the energy eigenvalue is arbitrary within the range 0 < E < m. The stability of the solution has not been addressed.
Temperature and entropy of Schwarzschild de Sitter space-time
NASA Astrophysics Data System (ADS)
Shankaranarayanan, S.
2003-04-01
In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity—the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild de Sitter space-time, we apply the method of complex paths to three different coordinate systems—spherically symmetric, Painlevé, and Lemaître. We show that the equilibrium temperature in Schwarzschild de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild de Sitter space-time satisfies the D-bound conjecture.
Fate of inhomogeneity in Schwarzschild-deSitter space-time
NASA Astrophysics Data System (ADS)
Nambu, Yasusada
1994-03-01
We investigate the global structure of the space-time with a spherically symmetric inhomogeneity using a metric junction, and classify all possible types. We found that a motion with a negative gravitational mass is possible although the energy condition of the matter is not violated. Using the result, formation of black hole and worm hole during the inflationary era is discussed.
Quantum spacetime of a charged black hole
NASA Astrophysics Data System (ADS)
Gambini, Rodolfo; Capurro, Esteban Mato; Pullin, Jorge
2015-04-01
We quantize spherically symmetric electrovacuum gravity. The algebra of Hamiltonian constraints can be made Abelian via a rescaling and linear combination with the diffeomorphism constraint. As a result the constraint algebra is a true Lie algebra. We complete the Dirac quantization procedure using loop quantum gravity techniques. We present explicitly the exact solutions of the physical Hilbert space annihilated by all constraints. The resulting quantum spacetimes resolve the singularity present in the classical theory inside charged black holes and allows us to extend the spacetime through where the singularity used to be into new regions. We argue that quantum discreteness of spacetime may also play a role in stabilizing the Cauchy horizons, though backreaction calculations are needed to confirm this point.
Gislason, E.A.; Polak-Dingels, P.; Rajan, M.S. )
1990-08-15
Total cross sections have been measured for Li{sup +} ions scattered by N{sub 2} and CO in the range {ital E}{Theta}{sub {ital R}}=5--1000 eV deg. Here {ital E} is the lab energy of the Li{sup +} beam, and {Theta}{sub {ital R}} is the resolution angle of the apparatus. From the data the spherically symmetric parts of the intermolecular potentials have been determined over a wide range of Li{sup +}-molecule distances including the attractive well region. The results are compared with other theoretical and experimental work on these systems.
Spacetime of Constant Scalar Curvature in N = 1 Supergravity
Gunara, Bobby Eka
2010-12-23
In this short paper we show the existence of solitonic solutions of four dimensional ungauged N = 1 supergravity coupled to arbitrary vector and chiral multiplets whose Ricci scalar curvature is constant. The Ricci scalar of spacetimes indeed depends on the {sigma}-model, namely the complex scalars and their first derivative. Then, we give two explicit models, namely static domain walls and static spherical symmetric black holes which are related to our previous works.
NASA Astrophysics Data System (ADS)
Shestakova, Tatyana P.
2015-01-01
Among theoretical issues in General Relativity the problem of constructing its Hamiltonian formulation is still of interest. The most of attempts to quantize Gravity are based upon Dirac generalization of Hamiltonian dynamics for system with constraints. At the same time there exists another way to formulate Hamiltonian dynamics for constrained systems guided by the idea of extended phase space. We have already considered some features of this approach in the previous MG12 Meeting by the example of a simple isotropic model. Now we apply the approach to a generalized spherically symmetric model which imitates the structure of General Relativity much better. In particular, making use of a global BRST symmetry and the Noether theorem, we construct the BRST charge that generates correct gauge transformations for all gravitational degrees of freedom.
Symmetries in flat space-times
Duncan, D.C.
1989-01-01
In the following flat spacetimes with a high degree of symmetry are studied. The first part completes the classification of all homogeneous flat spacetimes begun by Wolf. The second part explores classification of flat spacetimes with symmetry groups having codimension one orbits. In this case attention is restricted to spacetimes which model a centrally symmetric gravitational field.
NASA Astrophysics Data System (ADS)
Ben Achour, Jibril; Brahma, Suddhasattwa; Marcianò, Antonino
2017-07-01
Using self-dual Ashtekar variables, we investigate (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once local (pointwise) holonomy corrections are introduced, which leads to several obstructions in the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which have been suggested to be an effective signature change of the metric in the deep quantum region. We show in this paper that both those complications disappear when working with self-dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations. A possible path towards quantization of this model is briefly discussed.
NASA Astrophysics Data System (ADS)
Hillman, David
1995-11-01
Combinatorial spacetimes are a class of dynamical systems in which finite pieces of spacetime contain finite amounts of information. Most of the guiding principles for designing these systems are drawn from general relativity: the systems are deterministic; spacetime may be foliated into Cauchy surfaces; the law of evolution is local (there is a light-cone structure); and the geometry evolves locally (curvature may be present; big bangs are possible). However, the systems differ from general relativity in that spacetime is a combinatorial object, constructed by piecing together copies of finitely many types of allowed neighborhoods in a prescribed manner. Hence at least initially there is no metric, no concept of continuity or diffeomorphism. The role of diffeomorphism, however, is played by something called a "local equivalence map.". Here I attempt to begin to lay the mathematical foundations for the study of these systems. (Examples of such systems already exist in the literature. The most obvious is reversible cellular automata, which are flat combinatorial spacetimes. Other related systems are structurally dynamic cellular automata, L systems and parallel graph grammars.) In the 1+1-dimensional oriented case, sets of spaces may be described equivalently by matrices of nonnegative integers, directed graphs, or symmetric tensors; local equivalences between space sets are generated by simple matrix transformations. These equivalence maps turn out to be closely related to the flow equivalence maps between subshifts of finite type studied in symbolic dynamics. Also, the symmetric tensor algebra generated by equivalence transformations turns out to be isomorphic to the abstract tensor algebra generated by commutative cocommutative bialgebras. In higher dimensions I attempt to follow the same basic model, which is to define the class of n-dimensional space set descriptions and then generate local equivalences between these descriptions using elementary
Hydrodynamics in type B warped spacetimes
Carot, J.; Nunez, L.A.
2005-10-15
We discuss certain general features of type B warped spacetimes which have important consequences on the material content they may admit and its associated dynamics. We show that, for warped B spacetimes, if shear and anisotropy are nonvanishing, they have to be proportional. We also study some of the physics related to the warping factor and of the underlying decomposable metric. Finally we explore the only possible cases compatible with a type B warped geometry which satisfy the dominant energy conditions. As an example of the above mentioned consequences we consider a radiating fluid and two nonspherically symmetric metrics which depend upon an arbitrary parameter a, such that for a=0 spherical symmetry is recovered.
Anisotropic compact stars in Karmarkar spacetime
NASA Astrophysics Data System (ADS)
Newton Singh, Ksh.; Pant, Neeraj; Govender, M.
2017-01-01
We present a new class of solutions to the Einstein field equations for an anisotropic matter distribution in which the interior space-time obeys the Karmarkar condition. The necessary and sufficient condition required for a spherically symmetric space-time to be of Class One reduces the gravitational behavior of the model to a single metric function. By assuming a physically viable form for the grr metric potential we obtain an exact solution of the Einstein field equations which is free from any singularities and satisfies all the physical criteria. We use this solution to predict the masses and radii of well-known compact objects such as Cen X-3, PSR J0348+0432, PSR B0943+10 and XTE J1739-285.
Conformally symmetric traversable wormholes in f( G) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
2016-11-01
We discuss non-static conformally symmetric traversable wormholes for spherically symmetric spacetime using the model f(G)=α Gn, where n>0 and α is an arbitrary constant. We investigate wormhole solutions by taking two types of shape function and found that physically realistic wormholes exist only for even values of n. We also check the validity of flare-out condition, required for wormhole construction, for the shape functions deduced from two types of equation of state. It is found that this condition is satisfied by these functions in all cases except phantom case with non-static conformal symmetry.
Five-dimensional spherical gravitational collapse of anisotropic fluid with cosmological constant
NASA Astrophysics Data System (ADS)
Khan, Suhail; Shah, Hassan; Abbas, Ghulam
Our aim is to study five-dimensional spherically symmetric anisotropic collapse with a positive cosmological constant (PCC). For this purpose, five-dimensional spherically symmetric and Schwarzschild-de Sitter metrics are chosen in the interior and exterior regions respectively. A set of junction conditions is derived for the smooth matching of interior and exterior spacetimes. The apparent horizon is calculated and its physical significance is studied. It comes out that the whole collapsing process is influenced by the cosmological constant. The collapsing process under the influence of cosmological constant slows down and black hole size also reduced.
Hamiltonian of a spinning test particle in curved spacetime
Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra
2009-11-15
Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type S{sub Kerr}S (and S{sub Kerr}{sup 2}) through 3PN order, S{sub Kerr} being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.
Hamiltonian of a spinning test-particle in curved spacetime
NASA Astrophysics Data System (ADS)
Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra
2010-02-01
Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test-particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase-space algebra in the Newton-Wigner spin supplementary condition (SSC), suitably generalized to curved spacetime, and find that the phase-space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner (ADM) canonical Hamiltonian computed in PN theory in the test-particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type SKerr, (and SKerr^2) through 3PN order, SKerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test-particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order. )
Hamiltonian of a spinning test particle in curved spacetime
NASA Astrophysics Data System (ADS)
Barausse, Enrico; Racine, Etienne; Buonanno, Alessandra
2009-11-01
Using a Legendre transformation, we compute the unconstrained Hamiltonian of a spinning test particle in a curved spacetime at linear order in the particle spin. The equations of motion of this unconstrained Hamiltonian coincide with the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac brackets to derive the constrained Hamiltonian and the corresponding phase space algebra in the Newton-Wigner spin supplementary condition, suitably generalized to curved spacetime, and find that the phase space algebra (q,p,S) is canonical at linear order in the particle spin. We provide explicit expressions for this Hamiltonian in a spherically symmetric spacetime, both in isotropic and spherical coordinates, and in the Kerr spacetime in Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when expanded in post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner canonical Hamiltonian computed in PN theory in the test particle limit. Notably, we recover the known spin-orbit couplings through 2.5PN order and the spin-spin couplings of type SKerrS (and SKerr2) through 3PN order, SKerr being the spin of the Kerr spacetime. Our method allows one to compute the PN Hamiltonian at any order, in the test particle limit and at linear order in the particle spin. As an application we compute it at 3.5PN order.
Relativistic positioning in Schwarzschild space-time
NASA Astrophysics Data System (ADS)
Puchades, Neus; Sáez, Diego
2015-04-01
In the Schwarzschild space-time created by an idealized static spherically symmetric Earth, two approaches -based on relativistic positioning- may be used to estimate the user position from the proper times broadcast by four satellites. In the first approach, satellites move in the Schwarzschild space-time and the photons emitted by the satellites follow null geodesics of the Minkowski space-time asymptotic to the Schwarzschild geometry. This assumption leads to positioning errors since the photon world lines are not geodesics of any Minkowski geometry. In the second approach -the most coherent one- satellites and photons move in the Schwarzschild space-time. This approach is a first order one in the dimensionless parameter GM/R (with the speed of light c=1). The two approaches give different inertial coordinates for a given user. The differences are estimated and appropriately represented for users located inside a great region surrounding Earth. The resulting values (errors) are small enough to justify the use of the first approach, which is the simplest and the most manageable one. The satellite evolution mimics that of the GALILEO global navigation satellite system.
Resonant Dynamics and the Instability of Anti-de Sitter Spacetime.
Bizoń, Piotr; Maliborski, Maciej; Rostworowski, Andrzej
2015-08-21
We consider spherically symmetric Einstein-massless-scalar field equations with a negative cosmological constant in five dimensions and analyze the evolution of small perturbations of anti-de Sitter (AdS) spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing the instability of AdS under arbitrarily small perturbations.
Generalized Skyrmions and hairy black holes in asymptotically AdS4 spacetime
NASA Astrophysics Data System (ADS)
Perapechka, I.; Shnir, Ya.
2017-01-01
We investigate the properties of spherically symmetric black-hole solutions in the generalized Einstein-Skyrme model theory in four-dimensional asymptotically anti-de Sitter spacetime. The dependences of the Skyrmion fields on the cosmological constant and on the strength of the effective gravitational coupling are examined. We show that the increase of the absolute value of the cosmological constant qualitatively yields the same effect as increasing the effective gravitational coupling. We confirm that, similar to the model in asymptotically flat spacetime, a necessary condition for the existence of black holes with Skyrmionic hair is the inclusion of the Skyrme term.
Mezzacappa, A; Liebendörfer, M; Messer, O E; Hix, W R; Thielemann, F K; Bruenn, S W
2001-03-05
With exact three-flavor Boltzmann neutrino transport, we simulate the stellar core collapse, bounce, and postbounce evolution of a 13M star in spherical symmetry, the Newtonian limit, without invoking convection. In the absence of convection, prior spherically symmetric models, which implemented approximations to Boltzmann transport, failed to produce explosions. We consider exact transport to determine if these failures were due to the transport approximations made and to answer remaining fundamental questions in supernova theory. The model presented here is the first in a sequence of models beginning with different progenitors. In this model, a supernova explosion is not obtained.
Quantum corrected spherical collapse: A phenomenological framework
Ziprick, Jonathan; Kunstatter, Gabor
2010-08-15
A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter 'piles up' on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.
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
Computing spacetime curvature via differential-algebraic equations
Ashby, S.F.; Lee, S.L.; Petzold, L.R.; Saylor, P.E.; Seidel, E.
1996-01-01
The equations that govern the behavior of physical systems can often solved numerically using a method of lines approach and differential-algebraic equation (DAE) solvers. For example, such an approach can be used to solve the Einstein field equations of general relativity, and thereby simulate significant astrophysical events. In this paper, we describe some preliminary work in which two model problems in general relativity are formulated, spatially discretized, and then numerically solved as a DAE. In particular, we seek to reproduce the solution to the spherically symmetric Schwarzschild spacetime. This is an important testbed calculation in numerical relativity since the solution is the steady-state for the collision of two (or more) non-rotating black holes. Moreover, analytic late-time properties of the Schwarzschild spacetime are well known and can be used the accuracy of the simulation.
Causality and black holes in spacetimes with a preferred foliation
NASA Astrophysics Data System (ADS)
Bhattacharyya, Jishnu; Colombo, Mattia; Sotiriou, Thomas P.
2016-12-01
We develop a framework that facilitates the study of the causal structure of spacetimes with a causally preferred foliation. Such spacetimes may arise as solutions of Lorentz-violating theories, e.g. Hořava gravity. Our framework allows us to rigorously define concepts such as black/white holes and to formalize the notion of a ‘universal horizon’, that has been previously introduced in the simpler setting of static and spherically symmetric geometries. We also touch upon the issue of development and prove that universal horizons are Cauchy horizons when evolution depends on boundary data or asymptotic conditions. We establish a local characterisation of universal horizons in stationary configurations. Finally, under the additional assumption of axisymmetry, we examine under which conditions these horizons are cloaked by Killing horizons, which can act like usual event horizons for low-energy excitations.
Wormholes and nonsingular spacetimes in Palatini f (R ) gravity
NASA Astrophysics Data System (ADS)
Bambi, Cosimo; Cardenas-Avendano, Alejandro; Olmo, Gonzalo J.; Rubiera-Garcia, D.
2016-03-01
We reconsider the problem of f (R ) theories of gravity coupled to Born-Infeld theory of electrodynamics formulated in a Palatini approach, where metric and connection are independent fields. By studying electrovacuum configurations in a static and spherically symmetric spacetime, we find solutions which reduce to their Reissner-Nordström counterparts at large distances but undergo important nonperturbative modifications close to the center. Our new analysis reveals that the pointlike singularity is replaced by a finite-size wormhole structure, which provides a geodesically complete and thus nonsingular spacetime, despite the existence of curvature divergences at the wormhole throat. Implications of these results, in particular for the cosmic censorship conjecture, are discussed.
NASA Technical Reports Server (NTRS)
Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1976-01-01
A numerical method is presented of solving the radiative transfer equation in the comoving frame of a spherically symmetric expanding atmosphere in which both the line and the electron-scattering source function can depend on frequency (i.e., when there is partial frequency redistribution in the scattering process). This method is used to assess the adequacy of various assumptions regarding frequency redistribution in the comoving frame and to discuss the effects of electron scattering more accurately than previously possible. The methods developed here can be used in realistic model atmospheres to account for the (major) effects of electron scattering upon emergent flux profiles.
Closed Timelike Curves in Type II Non-Vacuum Spacetime
NASA Astrophysics Data System (ADS)
Ahmed, Faizuddin
2017-02-01
Here we present a cyclicly symmetric non-vacuum spacetime, admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The spacetime is asymptotically flat, free-from curvature singularities and a four-dimensional extension of the Misner space in curved spacetime. The spacetime is of type II in the Petrov classification scheme and the matter field pure radiation satisfy the energy condition.
Gravity induced from quantum spacetime
NASA Astrophysics Data System (ADS)
Beggs, Edwin J.; Majid, Shahn
2014-02-01
We show that tensoriality constraints in noncommutative Riemannian geometry in the two-dimensional bicrossproduct model quantum spacetime algebra [x, t] = λx drastically reduce the moduli of possible metrics g up to normalization to a single real parameter, which we interpret as a time in the past from which all timelike geodesics emerge and a corresponding time in the future at which they all converge. Our analysis also implies a reduction of moduli in n-dimensions and we study a suggested spherically symmetric classical geometry in n = 4 in detail, identifying two one-parameter subcases where the Einstein tensor matches that of a perfect fluid for (a) positive pressure, zero density and (b) negative pressure and positive density with ratio w_Q=-{1\\over 2}. The classical geometry is conformally flat and its geodesics motivate new coordinates which we extend to the quantum case as a new description of the quantum spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for n = 2 and includes the quantum Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as λ → 0. We also propose a ‘quantum Einstein tensor’ which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the quantum Ricci tensor and metric are viewed as deformations of their classical counterparts there would be an O(λ2) correction to the classical Einstein tensor and an O(λ) correction to the classical metric.
NASA Astrophysics Data System (ADS)
Peng, Jie; Zhu, Jianhua; Li, Tong
2016-06-01
The thermal lens effect of 2.1 μm Cr, Tm, Ho: YAG (CTH:YAG) solid-state laser under high pumping power condition is analyzed, and a symmetric spherical resonator which is insensitive to thermal focal length change is proposed to improve the beam quality of Fabry-Perot (F-P) resonator. Then the gradient-reflectivity mirror is introduced as output mirror to optimize the resonator mode and beam quality. Based on the scalar diffraction theory, the Fox-Li numerical iteration method and fast Fourier transform (FFT) algorithm are used to calculate the resonator mode and output power distribution of resonators with Gaussian, super-Gaussian and parabolic gradient mirror, respectively. By comparing the cavity loss and beam quality, one can find that the symmetric spherical resonator with a super-Gaussian mirror can provide the best output beam quality, it has the minimum cavity loss of 0.1907, the minimum far-field divergence angle of 1 mrad and the maximum power in the bucket (PIB) of 89.42%.
Geodesics in the static Mallett spacetime
Olum, Ken D.
2010-06-15
Mallett has exhibited a cylindrically symmetric spacetime containing closed timelike curves produced by a light beam circulating around a line singularity. I analyze the static version of this spacetime obtained by setting the intensity of the light to zero. Some null geodesics can escape to infinity, but all timelike geodesics in this spacetime originate and terminate at the singularity. Freely falling matter originally at rest quickly attains relativistic velocity inward and is destroyed at the singularity.
Symmetric Teleparallel Gravity: Some Exact Solutions and Spinor Couplings
NASA Astrophysics Data System (ADS)
Adak, Muzaffer; Sert, Özcan; Kalay, Mestan; Sari, Murat
2013-12-01
In this paper, we elaborate on the symmetric teleparallel gravity (STPG) written in a non-Riemannian space-time with nonzero nonmetricity, but zero torsion and zero curvature. First, we give a prescription for obtaining the nonmetricity from the metric in a peculiar gauge. Then, we state that under a novel prescription of parallel transportation of a tangent vector in this non-Riemannian geometry, the autoparallel curves coincide with those of the Riemannian space-times. Subsequently, we represent the symmetric teleparallel theory of gravity by the most general quadratic and parity conserving Lagrangian with lagrange multipliers for vanishing torsion and curvature. We show that our Lagrangian is equivalent to the Einstein-Hilbert Lagrangian for certain values of coupling coefficients. Thus, we arrive at calculating the field equations via independent variations. Then, we obtain in turn conformal, spherically symmetric static, cosmological and pp-wave solutions exactly. Finally, we discuss a minimal coupling of a spin-1/2 field to STPG.
Scalar hair on the black hole in asymptotically anti--de Sitter spacetime
Torii, Takashi; Maeda, Kengo; Narita, Makoto
2001-08-15
We examine the no-hair conjecture in asymptotically anti--de Sitter (AdS) spacetime. First, we consider a real scalar field as the matter field and assume static spherically symmetric spacetime. Analysis of the asymptotics shows that the scalar field must approach the extremum of its potential. Using this fact, it is proved that there is no regular black hole solution when the scalar field is massless or has a 'convex' potential. Surprisingly, while the scalar field has a growing mode around the local minimum of the potential, there is no growing mode around the local maximum. This implies that the local maximum is a kind of 'attractor' of the asymptotic scalar field. We give two examples of the new black hole solutions with a nontrivial scalar field configuration numerically in the symmetric or asymmetric double well potential models. We study the stability of these solutions by using the linear perturbation method in order to examine whether or not the scalar hair is physical. In the symmetric double well potential model, we find that the potential function of the perturbation equation is positive semidefinite in some wide parameter range and that the new solution is stable. This implies that the black hole no-hair conjecture is violated in asymptotically AdS spacetime.
Spherical gravitational collapse in N dimensions
Goswami, Rituparno; Joshi, Pankaj S.
2007-10-15
We investigate here spherically symmetric gravitational collapse in a space-time with an arbitrary number of dimensions and with a general type I matter field, which is a broad class that includes most of the physically reasonable matter forms. We show that given the initial data for matter in terms of the initial density and pressure profiles at an initial surface t=t{sub i} from which the collapse evolves, there exist the rest of the initial data functions and classes of solutions of Einstein equations which we construct here, such that the space-time evolution goes to a final state which is either a black hole or a naked singularity, depending on the nature of initial data and evolutions chosen, and subject to validity of the weak energy condition. The results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics. The formalism here combines the earlier results on gravitational collapse in four dimensions in a unified treatment. Also the earlier work is generalized to higher-dimensional space-times to allow a study of the effect of the number of dimensions on the possible final outcome of the collapse in terms of either a black hole or naked singularity. No restriction is adopted on the number of dimensions, and other limiting assumptions such as self-similarity of space-time are avoided, in order to keep the treatment general. Our methodology allows us to consider to an extent the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.
NASA Astrophysics Data System (ADS)
Gryb, Sean
2015-04-01
The notion of reference frame is a central theoretical construct for interpreting the physical implications of spacetime diffeomorphism invariance in General Relativity. However, the alternative formulation of classical General Relativity known as Shape Dynamics suggest that a subset of spacetime diffeomorphisms—namely hypersurface deformations—are, in a precise sense, dual to spatial conformal (or Weyl) invariance. Moreover, holographic gauge/gravity dualities suggest that bulk spacetime diffeomorphism invariance can be replaced by the properties of boundary CFTs. How can these new frameworks be compatible with the traditional notion of reference frame so fundamental to our interpretation of General Relativity? In this paper, we address this question by investigating the classical case of maximally symmetric spacetimes with a positive cosmological constant. We find that it is possible to define a notion of Shape Observer that represents a conformal reference frame dual to the notion of inertial reference frame in spacetime and provide a precise dictionary relating the two notions. We explicitly calculate the Hamilton-Jacobi functional for a theory of reparametrization invariant shape configurations dual to a theory of free inertial observers in de Sitter. These Shape Observers are holographic in the sense that they are defined on the asymptotic conformal boundaries of spacetime but know about bulk physics, and show that the dual theory is conformally invariant at the classical level. This leads to a first principles derivation of an exact classical holographic correspondence that can easily be generalized to more complicated situations and may lead to insights regarding the interpretation of the conformal invariance manifest in Shape Dynamics.
No hair conjecture, non-Abelian hierarchies, and anti-de Sitter spacetime
Radu, Eugen; Tchrakian, D. H.
2006-01-15
We consider globally regular and black holes solutions for the Einstein-Yang-Mills system with negative cosmological constant in d-spacetime dimensions. We find that the ADM mass of the spherically symmetric solutions generically diverges for d>4. Solutions with finite mass are found by considering corrections to the YM Lagrangian consisting in higher order terms of the Yang-Mills hierarchy. Such systems can occur in the low energy effective action of string theory. A discussion of the main properties of the solutions and the differences with respect to the four dimensional case is presented. The mass of these configurations is computed by using a counterterm method.
Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Lim, Yen-Kheng; Wang, Qing-hai
2017-01-01
An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small-bending-angle approximation for a lens system where the source, lens, and observer are coaligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to nonexistent null trajectories. The linear coefficient γ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by general relativity for small γ .
Toroidal configurations of perfect fluid in the Reissner-Nordström-(anti-)de Sitter spacetimes
Kucáková, Hana; Slaný, Petr; Stuchlík, Zdenĕk E-mail: petr.slany@fpf.slu.cz
2011-01-01
Influence of cosmological constant on toroidal fluid configurations around charged spherically symmetric black holes and naked singularities is demostrated by study of perfect-fluid tori with uniform distribution of specific angular momentum orbiting in the Reissner-Nordström-(anti-)de Sitter spacetimes. Toroidal configurations are allowed only in the spacetimes admitting existence of stable circular geodesics. Configurations with marginally closed equipotential (equipressure) surfaces crossing itself in a cusp allow accretion (through the inner cusp) and/or excretion (through the outer cusp) of matter from the toroidal configuration. Detailed classification of the Reissner-Nordström-(anti-)de Sitter spacetimes according to properties of the marginally stable tori is given. It is demonstrated that in the Reissner-Nordström-de Sitter naked-singularity spacetimes an interesting phenomenon of doubled tori can exist enabling exchange of matter between two tori in both inward and outward directions. In naked-singularity spacetimes the accretion onto the central singularity is impossible due to existence of a potential barrier.
Relative Locality in Curved Spacetime
NASA Astrophysics Data System (ADS)
Kowalski-Glikman, Jerzy; Rosati, Giacomo
2013-07-01
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a nontrivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are present. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (de Sitter) spacetimes, relying on their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with κ-Poincaré momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.
Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes
NASA Astrophysics Data System (ADS)
Stuchlík, Zdeněk; Schee, Jan
2015-12-01
In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.
The Boulware-Deser class of spacetimes radiates
NASA Astrophysics Data System (ADS)
Brassel, Byron P.; Maharaj, Sunil D.; Goswami, Rituparno
2017-08-01
We establish the result that the standard Boulware-Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein-Gauss-Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware-Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein-Gauss-Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.
Mazarakioti, Eleni C; Regier, Jeffery; Cunha-Silva, Luís; Wernsdorfer, Wolfgang; Pilkington, Melanie; Tang, Jinkui; Stamatatos, Theocharis C
2017-03-20
The introduction of the Schiff base ligand N-salicylidene-2-amino-5-chlorobenzoic acid (sacbH2) in 4f-metal chemistry has afforded a new dinuclear complex, [Dy2(NO3)4(sacbH)2(H2O)2(MeCN)2] (1), with the metal ions adopting a rare spherical tricapped trigonal prismatic coordination geometry. The deprotonated phenoxido O atoms of the organic chelate occupy the axial triangular faces of the prism and were found to be very close to the main anisotropy axes of the two Dy(III) ions. As a result, the {Dy(III)2} compound exhibits frequency- and temperature-dependent out-of-phase ac signals below ∼25 K in the absence of a static dc field, yielding an energy barrier of 109.3(1) K for the reversal of magnetization. Fast and efficient quantum tunneling of magnetization, attributed to the strong tails of signals below ∼15 K, was suppressed through the application of a small dc field, yielding entirely visible χM″ signals below 27 K. Single-crystal magnetic hysteresis studies confirmed the single-molecule magnet (SMM) behavior of 1; the hysteresis loops appear at temperatures below ∼5 K, which is one of the highest blocking temperatures in the field of 4f-SMMs to date. This joint magneto-structural and ab initio study demonstrates the ability of more common coordination numbers (i.e., 9), but with rare coordination geometries (i.e., spherical tricapped trigonal prismatic), to promote axiality that enhances the molecular anisotropy and subsequently the magnetization dynamics of the system.
1991-07-01
WL-TN-90-13 WL-TN- AD-A239 085 90-13 SPACETIME GEODESY ARKADY KHEYFETS July 1991 Final Report DTTI SAUGO 21991; Approved for public release...REPORT CATE 3. REPORT TYPE AND DATES COVERED July 1991 Final 4. TITLE AND SUBTITLE 5, FUNUING NUMBERS SPACETIME GEODESY PE: 61102F PR: ILIR 6. AUTHOR(S) TA...celestial mechanics problems involved in’ the development of a satellite-based Spacetime Common Grid (SCG). A mathematical formulation of the SCG principles
Particle motion in Horava-Lifshitz black hole space-times
Enolskii, Victor; Hartmann, Betti; Sirimachan, Parinya; Kagramanova, Valeria; Kunz, Jutta; Laemmerzahl, Claus
2011-10-15
We study the particle motion in the space-time of a Kehagias-Sfetsos black hole which is a static spherically symmetric solution of a Horava-Lifshitz gravity model. This model reduces to general relativity in the infrared limit and deviates slightly from detailed balance. Taking the viewpoint that the model is essentially a (3+1)-dimensional modification of general relativity we use the geodesic equation to determine the motion of massive and massless particles. We solve the geodesic equation exactly by using numerical techniques. We find that neither massless nor massive particles with nonvanishing angular momentum can reach the singularity at r=0. Next to bound and escape orbits that are also present in the Schwarzschild space-time we find that new types of orbits exist: manyworld bound orbits as well as two-world escape orbits. We also discuss observables such as the perihelion shift and the light deflection.
NASA Astrophysics Data System (ADS)
Sun, Wenke; Okubo, Shuhei; Fu, Guangyu; Araya, Akito
2009-06-01
Based on the authors' previous work, co-seismic deformations for a spherical symmetric earth model are summarized and reformulated. Unified expressions presented herein accommodate physical deformations: displacement, potential, gravity, geoid and strain changes. The corresponding Green's functions are derived by combining spheroidal and toroidal deformations. Sign errors in previous publications are corrected in these new formulas. These expressions are developed basically for a deformed earth surface because most traditional geodetic measurements are performed on the terrain surface. However, through development of space geodetic techniques, such as the satellite gravity missions, co-seismic gravity changes can be detected from space. In this case, the above dislocation theory (e.g., the co-seismic gravity change) cannot be applied directly to the observed data because the data do not include surface crustal deformation (the free air gravity change). Correspondingly, the contribution by the vertical displacement part must be removed from the traditional expressions. For this purpose, we present the corresponding expressions applicable to space observations. Some numerical technical problems are discussed. In addition, a smoothing technique is necessary to damp the high-frequency contribution so that the theory can be applied reasonably. Global co-seismic deformations caused by the 2004 Sumatra-Andaman earthquake (M9.3) are studied as an application of the new Green's function. That earthquake caused a global deformation detected by GPS, strain metres and even a satellite gravity mission. These global deformations are calculated based on the derived Green's functions and the seismic-wave derived earth model. A segment-summation scheme is used considering the slip distribution on a limited fault plane. The results are useful for interpreting observed deformations, especially those in the far field. The earthquake reveals global co-seismic deformations and effects
Field dynamics on the trapping horizon in Vaidya spacetime
NASA Astrophysics Data System (ADS)
Majhi, Abhishek
2017-07-01
In this article, we shed some light on the field theoretic aspect of the spherically symmetric trapping horizon in Vaidya spacetime. The effective field equations are that of a Chern-Simons theory coupled to bulk sources through two different couplings—one is purely geometric and the other is matter dependent. This is an effective generalization of the equilibrium horizon scenario where the Chern-Simons theory is coupled to the bulk geometry through a constant matter-independent coupling. Further, we note that the field equations pulled back to a cross section of the horizon are inadequate to manifest the nature of the horizon. Hence, contrary to the usual practice, the evolution equation needs to be considered at least while passing on to the quantum theory.
Scalar perturbations on Lemaitre-Tolman-Bondi spacetimes
Zibin, J. P.
2008-08-15
In recent years there has been growing interest in verifying the horizon-scale homogeneity of the Universe that follows from applying the Copernican principle to the observed isotropy. This program has been stimulated by the discovery that a very large void, centered near us, can explain supernova luminosity distance measurements without dark energy. It is crucial to confront such models with as wide a variety of data as possible. With this application in mind, we develop the relativistic theory of linear scalar perturbations on spherically symmetric dust (Lemaitre-Tolman-Bondi) spacetimes, using the covariant 1+1+2 formalism. We show that the evolution of perturbations is determined by a small set of new linear transfer functions. If decaying modes are ignored (to be consistent with the standard inflationary paradigm), the standard techniques of perturbation theory on homogeneous backgrounds, such as harmonic expansion, can be applied, and results closely paralleling those of familiar cosmological perturbation theory can be obtained.
Hartle, J.B. Isaac Newton Institute for the Mathematical Sciences, University of Cambridge, Cambridge CB3 0EH )
1995-02-15
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which neither require, nor always permit, a notion of state on a spacelike surface. In particular, it must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering, coarse-grained histories it may display. This spacetime notion of information coincides with the familiar one when quantum theory [ital is] formulable in terms of states on spacelike surfaces but generalizes this notion when it cannot be so formulated. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a fixed spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse grainings of sum-over-histories quantum mechanics that refer only to coordinates. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with nonunitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics.
Cosmological constant from quantum spacetime
NASA Astrophysics Data System (ADS)
Majid, Shahn; Tao, Wen-Qing
2015-06-01
We show that a hypothesis that spacetime is quantum with coordinate algebra [xi,t ]=λPxi , and spherical symmetry under rotations of the xi, essentially requires in the classical limit that the spacetime metric is the Bertotti-Robinson metric, i.e., a solution of Einstein's equations with a cosmological constant and a non-null electromagnetic field. Our arguments do not give the value of the cosmological constant or the Maxwell field strength, but they cannot both be zero. We also describe the quantum geometry and the full moduli space of metrics that can emerge as classical limits from this algebra.
Bruckman, W.
1986-11-15
The inverse scattering method of Belinsky and Zakharov is used to investigate axially symmetric stationary vacuum soliton solutions in the five-dimensional representation of the Brans-Dicke-Jordan theory of gravitation, where the scalar field of the theory is an element of a five-dimensional metric. The resulting equations for the spacetime metric are similar to those of solitons in general relativity, while the scalar field generated is the product of a simple function of the coordinates and an already known scalar field solution. A family of solutions is considered that reduce, in the absence of rotation, to the five-dimensional form of a well-known Weyl-Levi Civita axially symmetric static vacuum solution. With a suitable choice of parameters, this static limit becomes equivalent to the spherically symmetric solution of the Brans-Dicke theory. An exact metric, in which the Kerr-scalar McIntosh solution is a special case, is given explicitly.
NASA Astrophysics Data System (ADS)
Sun, Yuan; Xu, Hao; Zhao, Liu
2016-09-01
The holographic entanglement entropy is studied numerically in (4+1)-dimensional spherically symmetric Gauss-Bonnet AdS black hole spacetime with compact boundary. On the bulk side the black hole spacetime undergoes a van der Waals-like phase transition in the extended phase space, which is reviewed with emphasis on the behavior on the temperature-entropy plane. On the boundary, we calculated the regularized HEE of a disk region of different sizes. We find strong numerical evidence for the failure of equal area law for isobaric curves on the temperature-HEE plane and for the correctness of first law of entanglement entropy, and briefly give an explanation for why the latter may serve as a reason for the former, i.e. the failure of equal area law on the temperature-HEE plane.
Curvature of spacetime: A simple student activity
NASA Astrophysics Data System (ADS)
Wood, Monika; Smith, Warren; Jackson, Matthew
2016-12-01
The following is a description of an inexpensive and simple student experiment for measuring the differences between the three types of spacetime topology—Euclidean (flat), Riemann (spherical), and Lobachevskian (saddle) curvatures. It makes use of commonly available tools and materials, and requires only a small amount of construction. The experiment applies to astronomical topics such as gravity, spacetime, general relativity, as well as geometry and mathematics.
Partially massless graviton on beyond Einstein spacetimes
NASA Astrophysics Data System (ADS)
Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael
2017-06-01
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.
Note on cosmological Levi-Civita spacetimes in higher dimensions
NASA Astrophysics Data System (ADS)
Sarıoǧlu, Özgür; Tekin, Bayram
2009-04-01
We find a class of solutions to cosmological Einstein equations that generalizes the four dimensional cylindrically symmetric spacetimes to higher dimensions. The AdS soliton is a special member of this class with a unique singularity structure.
Vaz, Cenalo; Tibrewala, Rakesh; Singh, T. P.
2008-07-15
In a previous paper we studied the collapse of a spherically symmetric dust distribution (marginally bound Lemaitre-Tolman-Bondi) in d-dimensional anti-de Sitter spacetime and obtained the condition for the formation of trapped surfaces. Here we extend the analysis by giving the canonical theory for the same and subsequently quantize the system by solving the Wheeler-DeWitt equation. We show that for the case of small dust perturbations around a black hole the wave functionals so obtained describe a flux of dust particles from the region near the horizon with a thermal spectrum at the Hawking temperature and discuss the nontrivial dependence of this temperature on the number of spacetime dimensions and the cosmological constant.
Static spherical wormhole models in f (R, T) gravity
NASA Astrophysics Data System (ADS)
Yousaf, Z.; Ilyas, M.; Zaeem-ul-Haq Bhatti, M.
2017-06-01
This paper explores the possibility of the existence of wormhole geometries coupled with relativistic matter configurations by taking a particular model of f(R,T) gravity (where T is the trace of energy-momentum tensor). For this purpose, we take the static form of spherically symmetric spacetime and after assuming a specific form of matter and combinations of shape function, the validity of energy conditions is checked. We have discussed our results through graphical representation and studied the equilibrium background of wormhole models by taking an anisotropic fluid. The extra curvature quantities coming from f(R,T) gravity could be interpreted as a gravitational entity supporting these non-standard astrophysical wormhole models. We have shown that in the context of anisotropic fluid and R+α R^2+λ T gravity, wormhole models could possibly exist in few zones in the space of parameters without the need for exotic matter.
Diffraction by spherically symmetric inhomogeneous scatterers
Perel`man, A.Y.
1995-05-01
The problem of diffraction by scatterers optically inhomogeneous in the radial direction illuminated by sources with a fixed azimuthal structure is solved. Standard models are proposed for approximating the exact solution of the problem, in which partial potentials are represented in terms of exponential and exponential and cylindrical functions, and the corresponding algorithms for solving the problem are developed. A formula is deduced for the scattering cross section of a radially inhomogeneous sphere. 8 refs.
Bonnor stars in d spacetime dimensions
Lemos, Jose P. S.; Zanchin, Vilson T.
2008-03-15
Bonnor stars are regular static compact configurations in equilibrium, composed of an extremal dust fluid, i.e., a charged dust fluid where the mass density is equal to the charge density in appropriate units and up to a sign, joined to a suitable exterior vacuum solution, both within Newtonian gravity and general relativity. In four dimensions, these configurations obey the Majumdar-Papapetrou system of equations: in one case, the system is a particular setup of Newtonian gravity coupled to Coulomb electricity and electrically charged matter or fluid, in the other case, the system is a particular setup of general relativity coupled to Maxwell electromagnetism and electrically charged matter or fluid, where the corresponding gravitational potential is a specially simple function of the electric potential field and the fluid, when there is one, is made of extremal dust. Since the Majumdar-Papapetrou system can be generalized to d spacetime dimensions, as has been previously done, and higher-dimensional scenarios can be important in gravitational physics, it is natural to study this type of Bonnor solutions in higher dimensions, d{>=}4. As a preparation, we analyze Newton-Coulomb theory with an electrically charged fluid in a Majumdar-Papapetrou context, in d=n+1 spacetime dimensions, with n being the number of spatial dimensions. We show that within the Newtonian theory, in vacuum, the Majumdar-Papapetrou relation for the gravitational potential in terms of the electric potential, and its related Weyl relation, are equivalent, in contrast to general relativity where they are distinct. We study a class of spherically symmetric Bonnor stars within this theory. Under sufficient compactification they form point mass charged Newtonian singularities. We then study the analogue-type systems in the Einstein-Maxwell theory with an electrically charged fluid. Drawing on our previous work on the d-dimensional Majumdar-Papapetrou system, we restate some properties of this
Spacetime completeness of non-singular black holes in conformal gravity
NASA Astrophysics Data System (ADS)
Bambi, Cosimo; Modesto, Leonardo; Rachwał, Lesław
2017-05-01
We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new types of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r=0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.
Symmetrical Diphosphatetraazacyclooctatetraenes.
1980-06-26
aryl, alkyl, perfluoroalkyl and perfluoroalkylether radcalsl Rf is selected from perfluoroalkyl and perfluoroalkylether radicals 20 as represented by...process for synthesizing symmetrical diphosphatetraazacyclooctatetraenes by reacting perfluoroalkyl or perfluoroalkylether amidine with a...symmetrical diphosphatetraazacyclooctatetraene. The substituent Rf can he selected from perfluoroalkyl and pertluoroalkylether groups as represented hy the
Ramond, P. . Dept. of Physics)
1993-01-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Ramond, P.
1993-04-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes
NASA Astrophysics Data System (ADS)
Levi, Adam; Ori, Amos
2016-12-01
We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. Thus far, we have developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally coupled massless scalar field in Schwarzschild and Reissner-Nordström backgrounds for several quantum states. We present here the results for the RSET in the Schwarzschild case in the Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at r ≲2.78 M . Then we use the RSET results to explore violation of the weak and null energy conditions. We find that both conditions are violated all the way from r ≃4.9 M to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at r =3 M violates the averaged null energy condition.
Versatile Method for Renormalized Stress-Energy Computation in Black-Hole Spacetimes.
Levi, Adam; Ori, Amos
2016-12-02
We report here on a new method for calculating the renormalized stress-energy tensor (RSET) in black-hole (BH) spacetimes, which should also be applicable to dynamical BHs and to spinning BHs. This new method only requires the spacetime to admit a single symmetry. Thus far, we have developed three variants of the method, aimed for stationary, spherically symmetric, or axially symmetric BHs. We used this method to calculate the RSET of a minimally coupled massless scalar field in Schwarzschild and Reissner-Nordström backgrounds for several quantum states. We present here the results for the RSET in the Schwarzschild case in the Unruh state (the state describing BH evaporation). The RSET is type I at weak field, and becomes type IV at r≲2.78M. Then we use the RSET results to explore violation of the weak and null energy conditions. We find that both conditions are violated all the way from r≃4.9M to the horizon. We also find that the averaged weak energy condition is violated by a class of (unstable) circular timelike geodesics. Most remarkably, the circular null geodesic at r=3M violates the averaged null energy condition.
Milking the spherical cow - on aspherical dynamics in spherical coordinates
NASA Astrophysics Data System (ADS)
Pontzen, Andrew; Read, Justin I.; Teyssier, Romain; Governato, Fabio; Gualandris, Alessia; Roth, Nina; Devriendt, Julien
2015-08-01
Galaxies and the dark matter haloes that host them are not spherically symmetric, yet spherical symmetry is a helpful simplifying approximation for idealized calculations and analysis of observational data. The assumption leads to an exact conservation of angular momentum for every particle, making the dynamics unrealistic. But how much does that inaccuracy matter in practice for analyses of stellar distribution functions, collisionless relaxation, or dark matter core-creation? We provide a general answer to this question for a wide class of aspherical systems; specifically, we consider distribution functions that are `maximally stable', i.e. that do not evolve at first order when external potentials (which arise from baryons, large-scale tidal fields or infalling substructure) are applied. We show that a spherically symmetric analysis of such systems gives rise to the false conclusion that the density of particles in phase space is ergodic (a function of energy alone). Using this idea we are able to demonstrate that: (a) observational analyses that falsely assume spherical symmetry are made more accurate by imposing a strong prior preference for near-isotropic velocity dispersions in the centre of spheroids; (b) numerical simulations that use an idealized spherically symmetric setup can yield misleading results and should be avoided where possible; and (c) triaxial dark matter haloes (formed in collisionless cosmological simulations) nearly attain our maximally stable limit, but their evolution freezes out before reaching it.
New Features of Gravitational Collapse in Anti-de Sitter Spacetimes.
Santos-Oliván, Daniel; Sopuerta, Carlos F
2016-01-29
Gravitational collapse of a massless scalar field in spherically symmetric anti-de Sitter (AdS) spacetimes presents a new phenomenology with a series of critical points whose dynamics is discretely self-similar as in the asymptotically flat case. Each critical point is the limit of a branch of scalar field configurations that have bounced off the AdS boundary a fixed number of times before forming an apparent horizon. We present results from a numerical study that focus on the interfaces between branches. We find that there is a mass gap between branches and that subcritical configurations near the critical point form black holes with an apparent horizon mass that follows a power law of the form M(AH)-M(g)∝(p(c)-p)^(ξ), where M(g) is the mass gap and the exponent ξ≃0.7 appears to be universal.
Compact stars on pseudo-spheroidal spacetime compatible with observational data
NASA Astrophysics Data System (ADS)
Thomas, V. O.; Pandya, D. M.
2015-12-01
A new class of solutions for Einstein's field equations representing a static spherically symmetric anisotropic distribution of matter is obtained on the background of pseudo-spheroidal spacetime. We have prescribed the bounds of the model parameters k and p0 on the basis of the elementary criteria for physical acceptability, viz., regularity, stability and energy conditions. By taking the values of model parameters from the prescribed bounds, we have shown that our model is compatible with the observational data of a wide variety of compact stars like 4U 1820-30, PSR J1903{+}327, 4U 1608-52, Vela X-1, PSR J1614-2230, SMC X-4 and Cen X-3.
How Spherical Is a Cube (Gravitationally)?
ERIC Educational Resources Information Center
Sanny, Jeff; Smith, David
2015-01-01
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…
How Spherical Is a Cube (Gravitationally)?
ERIC Educational Resources Information Center
Sanny, Jeff; Smith, David
2015-01-01
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center. By integrating over ring elements of a spherical shell, we show that the…
Region with trapped surfaces in spherical symmetry, its core, and their boundaries
Bengtsson, Ingemar; Senovilla, Jose M. M.
2011-02-15
We consider the region T in spacetime containing future-trapped closed surfaces and its boundary B, and derive some of their general properties. We then concentrate on the case of spherical symmetry, but the methods we use are general and applicable to other situations. We argue that closed trapped surfaces have a nonlocal property, ''clairvoyance'', which is inherited by B. We prove that B is not a marginally trapped tube in general, and that it can have portions in regions whose whole past is flat. For asymptotically flat black holes, we identify a general past barrier, well inside the event horizon, to the location of B under physically reasonable conditions. We also define the core Z of the trapped region as that part of T which is indispensable to sustain closed trapped surfaces. We prove that the unique spherically symmetric dynamical horizon is the boundary of such a core, and we argue that this may serve to single it out. To illustrate the results, some explicit examples are discussed, namely, Robertson-Walker geometries and the imploding Vaidya spacetime.
Black hole hair formation in shift-symmetric generalised scalar-tensor gravity
NASA Astrophysics Data System (ADS)
Benkel, Robert; Sotiriou, Thomas P.; Witek, Helvi
2017-03-01
A linear coupling between a scalar field and the Gauss–Bonnet invariant is the only known interaction term between a scalar and the metric that: respects shift symmetry; does not lead to higher order equations; inevitably introduces black hole hair in asymptotically flat, 4-dimensional spacetimes. Here we focus on the simplest theory that includes such a term and we explore the dynamical formation of scalar hair. In particular, we work in the decoupling limit that neglects the backreaction of the scalar onto the metric and evolve the scalar configuration numerically in the background of a Schwarzschild black hole and a collapsing dust star described by the Oppenheimer–Snyder solution. For all types of initial data that we consider, the scalar relaxes at late times to the known, static, analytic configuration that is associated with a hairy, spherically symmetric black hole. This suggests that the corresponding black hole solutions are indeed endpoints of collapse.
NASA Astrophysics Data System (ADS)
Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio; Weinberg, Sean J.
2016-12-01
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.
Symmetries of asymptotically flat electrovacuum space-times and radiation
NASA Astrophysics Data System (ADS)
Bičák, J.; Pravdová, A.
1998-11-01
Symmetries compatible with asymptotic flatness and admitting gravitational and electromagnetic radiation are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in axially symmetric electrovacuum space-times in which at least locally a smooth null infinity in the sense of Penrose exists, the only second allowable symmetry is either the translational symmetry or the boost symmetry. Translationally invariant space-times with, in general, a straight "cosmic string" along the axis of symmetry are nonradiative although they can have a nonvanishing news function. The boost-rotation symmetric space-times are radiative. They describe "uniformly accelerated charged particles" or black holes which in general may also be rotating—the axial and an additional Killing vector are not assumed to be hypersurface orthogonal. The general functional forms of both gravitational and electromagnetic news functions, and of the mass aspect and total mass of asymptotically flat boost-rotation symmetric space-times at null infinity are obtained. The expressions for the mass are new even in the case of vacuum boost-rotation symmetric space-times with hypersurface orthogonal Killing vectors. In the Appendices some errors appearing in previous works are corrected.
Double conformal space-time algebra
NASA Astrophysics Data System (ADS)
Easter, Robert Benjamin; Hitzer, Eckhard
2017-01-01
The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G 4,8that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G 8,2 with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G 1,3. Two Conformal Space-Time subalgebras (CSTA) G 2,4 provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G 4,8 is a doubling product of two G 2,4 CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length
Constraining spacetime torsion with the Moon and Mercury
March, Riccardo; Bellettini, Giovanni; Tauraso, Roberto; Dell'Agnello, Simone
2011-05-15
We report a search for new gravitational physics phenomena based on Riemann-Cartan theory of general relativity including spacetime torsion. Starting from the parametrized torsion framework of Mao, Tegmark, Guth, and Cabi, we analyze the motion of test bodies in the presence of torsion, and, in particular, we compute the corrections to the perihelion advance and to the orbital geodetic precession of a satellite. We consider the motion of a test body in a spherically symmetric field, and the motion of a satellite in the gravitational field of the Sun and the Earth. We describe the torsion field by means of three parameters, and we make use of the autoparallel trajectories, which in general differ from geodesics when torsion is present. We derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of celestial mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter of the satellite. The computed secular variations show how the corrections to the perihelion advance and to the orbital de Sitter effect depend on the torsion parameters. All computations are performed under the assumptions of weak field and slow motion. To test our predictions, we use the measurements of the Moon's geodetic precession from lunar laser ranging data, and the measurements of Mercury's perihelion advance from planetary radar ranging data. These measurements are then used to constrain suitable linear combinations of the torsion parameters.
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.
Polyhomogeneous expansions from time symmetric initial data
NASA Astrophysics Data System (ADS)
Gasperín, E.; Valiente Kroon, J. A.
2017-10-01
We make use of Friedrich’s construction of the cylinder at spatial infinity to relate the logarithmic terms appearing in asymptotic expansions of components of the Weyl tensor to the freely specifiable parts of time symmetric initial data sets for the Einstein field equations. Our analysis is based on the assumption that a particular type of formal expansions near the cylinder at spatial infinity corresponds to the leading terms of actual solutions to the Einstein field equations. In particular, we show that if the Bach tensor of the initial conformal metric does not vanish at the point at infinity then the most singular component of the Weyl tensor decays near null infinity as O(\\tilde{r}-3\\ln \\tilde{r}) so that spacetime will not peel. We also provide necessary conditions on the initial data which should lead to a peeling spacetime. Finally, we show how to construct global spacetimes which are candidates for non-peeling (polyhomogeneous) asymptotics.
Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Shepherd, Ben L.; Winstanley, Elizabeth
2016-03-01
We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.
Quantum-Spacetime Phenomenology.
Amelino-Camelia, Giovanni
2013-01-01
I review the current status of phenomenological programs inspired by quantum-spacetime research. I stress in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of quantum-spacetime theories.
NASA Astrophysics Data System (ADS)
Perko, Howard
2017-01-01
Concepts from physical chemistry and more specifically surface tension are introduced to spacetime. Lagrangian equations of motion for membranes of curved spacetime manifold are derived. The equations of motion in spatial directions are dispersion equations and can be rearranged to Schrodinger's equation where Plank's constant is related to membrane elastic modulus. The equation of motion in the time-direction has two immediately recognizable solutions: electromagnetic waves and corpuscles. The corpuscular membrane solution can assume different genus depending on quantized amounts of surface energy. A metric tensor that relates empty flat spacetime to energetic curved spacetime is found that satisfies general relativity. Application of the surface tension to quantum electrodynamics and implications for quantum chromodynamics are discussed. Although much work remains, it is suggested that spacetime surface tension may provide a classical explanation that combines general relativity with field theories in quantum mechanics and atomic particle physics.
NASA Astrophysics Data System (ADS)
Visser, Matt
Analogue spacetimes (and more boldly, analogue models both of and for gravity), have attracted significant and increasing attention over the last decade and a half. Perhaps the most straightforward physical example, which serves as a template for most of the others, is Bill Unruh's model for a dumb hole,(mute black hole, acoustic black hole), wherein sound is dragged along by a moving fluid—and can even be trapped behind an acoustic horizon. This and related analogue models for curved spacetimes are useful in many ways: analogue spacetimes provide general relativists with extremely concrete physical models to help focus their thinking, and conversely the techniques of curved spacetime can sometimes help improve our understanding of condensed matter and/or optical systems by providing an unexpected and countervailing viewpoint. In this chapter, I shall provide a few simple examples of analogue spacetimes as general background for the rest of the contributions.
An axially symmetric solution of metric-affine gravity
NASA Astrophysics Data System (ADS)
Vlachynsky, E. J.; Tresguerres, R.; Obukhov, Yu N.; Hehl, F. W.
1996-12-01
We present an exact stationary axially symmetric vacuum solution of metric-affine gravity (MAG) which generalizes the recently reported spherically symmetric solution; besides the metric, it carries nonmetricity and torsion as post-Riemannian geometrical structures. The parameters of the solution are interpreted as mass and angular momentum and as dilation, shear and spin charges.
Separating metric perturbations in near-horizon extremal Kerr spacetimes
NASA Astrophysics Data System (ADS)
Chen, Baoyi; Stein, Leo C.
2017-09-01
Linear perturbation theory is a powerful toolkit for studying black hole spacetimes. However, the perturbation equations are hard to solve unless we can use separation of variables. In the Kerr spacetime, metric perturbations do not separate, but curvature perturbations do. The cost of curvature perturbations is a very complicated metric-reconstruction procedure. This procedure can be avoided using a symmetry-adapted choice of basis functions in highly symmetric spacetimes, such as near-horizon extremal Kerr. In this paper, we focus on this spacetime and (i) construct the symmetry-adapted basis functions; (ii) show their orthogonality; and (iii) show that they lead to separation of variables of the scalar, Maxwell, and metric perturbation equations. This separation turns the system of partial differential equations into one of ordinary differential equations over a compact domain, the polar angle.
Asymptotically flat radiative space-times with boost-rotation symmetry: The general structure
Biicak, J.; Schmidt, B. )
1989-09-15
This paper deals for the first time with boost-rotation-symmetric space-times from a unified point of view. Boost-rotation-symmetric space-times are the only explicitly known exact solutions of the Einstein vacuum field equations which describe moving singularities or black holes, are radiative and asymptotically flat in the sense that they admit global, though not complete, smooth null infinity, as well as spacelike and timelike infinities. They very likely represent the exterior fields of uniformly accelerated sources in general relativity and may serve as tests of various approximation methods, as nontrivial illustrations of the theory of the asymptotic structure of radiative space-times, and as test beds in numerical relativity. Examples are the {ital C}-metric or the solutions of Bonnor and Swaminarayan. The space-times are defined in a geometrical manner and their global properties are studied in detail, in particular their asymptotic structure. It is demonstrated how one can construct any asymptotically flat boost-rotation-symmetric space-time starting from the boost-rotation-symmetric solution of the flat-space wave equation. The problem of uniformly accelerated sources in special relativity is also discussed. The radiative properties and specific examples of the boost-rotation-symmetric space-times will be analyzed in a following paper.
Covariance in models of loop quantum gravity: Spherical symmetry
NASA Astrophysics Data System (ADS)
Bojowald, Martin; Brahma, Suddhasattwa; Reyes, Juan D.
2015-08-01
Spherically symmetric models of loop quantum gravity have been studied recently by different methods that aim to deal with structure functions in the usual constraint algebra of gravitational systems. As noticed by Gambini and Pullin, a linear redefinition of the constraints (with phase-space dependent coefficients) can be used to eliminate structure functions, even Abelianizing the more difficult part of the constraint algebra. The Abelianized constraints can then easily be quantized or modified by putative quantum effects. As pointed out here, however, the method does not automatically provide a covariant quantization, defined as an anomaly-free quantum theory with a classical limit in which the usual (off-shell) gauge structure of hypersurface deformations in space-time appears. The holonomy-modified vacuum theory based on Abelianization is covariant in this sense, but matter theories with local degrees of freedom are not. Detailed demonstrations of these statements show complete agreement with results of canonical effective methods applied earlier to the same systems (including signature change).
Resonance interatomic energy in a Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Zhou, Wenting; Yu, Hongwei
2017-08-01
We study, in the Schwarzschild spacetime, the resonance interatomic energy (RIE) of two static identical atoms with an interatomic separation L along the radial direction and correlated by a symmetric/antisymmetric entangled state. The atoms are assumed to be coupled to massless scalar fields in the Boulware, Unruh, and Hartle-Hawking vacua, and approximate analytical results are obtained both at infinity and near the horizon. Our results show that at infinity, the RIE approaches that in a flat spacetime, while, near the horizon, they can deviate dramatically from each other. Besides, different from other atomic radiative properties such as the Lamb shift of a single atom or the interatomic energy between two uncorrelated atoms, which can be obviously affected by the thermal character of quantum fields, the RIE of two atoms in a symmetric/antisymmetric entangled state in the Boulware, Unruh, and Hartle-Hawking vacua are exactly the same as a result of the fact that the RIE of two such atoms depends only on the atomic self-reaction, i.e., it does not feel the vacuum fluctuations. This suggests that the RIE of two static atoms in a symmetric/antisymmetric entangled state outside a black hole is oblivious to the Hawking radiation, in contrast to those uncorrelated atoms.
Electron Optics for Biologists: Physical Origins of Spherical Aberrations
ERIC Educational Resources Information Center
Geissler, Peter; Zadunaisky, Jose
1974-01-01
Reports on the physical origins of spherical aberrations in axially symmetric electrostatic lenses to convey the essentials of electon optics to those who must think critically about the resolution of the electron microscope. (GS)
Test membranes in Riemann-Cartan spacetimes
Vasilic, Milovan; Vojinovic, Marko
2010-01-15
The dynamics of branelike extended objects in spacetimes with torsion is derived from the conservation equations of stress-energy and spin tensors. Thus obtained world-sheet equations are applied to macroscopic test membranes made of spinning matter. Specifically, we consider membranes with maximally symmetric distribution of stress energy and spin. These are characterized by two constants only: the tension and spin magnitude. By solving the world-sheet equations, we discover a similarity between such membranes in Riemann-Cartan backgrounds, and string theory membranes in low-energy string backgrounds. In the second part of the paper, we apply this result to cylindrical membranes wrapped around the extra compact dimension of a (D+1)-dimensional spacetime. In the narrow membrane limit, we discover how effective macroscopic strings couple to torsion. An observed similarity with the string sigma model is noted.
Non-Pauli transitions from spacetime noncommutativity.
Balachandran, A P; Joseph, Anosh; Padmanabhan, Pramod
2010-07-30
The consideration of noncommutative spacetimes in quantum theory can be plausibly advocated from physics at the Planck scale. Typically, this noncommutativity is controlled by fixed "vectors" or "tensors" with numerical entries like θμν for the Moyal spacetime. In approaches enforcing Poincaré invariance, these deform or twist the method of (anti)symmetrization of identical particle state vectors. We argue that the Earth's rotation and movements in the cosmos are "sudden" events to Pauli-forbidden processes. This induces (twisted) bosonic components in state vectors of identical spinorial particles. These components induce non-Pauli transitions. From known limits on such transitions, we infer that the energy scale for noncommutativity is ≳10(24) TeV. This suggests a new energy scale beyond the Planck scale.
Emergent spacetime & quantum entanglement in matrix theory
NASA Astrophysics Data System (ADS)
Sahakian, Vatche; Tawabutr, Yossathorn; Yan, Cynthia
2017-08-01
In the context of the Bank-Fishler-Shenker-Susskind Matrix theory, we analyze a spherical membrane in light-cone M theory along with two asymptotically distant probes. In the appropriate energy regime, we find that the membrane behaves like a smeared Matrix black hole; and the spacetime geometry seen by the probes can become non-commutative even far away from regions of Planckian curvature. This arises from non-linear Matrix interactions where fast matrix modes lift a flat direction in the potential — akin to the Paul trap phenomenon in atomic physics. In the regime where we do have a notion of emergent spacetime, we show that there is non-zero entanglement entropy between supergravity modes on the membrane and the probes. The computation can easily be generalized to other settings, and this can help develop a dictionary between entanglement entropy and local geometry — similar to Ryu-Takayanagi but instead for asymptotically flat backgrounds.
Spherical harmonics in texture analysis
NASA Astrophysics Data System (ADS)
Schaeben, Helmut; van den Boogaart, K. Gerald
2003-07-01
The objective of this contribution is to emphasize the fundamental role of spherical harmonics in constructive approximation on the sphere in general and in texture analysis in particular. The specific purpose is to present some methods of texture analysis and pole-to-orientation probability density inversion in a unifying approach, i.e. to show that the classic harmonic method, the pole density component fit method initially introduced as a distinct alternative, and the spherical wavelet method for high-resolution texture analysis share a common mathematical basis provided by spherical harmonics. Since pole probability density functions and orientation probability density functions are probability density functions defined on the sphere Ω3⊂ R3 or hypersphere Ω4⊂ R4, respectively, they belong at least to the space of measurable and integrable functions L1( Ωd), d=3, 4, respectively. Therefore, first a basic and simplified method to derive real symmetrized spherical harmonics with the mathematical property of providing a representation of rotations or orientations, respectively, is presented. Then, standard orientation or pole probability density functions, respectively, are introduced by summation processes of harmonic series expansions of L1( Ωd) functions, thus avoiding resorting to intuition and heuristics. Eventually, it is shown how a rearrangement of the harmonics leads quite canonically to spherical wavelets, which provide a method for high-resolution texture analysis. This unified point of view clarifies how these methods, e.g. standard functions, apply to texture analysis of EBSD orientation measurements.
NASA Technical Reports Server (NTRS)
1997-01-01
Developed largely through a Small Business Innovation Research contract through Langley Research Center, Interactive Picture Corporation's IPIX technology provides spherical photography, a panoramic 360-degrees. NASA found the technology appropriate for use in guiding space robots, in the space shuttle and space station programs, as well as research in cryogenic wind tunnels and for remote docking of spacecraft. Images of any location are captured in their entirety in a 360-degree immersive digital representation. The viewer can navigate to any desired direction within the image. Several car manufacturers already use IPIX to give viewers a look at their latest line-up of automobiles. Another application is for non-invasive surgeries. By using OmniScope, surgeons can look more closely at various parts of an organ with medical viewing instruments now in use. Potential applications of IPIX technology include viewing of homes for sale, hotel accommodations, museum sites, news events, and sports stadiums.
Physics on noncommutative spacetimes
NASA Astrophysics Data System (ADS)
Padmanabhan, Pramod
The structure of spacetime at the Planck scale remains a mystery to this date with a lot of insightful attempts to unravel this puzzle. One such attempt is the proposition of a 'pointless' structure for spacetime at this scale. This is done by studying the geometry of the spacetime through a noncommutative algebra of functions defined on it. We call such spacetimes 'noncommutative spacetimes'. This dissertation probes physics on several such spacetimes. These include compact noncommutative spaces called fuzzy spaces and noncompact spacetimes. The compact examples we look at are the fuzzy sphere and the fuzzy Higg's manifold. The noncompact spacetimes we study are the Groenewold-Moyal plane and the Bcn⃗ plane. A broad range of physical effects are studied on these exotic spacetimes. We study spin systems on the fuzzy sphere. The construction of Dirac and chirality operators for an arbitrary spin j is studied on both S2F and S2 in detail. We compute the spectrums of the spin 1 and spin 32 Dirac operators on S2F . These systems have novel thermodynamical properties which have no higher dimensional analogs, making them interesting models. The fuzzy Higg's manifold is found to exhibit topology change, an important property for any theory attempting to quantize gravity. We study how this change occurs in the classical setting and how quantizing this manifold smoothens the classical conical singularity. We also show the construction of the star product on this manifold using coherent states on the noncommutative algebra describing this noncommutative space. On the Moyal plane we develop the LSZ formulation of scalar quantum field theory. We compute scattering amplitudes and remark on renormalization of this theory. We show that the LSZ formalism is equivalent to the interaction representation formalism for computing scattering amplitudes on the Moyal plane. This result is true for on-shell Green's functions and fails to hold for off-shell Green's functions. With the
Christiansen, Wayne A.; Ng, Y. Jack; Floyd, David J. E.; Perlman, Eric S.
2011-04-15
Plausibly spacetime is foamy on small distance scales, due to quantum fluctuations. We elaborate on the proposal to detect spacetime foam by looking for seeing disks in the images of distant quasars and active galactic nuclei. This is a null test in the sense that the continued presence of unresolved point sources at the milliarcsecond level in samples of distant compact sources puts severe constraints on theories of quantized spacetime foam at the Planckian level. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We then deal with recent data and the constraints they put on spacetime foam models. While time lags from distant pulsed sources such as gamma ray bursts have been posited as a possible test of spacetime foam models, we demonstrate that the time-lag effect is rather smaller than has been calculated, due to the equal probability of positive and negative fluctuations in the speed of light inherent in such models. Thus far, images of high-redshift quasars from the Hubble ultra-deep field provide the most stringent test of spacetime foam theories. While random-walk models ({alpha}=1/2) have already been ruled out, the holographic ({alpha}=2/3) model remains viable. Here {alpha}{approx}1 parametrizes the different spacetime foam models according to which the fluctuation of a distance l is given by {approx}l{sup 1-{alpha}l}{sub P}{sup {alpha}} with l{sub P} being the Planck length. Indeed, we see a slight wavelength-dependent blurring in the ultra-deep field images selected for this study. Using existing data in the Hubble Space Telescope (HST) archive we find it is impossible to rule out the {alpha}=2/3 model, but exclude all models with {alpha}<0.65. By comparison, current gamma ray burst time-lag observations only exclude models with {alpha}<0.3.
Introduction to multifractional spacetimes
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca
2012-10-01
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display discrete symmetries in the ultraviolet and ordinary Poincaré symmetries in the infrared. Under certain reasonable assumptions, field theories (including gravity) on multifractional geometries are generally argued to be perturbatively renormalizable. We also sketch the relation with other field theories of quantum gravity based on the renormalization group.
Introduction to multifractional spacetimes
Calcagni, Gianluca
2012-09-24
We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display discrete symmetries in the ultraviolet and ordinary Poincare symmetries in the infrared. Under certain reasonable assumptions, field theories (including gravity) on multifractional geometries are generally argued to be perturbatively renormalizable. We also sketch the relation with other field theories of quantum gravity based on the renormalization group.
Conformally symmetric traversable wormholes
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
2007-10-15
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
NASA Astrophysics Data System (ADS)
Salom, Igor; Dmitrašinović, V.
2017-07-01
We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3 ⊗ SO(3)rot ⊂ O (2) ⊗ SO(3)rot ⊂ U (3) ⋊S2 ⊂ O (6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O (2) is the ;democracy transformation;, or ;kinematic rotation; group for three particles; SO(3)rot is the 3D rotation group, and U (3) , O (6) are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3)rot ⊂ SU (3) degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K ≤ 6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ , ρ) with coefficients given as algebraic numbers unless the ;operator method; is chosen for the lifting of the SO(3)rot ⊂ SU (3) multiplicity and the dimension of the degenerate subspace is greater than four - in which case one must resort to numerical diagonalization; the latter condition is not met by any K ≤ 15 harmonic, or by any L ≤ 7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics) in two ways: 1) by explicit evaluation of integrals and 2) by reduction to known SU (3) Clebsch-Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.
NASA Astrophysics Data System (ADS)
Barbosa, D.; de Freitas, U.; Bezerra de Mello, E. R.
2011-03-01
We analyze the induced self-energy and self-force on a scalar point-like charged test particle placed at rest in the spacetime of a global monopole admitting a general spherically symmetric inner structure to it. In order to develop this analysis we calculate the three-dimensional Green's function associated with this physical system. We explicitly show that for points outside the monopole's core the scalar self-energy presents two distinct contributions. The first one is induced by the non-trivial topology of the global monopole considered as a point-like defect and the second is a correction induced by the non-vanishing inner structure attributed to it. For points inside the monopole, the self-energy also present a similar structure, where now the first contribution depends on the geometry of the spacetime inside. As illustrations of the general procedure adopted, two specific models, namely flower-pot and the ballpoint-pen, are considered for the region inside. For these two different situations, we were able to obtain exact expressions for the self-energies and self-forces in the regions outside and inside the global monopole.
Comments on black holes in bubbling spacetimes
NASA Astrophysics Data System (ADS)
Horowitz, Gary T.; Kunduri, Hari K.; Lucietti, James
2017-06-01
In five-dimensional minimal supergravity, there are spherical black holes with nontrivial topology outside the horizon which have the same conserved charges at infinity as the BMPV solution. We show that some of these black holes have greater entropy than the BMPV solution. These spacetimes are all asymptotically flat, stationary, and supersymmetric. We also show that there is a limit in which the black hole shrinks to zero size and the solution becomes a nonsingular "bubbling" geometry. Thus, these solutions provide explicit analytic examples of placing black holes inside solitons.
Conformally non-flat spacetime representing dense compact objects
NASA Astrophysics Data System (ADS)
Singh, Ksh. Newton; Bhar, Piyali; Rahaman, Farook; Pant, Neeraj; Rahaman, Mansur
2017-06-01
A new conformally non-flat interior spacetime embedded in five-dimensional (5D) pseudo Euclidean space is explored in this paper. We proceed our calculation with the assumption of spherically symmetric anisotropic matter distribution and Karmarkar condition (necessary condition for class one). This solution is free from geometrical singularity and well-behaved in all respects. We ansatz a new type of metric potential g11 and solve for the metric potential g00 via Karmarkar condition. Further, all the physical parameters are determined from Einstein’s field equations using the two metric potentials. All the constants of integration are determined using boundary conditions. Due to its conformally non-flat character, it can represent bounded configurations. Therefore, we have used it to model two compact stars Vela X-1 and Cyg X-2. Indeed, the obtained masses and radii of these two objects from our solution are well matched with those observed values given in [T. Gangopadhyay et al., Mon. Not. R. Astron. Soc. 431, 3216 (2013)] and [J. Casares et al., Mon. Not. R. Astron. Soc. 401, 2517 (2010)]. The equilibrium of the models is investigated from generalized TOV-equation. We have adopted [L. Herrera’s, Phys. Lett. A 165, 206 (1992)] method and static stability criterion of Harisson-Zeldovich-Novikov [B. K. Harrison et al., Gravitational Theory and Gravitational Collapse (University of Chicago Press, 1965); Ya. B. Zeldovich and I. D. Novikov, Relativistic Astrophysics, Vol. 1, Stars and Relativity (University of Chicago Press, 1971)] to analyze the stability of the models.
On Einstein warped products with a quarter-symmetric connection
NASA Astrophysics Data System (ADS)
Pahan, Sampa; Pal, Buddhadev; Bhattacharyya, Arindam
This paper characterizes the warping functions for a multiply generalized Robertson-Walker space-time to get an Einstein space M with a quarter-symmetric connection for different dimensions of M (i.e. (1). dim M = 2, (2). dim M ≥ 3) when all the fibers are Ricci flat. Then we have also computed the warping functions for a Ricci flat Einstein multiply warped product spaces M with a quarter-symmetric connection for different dimensions of M (i.e. (1). dim M = 2, (2). dim M = 3, (3). dim M ≥ 4) and all the fibers are Ricci flat. In the last section, we have given two examples of multiply generalized Robertson-Walker space-time with respect to quarter-symmetric connection.
Spectral dimension with deformed spacetime signature
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Trześniewski, Tomasz
2017-07-01
Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature. This effect is a consequence of quantum modifications of the hypersurface deformation algebra, which in the linearized case is equivalent to a deformed version of the Poincaré algebra. In this paper the latter relation is explored for the LQG-inspired hypersurface deformation algebra that is characterized by the above mentioned signature change. While the exact form of the deformed Poincaré algebra is not uniquely determined, the algebra under consideration is representative enough to capture a number of qualitative features. In particular, the analysis reveals that the signature change can be associated with two symmetric invariant energy scales, which separate three physically disconnected momentum subspaces. Furthermore, the invariant measure on momentum space is derived, which allows to properly define the average return probability, characterizing a fictitious diffusion process on spacetime. The diffusion is subsequently studied in the momentum representation for all possible variants of the model. Finally, the spectral dimension of spacetime is calculated in each case as a function of the scale parameter. In the most interesting situation the deformation is of the asymptotically ultralocal type and the spectral dimension reduces to dS=1 in the UV limit.
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay
In general relativity space-time ends at singularities. The big bang is considered as the Beginning and the big crunch, the End. However these conclusions are arrived at by using general relativity in regimes which lie well beyond its physical domain of validity. Examples where detailed analysis is possible show that these singularities are naturally resolved by quantum geometry effects. Quantum space-times can be vastly larger than what Einstein had us believe. These non-trivial space-time extensions enable us to answer of some long standing questions and resolve of some puzzles in fundamental physics. Thus, a century after Minkowski's revolutionary ideas on the nature of space and time, yet another paradigm shift appears to await us in the wings.
Brink, Jeandrew
2010-01-15
The problem of obtaining an explicit representation for the fourth invariant of geodesic motion (generalized Carter constant) of an arbitrary stationary axisymmetric vacuum spacetime generated from an Ernst potential is considered. The coupling between the nonlocal curvature content of the spacetime as encoded in the Weyl tensor, and the existence of a Killing tensor is explored and a constructive, algebraic test for a fourth-order Killing tensor suggested. The approach used exploits the variables defined for the Baecklund transformations to clarify the relationship between Weyl curvature, constants of geodesic motion, expressed as Killing tensors, and the solution-generation techniques. A new symmetric noncovariant formulation of the Killing equations is given. This formulation transforms the problem of looking for fourth-order Killing tensors in 4D into one of looking for four interlocking two-manifolds admitting fourth-order Killing tensors in 2D.
Axially symmetric static sources of gravitational field
NASA Astrophysics Data System (ADS)
Hernandez-Pastora, J. L.; Herrera, L.; Martin, J.
2016-12-01
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match smoothly to some exterior solution of the Weyl family, thereby representing globally regular models describing non-spherical sources of gravitational field. In the spherically symmetric limit, all our models converge to the well known incompressible perfect fluid solution. The key stone of our approach is based on an ansatz allowing to define the interior metric in terms of the exterior metric functions evaluated at the boundary source. Some particular sources are obtained, and the physical variables of the energy-momentum tensor are calculated explicitly, as well as the geometry of the source in terms of the relativistic multipole moments. The total mass of different configurations is also calculated, it is shown to be equal to the monopole of the exterior solution.
How Spherical Is a Cube (Gravitationally)?
NASA Astrophysics Data System (ADS)
Sanny, Jeff; Smith, David
2015-02-01
An important concept that is presented in the discussion of Newton's law of universal gravitation is that the gravitational effect external to a spherically symmetric mass distribution is the same as if all of the mass of the distribution were concentrated at the center.1,2 By integrating over ring elements of a spherical shell, we show that the gravitational force on a point mass outside the shell is the same as that of a particle with the same mass as the shell at its center. This derivation works for objects with spherical symmetry while depending on the fact that the gravitational force between two point masses varies inversely as the square of their separation.3 If these conditions are not met, then the problem becomes more difficult. In this paper, we remove the condition of spherical symmetry and examine the gravitational force between two uniform cubes.
Effective pair potentials for spherical nanoparticles
NASA Astrophysics Data System (ADS)
van Zon, Ramses
2009-02-01
An effective description for rigid spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, as can occur for some forms of the pair potentials, the effective potential generally has non-analytic points. It is shown that for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Even when only non-overlapping situations are possible, the auxiliary potentials facilitate the formulation of the effective potentials. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered and shown to be related to those for solid nanoparticles. For hollow nanoparticles overlap is more physical, since this covers the case of a smaller particle embedded in a larger, hollow nanoparticle. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London-van der Waals, Morse, Buckingham, and Lennard-Jones potentials. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure.
Deformed relativity symmetries and the local structure of spacetime
NASA Astrophysics Data System (ADS)
Letizia, Marco; Liberati, Stefano
2017-02-01
A spacetime interpretation of deformed relativity symmetry groups was recently proposed by resorting to Finslerian geometries, seen as the outcome of a continuous limit endowed with first-order corrections from the quantum gravity regime. In this work, we further investigate such connections between deformed algebras and Finslerian geometries by showing that the Finsler geometries associated with the generalization of the Poincaré group (the so-called κ -Poincaré Hopf algebra) are maximally symmetric spacetimes which are also of the Berwald type: Finslerian spacetimes for which the connections are substantially Riemannian, belonging to the unique class for which the weak equivalence principle still holds. We also extend this analysis by considering a generalization of the de Sitter group (the so-called q -de Sitter group) and showing that its associated Finslerian geometry reproduces locally the one from the κ -Poincaré group, and that it itself can be recast in a Berwald form in an appropriate limit.
The Newtonian limit of spacetimes for accelerated particles and black holes
NASA Astrophysics Data System (ADS)
Bičák, Jiří; Kofroň, David
2009-01-01
Solutions of vacuum Einstein’s field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor-Swaminarayan solutions, self-accelerating “dipole particles”, and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes.
Conformal Ricci collineations in LRS Bianchi type V spacetimes with perfect fluid matter
NASA Astrophysics Data System (ADS)
Khan, Fawad; Hussain, Tahir; Akhtar, Sumaira Saleem
2017-08-01
Considering the perfect fluid as a source of energy-momentum tensor, we have classified locally rotationally symmetric (LRS) Bianchi type V spacetimes according to their conformal Ricci collineations (CRCs). It is shown that the LRS Bianchi type V spacetimes with perfect fluid matter admit 9- or 15-dimensional Lie algebra of CRCs when the Ricci tensor is non-degenerate, while the group of CRCs is infinite for degenerate Ricci tensor.
Emergent spacetime for quantum gravity
NASA Astrophysics Data System (ADS)
Yang, Hyun Seok
2016-07-01
We emphasize that noncommutative (NC) spacetime necessarily implies emergent spacetime if spacetime at microscopic scales should be viewed as NC. In order to understand NC spacetime correctly, we need to deactivate the thought patterns that we have installed in our brains and taken for granted for so many years. Emergent spacetime allows a background-independent formulation of quantum gravity that will open a new perspective to resolve the notorious problems in theoretical physics such as the cosmological constant problem, hierarchy problem, dark energy, dark matter and cosmic inflation.
Uniqueness of Kerr space-time near null infinity
Wu Xiaoning; Bai Shan
2008-12-15
We reexpress the Kerr metric in standard Bondi-Sachs coordinates near null infinity I{sup +}. Using the uniqueness result of the characteristic initial value problem, we prove the Kerr metric is the only asymptotically flat, stationary, axially symmetric, type-D solution of the vacuum Einstein equation. The Taylor series of Kerr space-time is expressed in terms of Bondi-Sachs coordinates, and the Newman-Penrose constants have been calculated.
Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics
ERIC Educational Resources Information Center
Newmarch, J. D.; Golding, R. M.
1978-01-01
The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)
Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics
ERIC Educational Resources Information Center
Newmarch, J. D.; Golding, R. M.
1978-01-01
The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)
Fundamental photon orbits: Black hole shadows and spacetime instabilities
NASA Astrophysics Data System (ADS)
Cunha, Pedro V. P.; Herdeiro, Carlos A. R.; Radu, Eugen
2017-07-01
The standard black holes (BHs) in general relativity, as well as other ultracompact objects (with or without an event horizon) admit planar circular photon orbits. These light rings (LRs) determine several spacetime properties. For instance, stable LRs trigger instabilities and, in spherical symmetry, (unstable) LRs completely determine BH shadows. In generic stationary, axisymmetric spacetimes, nonplanar bound photon orbits may also exist, regardless of the integrability properties of the photon motion. We suggest a classification of these fundamental photon orbits (FPOs) and, using Poincaré maps, determine a criterion for their stability. For the Kerr BH, all FPOs are unstable (similar to its LRs) and completely determine the Kerr shadow. But in non-Kerr spacetimes, stable FPOs may also exist, even when all LRs are unstable, triggering new instabilities. We illustrate this for the case of Kerr BHs with Proca hair, wherein, moreover, qualitatively novel shadows with a cuspy edge exist, a feature that can be understood from the interplay between stable and unstable FPOs. FPOs are the natural generalization of LRs beyond spherical symmetry and should generalize the LRs key role in different spacetime properties.
Circle of least confusion of a spherical reflector.
Hosken, Robert W
2007-06-01
A simple, tractable equation is provided for determining the size and location of the circle of least confusion of a concave spherical reflector. This method is exact for the object at infinity and with wave effects neglected. Designers of large radius Arecibo-like telescopes, both radio and optical, with symmetrical, spherical primaries should find the method useful. The mathematical results are valid for apertures with an angle of incidence up to 45 degrees. Comparisons of the location of the disk of least confusion with longitudinal spherical aberration and the radius of the disk with transverse spherical aberration are presented.
Solutions on a brane in a bulk spacetime with Kalb–Ramond field
Chakraborty, Sumanta SenGupta, Soumitra
2016-04-15
Effective gravitational field equations on a brane have been derived, when the bulk spacetime is endowed with the second rank antisymmetric Kalb–Ramond field. Since both the graviton and the Kalb–Ramond field are closed string excitations, they can propagate in the bulk. After deriving the effective gravitational field equations on the brane, we solve them for a static spherically symmetric solution. It turns out that the solution so obtained represents a black hole or naked singularity depending on the parameter space of the model. The stability of this model is also discussed. Cosmological solutions to the gravitational field equations have been obtained, where the Kalb–Ramond field is found to behave as normal pressure free matter. For certain specific choices of the parameters in the cosmological solution, the solution exhibits a transition in the behaviour of the scale factor and hence a transition in the expansion history of the universe. The possibility of accelerated expansion of the universe in this scenario is also discussed.
NASA Astrophysics Data System (ADS)
Kay, Bernard S.; Lupo, Umberto
2016-11-01
We conjecture that (when the notion of Hadamard state is suitably adapted to spacetimes with timelike boundaries) there is no isometry-invariant Hadamard state for the massive or massless covariant Klein-Gordon equation defined on the region of the Kruskal spacetime to the left of a surface of constant Schwarzschild radius in the right Schwarzschild wedge when Dirichlet boundary conditions are put on that surface. We also prove that, with a suitable definition for ‘boost-invariant Hadamard state’ (which we call ‘strongly boost-invariant globally Hadamard’) which takes into account both the existence of the timelike boundary and the special infra-red pathology of massless fields in 1+1 dimensions, there is no such state for the massless wave equation on the region of 1+1 Minkowski space to the left of an eternally uniformly accelerating mirror—with Dirichlet boundary conditions at the mirror. We argue that this result is significant because, as we point out, such a state does exist if there is also a symmetrically placed decelerating mirror in the left wedge (and the region to the left of this mirror is excluded from the spacetime). We expect a similar existence result to hold for Kruskal when there are symmetrically placed spherical boxes in both right and left Schwarzschild wedges. Our Kruskal no-go conjecture raises basic questions about the nature of the black holes in boxes considered in black hole thermodynamics. If true, it would lend further support to the conclusion of Kay (2015 Gen. Relativ. Gravit. 47 1-27) that the nearest thing to a description of a black hole in equilibrium in a box in terms of a classical spacetime with quantum fields propagating on it has, for the classical spacetime, the exterior Schwarzschild solution, with the classical spacetime picture breaking down near the horizon. Appendix B to the paper points out the existence of, and partially fills, a gap in the proofs of the theorems in Kay and Wald (1991 Phys. Rep. 207 49-136).
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
NASA Astrophysics Data System (ADS)
Bojowald, Martin
2016-07-01
The equations of Hamiltonian gravity are often considered ugly cousins of the elegant and manifestly covariant versions found in the Lagrangian theory. However, both formulations are fundamental in their own rights because they make different statements about the nature of spacetime and its symmetries. These implications, along with the history of their derivation and an introduction of recent mathematical support, are the topic of this essay.
Crack problems in cylindrical and spherical shells
NASA Technical Reports Server (NTRS)
Erdogan, F.
1976-01-01
Standard plate or shell theories were used as a starting point to study the fracture problems in thin-walled cylindrical and spherical shells, assuming that the plane of the crack is perpendicular to the surface of the sheet. Since recent studies have shown that local shell curvatures may have a rather considerable effect on the stress intensity factor, the crack problem was considered in conjunction with a shell rather than a plate theory. The material was assumed to be isotropic and homogeneous, so that approximate solutions may be obtained by approximating the local shell crack geometry with an ideal shell which has a solution, namely a spherical shell with a meridional crack, a cylindrical shell with a circumferential crack, or a cylindrical shell with an axial crack. A method of solution for the specially orthotropic shells containing a crack was described; symmetric and skew-symmetric problems are considered in cylindrical shells with an axial crack.
Classification of spacetimes with symmetry
NASA Astrophysics Data System (ADS)
Hicks, Jesse W.
Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we. i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes; ii) create digital databases of the classification for easy access and use for researchers; iii) create software to classify any spacetime metric with symmetry against the new database; iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics; v) classify spacetimes with symmetry in the book Exact Solutions to Einstein's Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov's paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.
Spacetime structure and vacuum entanglement
NASA Astrophysics Data System (ADS)
Martín-Martínez, Eduardo; Smith, Alexander R. H.; Terno, Daniel R.
2016-02-01
We derive the structure of the density matrix for two Unruh-DeWitt detectors coupled to a massless scalar field to all orders of perturbation theory, in spacetimes admitting a well-defined Wightman function. Calculating all of its leading terms enables us to fully characterize observable correlations, entanglement, and quantum discord. We apply these results to study detector responses in two locally flat topologically nontrivial spacetimes constructed from identifications of Minkowski space. We demonstrate how local statistics and detector-detector correlations depend on the global spacetime structure. In particular, we show that if the spacetime has a preferred direction, this direction may be inferred from the dependence of correlations between the two detectors on their orientation. While using such measurements to distinguish spacetimes with identical local geometry is apparently impractical, this effect points to fundamental connections between quantum field correlations and the structure of spacetime. This relationship may also be relevant in the phenomenology of the early Universe.
Introducing surface tension to spacetime
NASA Astrophysics Data System (ADS)
Perko, H. A.
2017-05-01
Concepts from physical chemistry of surfaces and surface tension are applied to spacetime. More specifically, spacetime is modeled as a spatial fluid continuum bound together by a multi-dimensional membrane of time. A metric tensor that relates empty flat spacetime to energetic curved spacetime is found. Equations of motion for an infinitesimal unit of spacetime are derived. The equation of motion in a time-like direction is a Klein-Gordon type equation. The equations of motion in space-like directions take the form of Schrodinger’s equation where Plank’s constant is related to membrane elastic modulus. Although much work remains, it is suggested that the spacetime surface tension may serve as a mechanical model for many phenomena in quantum mechanics and atomic particle physics.
Magnetic fields of spherical compact stars in a braneworld
Ahmedov, B. J.; Fattoyev, F. J.
2008-08-15
We study the stellar magnetic field configuration in dependence on brane tension and present solutions of Maxwell equations in the external background space-time of a magnetized spherical star in a Randall-Sundrum II type braneworld. The star is modeled as a sphere consisting of perfect highly magnetized fluid with infinite conductivity and a frozen-in magnetic field. With respect to solutions for magnetic fields found in the Schwarzschild space-time, brane tension introduces enhancing corrections to the exterior magnetic field which could be relevant for the magnetic fields of magnetized compact objects as pulsars and magnetars and may provide observational evidence for the brane tension.
NASA Astrophysics Data System (ADS)
de, Uday Chand; Velimirović, Ljubica; Mallick, Sahanous
2017-09-01
The object of the present paper is to study a spacetime admitting conharmonic curvature tensor and some geometric properties related to this spacetime. It is shown that in a conharmonically flat spacetime with cyclic parallel Ricci tensor, the energy-momentum tensor is cyclic parallel and conversely. Finally, we prove that for a radiative perfect fluid spacetime if the energy-momentum tensor satisfying the Einstein’s equations without cosmological constant is generalized recurrent, then the fluid has vanishing vorticity and the integral curves of the vector field U are geodesics.
Spacetime in modern physical theories
NASA Astrophysics Data System (ADS)
Klatt, Carrie
In this thesis we examine the relationship between the gravitational field and spacetime in three modern physical theories: general relativity, the field theoretic approach, and geometrodynamics. Our analysis is based on two questions: first, is gravity best understood as a field in a spacetime background or is the gravitational field indistinguishable from spacetime? Here we compare the field theoretic approach to gravity presented by Feynman and Weinberg, where spacetime is at first taken to be a flat background, to general relativity, where we find that the equivalence principle in conjunction with the geodesic hypothesis allows us to consider the gravitational field as being indistinguishable from curved spacetime. Second, what does it mean to say that spacetime (or alternatively, matter) has a privileged status in a theory? That is, is it sensible to say that one object in a theory, such as spacetime, can be derived from another object in the theory, for example, matter? Here we compare general relativity, where matter and spacetime are considered to be primary notions in the theory, to Wheeler's geometrodynamics, where all objects in the universe, including matter, charge and electromagnetism, are to be explained as manifestations of curved spacetime. By considering these issues, it is hoped that we will be able to contribute to the analysis of similar topics in theories of quantum gravity such as string theory.
Spherical cows in dark matter indirect detection
NASA Astrophysics Data System (ADS)
Bernal, Nicolás; Necib, Lina; Slatyer, Tracy R.
2016-12-01
Dark matter (DM) halos have long been known to be triaxial, but in studies of possible annihilation and decay signals they are often treated as approximately spherical. In this work, we examine the asymmetry of potential indirect detection signals of DM annihilation and decay, exploiting the large statistics of the hydrodynamic simulation Illustris. We carefully investigate the effects of the baryons on the sphericity of annihilation and decay signals for both the case where the observer is at 8.5 kpc from the center of the halo (exemplified in the case of Milky Way-like halos), and for an observer situated well outside the halo. In the case of Galactic signals, we find that both annihilation and decay signals are expected to be quite symmetric, with axis ratios very different from 1 occurring rarely. In the case of extragalactic signals, while decay signals are still preferentially spherical, the axis ratio for annihilation signals has a much flatter distribution, with elongated profiles appearing frequently. Many of these elongated profiles are due to large subhalos and/or recent mergers. Comparing to gamma-ray emission from the Milky Way and X-ray maps of clusters, we find that the gamma-ray background appears less spherical/more elongated than the expected DM signal from the large majority of halos, and the Galactic gamma ray excess appears very spherical, while the X-ray data would be difficult to distinguish from a DM signal by elongation/sphericity measurements alone.
Spontaneous symmetry breaking in wormholes spacetimes with matter
NASA Astrophysics Data System (ADS)
Hoffmann, Christian; Ioannidou, Theodora; Kahlen, Sarah; Kleihaus, Burkhard; Kunz, Jutta
2017-04-01
When bosonic matter in the form of a complex scalar field is added to Ellis wormholes, the phenomenon of spontaneous symmetry breaking is observed. Symmetric solutions possess full reflection symmetry with respect to the radial coordinate of the two asymptotically flat spacetime regions connected by the wormhole, whereas asymmetric solutions do not possess this symmetry. Depending on the size of the throat, at bifurcation points pairs of asymmetric solutions arise from or merge with the symmetric solutions. These asymmetric solutions are energetically favored. When the backreaction of the boson field is taken into account, this phenomenon is retained. Moreover, in a certain region of the solution space both symmetric and asymmetric solutions exhibit a transition from single throat to double throat configurations.
NASA Astrophysics Data System (ADS)
Lemos, José P. S.; Zanchin, Vilson T.
2017-05-01
We show that Guilfoyle's exact solutions of the Einstein-Maxwell equations for spherical symmetric static electrically charged matter with a Reissner-Nordström exterior possess a bewildering plethora of different types of solutions. For the parameter space of the solutions we use two normalized variables, q2/R2 and r0/R , where q is the total electric charge, r0 is the radius of the object, and R is a length representing the square root of the inverse energy density of the matter. The two other parameters, the mass m and the Guilfoyle parameter a , both dependent on q , r0 and R , are analyzed in detail. The full parameter space of solutions q2/R2×r0/R is explored with the corresponding types of solutions being identified and analyzed. The different types of solutions are regular charged stars, including charged dust stars and stars saturating the Buchdahl-Andréasson bound, quasiblack holes, regular charged black holes with a de Sitter core, regular black holes with a core of phantom charged matter, other exotic regular black holes, Schwarzschild stars, Schwarzschild black holes, Kasner spacetimes, pointlike and planar naked singularities, and the Minkowski spacetime. Allowing for q2<0 , in which case it is not possible to interpret q as electric charge, also yields new solutions, some of which are interesting and regular, others are singular. Some of these types of solutions as well as the matter properties have been previously found and studied, here the full spectrum being presented in a unified manner.
Mass ladder operators from spacetime conformal symmetry
NASA Astrophysics Data System (ADS)
Cardoso, Vitor; Houri, Tsuyoshi; Kimura, Masashi
2017-07-01
Ladder operators can be useful constructs, allowing for unique insight and intuition. In fact, they have played a special role in the development of quantum mechanics and field theory. Here, we introduce a novel type of ladder operators, which map a scalar field onto another massive scalar field. We construct such operators, in arbitrary dimensions, from closed conformal Killing vector fields, eigenvectors of the Ricci tensor. As an example, we explicitly construct these objects in anti-de Sitter (A d S ) spacetime and show that they exist for masses above the Breitenlohner-Freedman bound. Starting from a regular seed solution of the massive Klein-Gordon equation, mass ladder operators in AdS allow one to build a variety of regular solutions with varying boundary condition at spatial infinity. We also discuss mass ladder operator in the context of spherical harmonics, and the relation between supersymmetric quantum mechanics and so-called Aretakis constants in an extremal black hole.
Nonadiabatic charged spherical gravitational collapse
Di Prisco, A.; Herrera, L.; Le Denmat, G.; MacCallum, M. A. H.; Santos, N. O.
2007-09-15
We present a complete set of the equations and matching conditions required for the description of physically meaningful charged, dissipative, spherically symmetric gravitational collapse with shear. Dissipation is described with both free-streaming and diffusion approximations. The effects of viscosity are also taken into account. The roles of different terms in the dynamical equation are analyzed in detail. The dynamical equation is coupled to a causal transport equation in the context of Israel-Stewart theory. The decrease of the inertial mass density of the fluid, by a factor which depends on its internal thermodynamic state, is reobtained, with the viscosity terms included. In accordance with the equivalence principle, the same decrease factor is obtained for the gravitational force term. The effect of the electric charge on the relation between the Weyl tensor and the inhomogeneity of the energy density is discussed.
Hawking, S.W.
1988-02-15
Any reasonable theory of quantum gravity will allow closed universes to branch off from our nearly flat region of spacetime. I describe the possible quantum states of these closed universes. They correspond to wormholes which connect two asymptotically Euclidean regions, or two parts of the same asymptotically Euclidean region. I calculate the influence of these wormholes on ordinary quantum fields at low energies in the asymptotic region. This can be represented by adding effective interactions in flat spacetime which create or annihilate closed universes containing certain numbers of particles. The effective interactions are small except for closed universes containing scalar particles in the spatially homogeneous mode. If these scalar interactions are not reduced by sypersymmetry, it may be that any scalar particles we observe would have to be bound states of particles of higher spin, such as the pion. An observer in the asymptotically flat region would not be able to measure the quantum state of closed universes that branched off. He would therefore have to sum over all possibilities for the closed universes. This would mean that the final state would appear to be a mixed quantum state, rather than a pure quantum state.
NASA Astrophysics Data System (ADS)
Chapline, George
It has been shown that a nonlinear Schrödinger equation in 2+1 dimensions equipped with an SU(N) Chern-Simons gauge field can provide an exact description of certain self-dual Einstein spaces in the limit N-=∞. Ricci flat Einstein spaces can then be viewed as arising from a quantum pairing of the classical self-dual and anti-self-dual solutions. In this chapter, we will outline how this theory of empty space-time might be generalized to include matter and vacuum energy by transplanting the nonlinear Schrödinger equation used to construct Einstein spaces to the 25+1-dimensional Lorentzian Leech lattice. If the distinguished 2 spatial dimensions underlying the construction of Einstein spaces are identified with a hexagonal lattice section of the Leech lattice, the wave-function becomes an 11 × 11 matrix that can represent fermion and boson degrees of freedom (DOF) associated with 2-form and Yang-Mills gauge symmetries. The resulting theory of gravity and matter in 3+1 dimensions is not supersymmetric, which provides an entry for a vacuum energy. Indeed, in the case of a Lemaitre cosmological model, the emergent space-time will naturally have a vacuum energy on the order of the observed cosmological constant.
Prescribed mean curvature graphs with Neumann boundary conditions in some FLRW spacetimes
NASA Astrophysics Data System (ADS)
Mawhin, Jean; Torres, Pedro J.
2016-12-01
We identify a family of Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes such that the radially symmetric prescribed curvature problem with Neumann boundary condition is solvable on a ball of small radius. Such family contains some examples of interest in Cosmology.
Quantum field theory in the space-time of a cosmic string
Linet, B.
1987-01-15
For a massive scalar field in the static cylindrically symmetric space-time describing a cosmic string, we determine explicitly the Euclidean Green's function. We obtain also an alternative local form which allows us to calculate the vacuum energy-momentum tensor. In the case of a conformal scalar field, we carry out completely the calculations.
Structure of random discrete spacetime
NASA Technical Reports Server (NTRS)
Brightwell, Graham; Gregory, Ruth
1991-01-01
The usual picture of spacetime consists of a continuous manifold, together with a metric of Lorentzian signature which imposes a causal structure on the spacetime. A model, first suggested by Bombelli et al., is considered in which spacetime consists of a discrete set of points taken at random from a manifold, with only the causal structure on this set remaining. This structure constitutes a partially ordered set (or poset). Working from the poset alone, it is shown how to construct a metric on the space which closely approximates the metric on the original spacetime manifold, how to define the effective dimension of the spacetime, and how such quantities may depend on the scale of measurement. Possible desirable features of the model are discussed.
Structure of random discrete spacetime
NASA Technical Reports Server (NTRS)
Brightwell, Graham; Gregory, Ruth
1991-01-01
The usual picture of spacetime consists of a continuous manifold, together with a metric of Lorentzian signature which imposes a causal structure on the spacetime. A model, first suggested by Bombelli et al., is considered in which spacetime consists of a discrete set of points taken at random from a manifold, with only the causal structure on this set remaining. This structure constitutes a partially ordered set (or poset). Working from the poset alone, it is shown how to construct a metric on the space which closely approximates the metric on the original spacetime manifold, how to define the effective dimension of the spacetime, and how such quantities may depend on the scale of measurement. Possible desirable features of the model are discussed.
NASA Astrophysics Data System (ADS)
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Numerical study of the gravitational shock wave inside a spherical charged black hole
NASA Astrophysics Data System (ADS)
Eilon, Ehud; Ori, Amos
2016-11-01
We numerically investigate the interior of a four-dimensional, asymptotically flat, spherically symmetric charged black hole perturbed by a scalar field Φ . Previous study by Marolf and Ori indicated that late infalling observers will encounter an effective shock wave as they approach the left portion of the inner horizon. This shock manifests itself as a sudden change in the values of various fields, within a tremendously short interval of proper time τ of the infalling observers. We confirm this prediction numerically for both test and self-gravitating scalar-field perturbations. In both cases we demonstrate the effective shock in the scalar field by exploring Φ (τ ) along a family of infalling timelike geodesics. In the self-gravitating case we also demonstrate the shock in the area coordinate r by exploring r (τ ). We confirm the theoretical prediction concerning the shock sharpening rate, which is exponential in the time of infall into the black hole. In addition we numerically probe the early stages of shock formation. We also employ a family of null (rather than timelike) ingoing geodesics to probe the shock in r . We use a finite-difference numerical code with double-null coordinates combined with a recently developed adaptive gauge method in order to solve the (Einstein+scalar ) field equations and to evolve the spacetime (and scalar field)—from the region outside the black hole down to the vicinity of the Cauchy horizon and the spacelike r =0 singularity.
Cotangent bundle over all the compact Hermitian symmetric spaces and projective superspace
NASA Astrophysics Data System (ADS)
Arai, Masato
2014-05-01
We construct the N = 2 supersymmetric nonlinear sigma model on the cotangent bundle over the compact Hermitian symmetric space E7/E6 × U(1) by using the projective superspace formalism which is an off-shell superfield formulation in four-dimensional space-time. We also give a simple formula giving the hyper-Kahler potential of the cotangent bundle over all the compact Hermitian symmetric spaces.
Panprasitwech, Oranit; Laohakosol, Vichian; Chaichana, Tuangrat
2010-11-11
Explicit formulae for continued fractions with symmetric patterns in their partial quotients are constructed in the field of formal power series. Similar to the work of Cohn in 1996, which generalized the so-called folding lemma to {kappa}-fold symmetry, the notion of {kappa}-duplicating symmetric continued fractions is investigated using a modification of the 1995 technique due to Clemens, Merrill and Roeder.
Relativistic scattered-wave theory. II - Normalization and symmetrization. [of Dirac wavefunctions
NASA Technical Reports Server (NTRS)
Yang, C. Y.
1978-01-01
Formalisms for normalization and symmetrization of one-electron Dirac scattered-wave wavefunctions are presented. The normalization integral consists of one-dimensional radial integrals for the spherical regions and an analytic expression for the intersphere region. Symmetrization drastically reduces the size of the secular matrix to be solved. Examples for planar Pb2Se2 and tetrahedral Pd4 are discussed.
Relativistic scattered-wave theory. II - Normalization and symmetrization. [of Dirac wavefunctions
NASA Technical Reports Server (NTRS)
Yang, C. Y.
1978-01-01
Formalisms for normalization and symmetrization of one-electron Dirac scattered-wave wavefunctions are presented. The normalization integral consists of one-dimensional radial integrals for the spherical regions and an analytic expression for the intersphere region. Symmetrization drastically reduces the size of the secular matrix to be solved. Examples for planar Pb2Se2 and tetrahedral Pd4 are discussed.
New Spherical Scalar Modes on the de Sitter Expanding Universe
NASA Astrophysics Data System (ADS)
Pascu, Gabriel
2012-07-01
New spherical scalar modes on the expanding part of Sitter spacetime, eigenfunctions of a conserved Hamiltonian-like operator are found by solving the Klein-Gordon equation in the appropriate coordinate chart, with the help of a time evolution picture technique specially developed for spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) charts. Transition coefficients are computed between these modes and the rest of the scalar spherical and plane wave modes, either momentum or energy eigenfunctions on the spatially flat FLRW chart.
Newtonian wormholes with spherical symmetry and tidal forces on test particles
NASA Astrophysics Data System (ADS)
Luz, Paulo; Lemos, José P. S.
2015-06-01
A spherically symmetric wormhole in Newtonian gravitation in curved space, enhanced with a connection between the mass density and the Ricci scalar, is presented. The wormhole, consisting of two connected asymptotically flat regions, inhabits a spherically symmetric curved space. The gravitational potential, gravitational field and the pressure that supports the fluid that permeates the Newtonian wormhole are computed. Particle dynamics and tidal effects in this geometry are studied. The possibility of having Newtonian black holes in this theory is sketched.
Topology and incompleteness for 2+1-dimensional cosmological spacetimes
NASA Astrophysics Data System (ADS)
Fajman, David
2016-12-01
We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
Topology and incompleteness for 2+1-dimensional cosmological spacetimes
NASA Astrophysics Data System (ADS)
Fajman, David
2017-06-01
We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.
Nonequilibrium thermodynamics of spacetime.
Eling, Christopher; Guedens, Raf; Jacobson, Ted
2006-03-31
It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the horizon. Here we show that a curvature correction to the entropy that is polynomial in the Ricci scalar requires a nonequilibrium treatment. The corresponding field equation is derived from the entropy balance relation dS=deltaQ/T+diS, where diS is a bulk viscosity entropy production term that we determine by imposing energy-momentum conservation. Entropy production can also be included in pure Einstein theory by allowing for shear viscosity of the horizon.
Plane symmetric thin-shell wormholes: Solutions and stability
Lemos, Jose P. S.; Lobo, Francisco S. N.
2008-08-15
Using the cut-and-paste procedure, we construct static and dynamic, plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes can be interpreted as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around static solutions is also explored. It is found that thin-shell wormholes made of a dark energy fluid or of a cosmological constant fluid are stable, while thin-shell wormholes made of phantom energy are unstable.
Applications of holographic spacetime
NASA Astrophysics Data System (ADS)
Torres, Terrence J.
Here we present an overview of the theory of holographic spacetime (HST), originally devised and primarily developed by Tom Banks and Willy Fischler, as well as its various applications and predictions for cosmology and particle phenomenology. First we cover the basic theory and motivation for holographic spacetime and move on to present the latest developments therein as of the time of this writing. Then we indicate the origin of the quantum degrees of freedom in the theory and then present a correspondence with low energy effective field theory. Further, we proceed to show the general origins of inflation and the cosmic microwave background (CMB) within the theory of HST as well as predict the functional forms of two and three point correlation functions for scalar and tensor curvature fluctuations in the early universe. Next, we constrain the theory parameters by insisting on agreement with observational bounds on the scalar spectral index of CMB fluctuations from the Planck experiment as well as theoretical bounds on the number of e-folds of inflation. Finally, we argue that HST predicts specific gauge structures for the low-energy effective field theory at the present era and proceed to construct a viable supersymmetric model extension. Constraints on model parameters and couplings are then calculated by numerically minimizing the theory's scalar potential and comparing the resultant model mass spectra to current observational limits from the LHC SUSY searches. In the end we find that the low-energy theory, while presenting a little hierarchy problem, is fully compatible with current observational limits. Additionally, the high-energy underlying theory is generically compatible with observational constraints stemming from inflation, and predictions on favored model parameters are given.
The spherical birdcage resonator
NASA Astrophysics Data System (ADS)
Harpen, Michael D.
A description of the operation of a spherical resonator capable of producing a uniform magnetic induction throughout a spherical volume is presented. Simple closed-form expressions for the spectrum of resonant frequencies are derived for both the low-pass and the high-pass configuration of the resonator and are shown to compare favorably with observation in an experimental coil system. It is shown that the spherical resonator produces a uniform spherical field of view when used as a magnetic resonance imaging radiofrequency coil.
Nonlocal gravity: Conformally flat spacetimes
NASA Astrophysics Data System (ADS)
Bini, Donato; Mashhoon, Bahram
2016-04-01
The field equations of the recent nonlocal generalization of Einstein’s theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of conformally flat spacetimes. Even in this simple case, the field equations are intractable. Therefore, to gain insight into the nature of these equations, we investigate the structure of nonlocal gravity (NLG) in 2D spacetimes. While any smooth 2D spacetime is conformally flat and satisfies Einstein’s field equations, only a subset containing either a Killing vector or a homothetic Killing vector can satisfy the field equations of NLG.
Stability and superluminality of spherical DBI Galileon solutions
Goon, Garrett L.; Hinterbichler, Kurt; Trodden, Mark
2011-04-12
We showed that, when considered as local modifications to gravity, such as in the solar system, there exists a region of parameter space in which spherically symmetric static solutions to a particular class of modified gravity theories exist and are stable.
Plasma oscillations in spherical Gaussian shaped ultracold neutral plasma
Chen, Tianxing; Lu, Ronghua Guo, Li; Han, Shensheng
2016-04-15
The collective plasma oscillations are investigated in ultracold neutral plasma with a non-uniform density profile. Instead of the plane configuration widely used, we derive the plasma oscillation equations with spherically symmetric distribution and Gaussian density profile. The damping of radial oscillation is found. The Tonks–Dattner resonances of the ultracold neutral plasma with an applied RF field are also calculated.
Stability and superluminality of spherical DBI Galileon solutions
Goon, Garrett L.; Hinterbichler, Kurt; Trodden, Mark
2011-04-12
We showed that, when considered as local modifications to gravity, such as in the solar system, there exists a region of parameter space in which spherically symmetric static solutions to a particular class of modified gravity theories exist and are stable.
Electrodynamics and Spacetime Geometry: Foundations
NASA Astrophysics Data System (ADS)
Cabral, Francisco; Lobo, Francisco S. N.
2016-11-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Central tetrads and quantum spacetimes
NASA Astrophysics Data System (ADS)
Borowiec, Andrzej; Jurić, Tajron; Meljanac, Stjepan; Pachoł, Anna
2016-06-01
In this paper, we perform a parallel analysis to the model proposed in [E. J. Beggs and S. Majid, Gravity induced from quantum spacetime, Class. Quantum Grav. 31 (2014) 035020, arXiv: 1305.2403 [gr-qc
Electrodynamics and Spacetime Geometry: Foundations
NASA Astrophysics Data System (ADS)
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Braids, shuffles and symmetrizers
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2009-07-01
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined. Dedicated to the memory of Aleosha Zamolodchikov.
Leung, Ka-Ngo
2006-11-21
A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.
The solid angle (geometry factor) for a spherical surface source and an arbitrary detector aperture
Favorite, Jeffrey A.
2016-01-13
It is proven that the solid angle (or geometry factor, also called the geometrical efficiency) for a spherically symmetric outward-directed surface source with an arbitrary radius and polar angle distribution and an arbitrary detector aperture is equal to the solid angle for an isotropic point source located at the center of the spherical surface source and the same detector aperture.
Computer program for determination of natural frequencies of closed spherical sandwich shells
NASA Technical Reports Server (NTRS)
Wilkinson, J. P. D.
1967-01-01
Solutions for the axially symmetric motion of an elastic spherical sandwich shell have been obtained from a theory of shells which includes the effects of transverse shear deformation and rotary inertia. Frequency equations and mode shapes are derived for the full vibrations of a closed spherical shell.
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
Fractal properties of quantum spacetime.
Benedetti, Dario
2009-03-20
We show that, in general, a spacetime having a quantum group symmetry has also a scale-dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what is observed in some approaches to quantum gravity. In particular, we analyze the cases of a quantum sphere and of kappa-Minkowski spacetime, the latter being relevant in the context of quantum gravity.
Rapidly rotating spacetimes and collisional super-Penrose process
NASA Astrophysics Data System (ADS)
Zaslavskii, O. B.
2016-05-01
We consider generic axially symmetric rotating spacetimes and examine particle collisions in the ergoregion. The results are generic and agree with those obtained in the particular case of the rotating Teo wormhole in Tsukamoto and Bambi, Phys Rev D 91:104040, 2015. It is shown that for sufficiently rapid rotation, the energy of a particle escaping to infinity can become arbitrary large (so-called super-Penrose process). Moreover, this energy is typically much larger than the center-of mass energy of colliding particles. In this sense the situation differs radically from that for collisions near black holes.
Space-time compressive imaging.
Treeaporn, Vicha; Ashok, Amit; Neifeld, Mark A
2012-02-01
Compressive imaging systems typically exploit the spatial correlation of the scene to facilitate a lower dimensional measurement relative to a conventional imaging system. In natural time-varying scenes there is a high degree of temporal correlation that may also be exploited to further reduce the number of measurements. In this work we analyze space-time compressive imaging using Karhunen-Loève (KL) projections for the read-noise-limited measurement case. Based on a comprehensive simulation study, we show that a KL-based space-time compressive imager offers higher compression relative to space-only compressive imaging. For a relative noise strength of 10% and reconstruction error of 10%, we find that space-time compressive imaging with 8×8×16 spatiotemporal blocks yields about 292× compression compared to a conventional imager, while space-only compressive imaging provides only 32× compression. Additionally, under high read-noise conditions, a space-time compressive imaging system yields lower reconstruction error than a conventional imaging system due to the multiplexing advantage. We also discuss three electro-optic space-time compressive imaging architecture classes, including charge-domain processing by a smart focal plane array (FPA). Space-time compressive imaging using a smart FPA provides an alternative method to capture the nonredundant portions of time-varying scenes.
NASA Astrophysics Data System (ADS)
Olsson, Peter
2016-03-01
A new directional decomposition of the acoustic 3D wave equation is derived for spherically symmetric geometries, where the wave fields do not need to possess such a symmetry. This provides an alternative basis for various applications of techniques like invariant embedding and time domain Green functions in spherically symmetric geometries. Contrary to previous results on spherical wave splittings, the new decomposition is given in a very explicit form. The wave equation considered incorporates effects from radially varying compressibility and density, but also from anisotropic density, a property of certain so called metafluids. By applying the new spherical wave splitting, we show that all spherically symmetric acoustic metafluid cloaks are diffeomorphic images of a homogeneous and isotropic spherical ball of perfect fluid.
Weakly turbulent instability of anti-de Sitter spacetime.
Bizoń, Piotr; Rostworowski, Andrzej
2011-07-15
We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) space by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS space is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.
NASA Astrophysics Data System (ADS)
Wiltshire, David L.; Visser, Matt; Scott, Susan M.
2009-01-01
List of illustrations; Contributors; Foreword; Part I. General Relativity: Classical Studies of the Kerr Geometry: 1. The Kerr spacetime: a brief introduction Matt Visser; 2. The Kerr and Kerr-Schild metrics Roy P. Kerr; 3. Roy Kerr and twistor theory Roger Penrose; 4. Global and local problems solved by the Kerr metric Brandon Carter; 5. Four decades of black hole uniqueness theorems David C. Robinson; 6. Ray-traced visualisations Benjamin R. Lewis, Susan M. Scott; Part II. Astrophysics: The Ongoing Observational Revolution: 7. The ergosphere and dyadosphere of the Kerr black hole Remo Ruffini; 8. Supermassive Black Holes Fulvio Melia; 9. The X-ray spectra of accreting Kerr black holes Andrew C. Fabian, Giovanni Miniutti; 10. Cosmological flashes from rotating black holes Maurice H.P.M. van Putten; Part III. Quantum Gravity: Rotating Black Holes at the Theoretical Frontiers: 11. Horizon constraints and black hole entropy Steve Carlip; 12. Higher dimensional generalizations of the Kerr black hole Gary T. Horowitz; Part IV. Appendices: 13. Gravitational field of a spinning mass … Roy P. Kerr; 14. Gravitational collapse and rotation Roy P. Kerr; Index.
Nonorientable spacetime tunneling
NASA Astrophysics Data System (ADS)
González-Díaz, Pedro F.; Garay, Luis J.
1999-03-01
Misner space is generalized to have the nonorientable topology of a Klein bottle, and it is shown that, in a classical spacetime with multiply connected space slices having such a topology, closed timelike curves are formed. Different regions on the Klein bottle surface can be distinguished which are separated by apparent horizons fixed at particular values of the two angular variables that enter the metric. Around the throat of this tunnel (which we denote a Klein bottlehole), the position of these horizons dictates an ordinary and exotic matter distribution such that, in addition to the known diverging lensing action of wormholes, a converging lensing action is also present at the mouths. Associated with this matter distribution, the accelerating version of this Klein bottlehole shows four distinct chronology horizons, each with its own nonchronal region. A calculation of the quantum vacuum fluctuations performed by using the regularized two-point Hadamard function shows that each chronology horizon nests a set of polarized hypersurfaces where the renormalized momentum-energy tensor diverges. This quantum instability can be prevented if we take the accelerating Klein bottlehole to be a generalization of a modified Misner space in which the period of the closed spatial direction is time dependent. In this case, the nonchronal regions and closed timelike curves cannot exceed a minimum size of the order the Planck scale.
Averaging Schwarzschild spacetime
NASA Astrophysics Data System (ADS)
Tegai, S. Ph.; Drobov, I. V.
2017-07-01
We tried to average the Schwarzschild solution for the gravitational point source by analogy with the same problem in Newtonian gravity or electrostatics. We expected to get a similar result, consisting of two parts: the smoothed interior part being a sphere filled with some matter content and an empty exterior part described by the original solution. We considered several variants of generally covariant averaging schemes. The averaging of the connection in the spirit of Zalaletdinov's macroscopic gravity gave unsatisfactory results. With the transport operators proposed in the literature it did not give the expected Schwarzschild solution in the exterior part of the averaged spacetime. We were able to construct a transport operator that preserves the Newtonian analogy for the outward region but such an operator does not have a clear geometrical meaning. In contrast, using the curvature as the primary averaged object instead of the connection does give the desired result for the exterior part of the problem in a fine way. However for the interior part, this curvature averaging does not work because the Schwarzschild curvature components diverge as 1 /r3 near the center and therefore are not integrable.
Souza Dutra, A. de; Santos, V. G. C. S. dos; Amaro de Faria, A. C. Jr.
2007-06-15
Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier; Gutierrez, German
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Charged compact stellar model in Finch-Skea spacetime
NASA Astrophysics Data System (ADS)
Ratanpal, B. S.; Pandya, D. M.; Sharma, R.; Das, S.
2017-04-01
Making use of the Finch and Skea ansatz (Class. Quantum Gravity 6:467, 1989), we present a new class of solutions for a compact stellar object whose exterior space-time is described by the Riessner-Nordström metric. We generate the solution by assuming a specific charge distribution and show its relevance in the context of relativistic spherical objects possessing a net charge. In particular, we analyze the impact of charge on the mass-radius (M-R) relationship of compact stellar objects.
Interacting shells in AdS spacetime and chaos
NASA Astrophysics Data System (ADS)
Brito, Richard; Cardoso, Vitor; Rocha, Jorge V.
2016-07-01
We study the simplest two-body problem in asymptotically anti-de Sitter spacetime: two, infinitely thin, concentric spherical shells of matter. We include only gravitational interaction between the two shells, but we show that the dynamics of this system is highly nontrivial. We observe prompt collapse to a black hole, delayed collapse and even perpetual oscillatory motion, depending on the initial location of the shells (or their energy content). The system exhibits critical behavior, and we show strong hints that it is also chaotic.
Wide scanning spherical antenna
NASA Technical Reports Server (NTRS)
Shen, Bing (Inventor); Stutzman, Warren L. (Inventor)
1995-01-01
A novel method for calculating the surface shapes for subreflectors in a suboptic assembly of a tri-reflector spherical antenna system is introduced, modeled from a generalization of Galindo-Israel's method of solving partial differential equations to correct for spherical aberration and provide uniform feed to aperture mapping. In a first embodiment, the suboptic assembly moves as a single unit to achieve scan while the main reflector remains stationary. A feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan thereby eliminating the need to oversize the main spherical reflector. In an alternate embodiment, both the main spherical reflector and the suboptic assembly are fixed. A flat mirror is used to create a virtual image of the suboptic assembly. Scan is achieved by rotating the mirror about the spherical center of the main reflector. The feed horn is tilted during scan to maintain the illuminated area on the main spherical reflector fixed throughout the scan.
Elastic dipole response of spherical nuclei
Bastrukov, S.I.
1992-10-01
Within the framework of the nuclear fluid-dynamics the isoscalar dipole response of spherical nuclei is studied. Two kinds of elastic-like transverse oscillations of incompressible nucleus are found to be result in E1, T = 0 and M1, T = 0 spin-independent resonances. The isoscalar electric mode is accompanied by excitation in the nucleus volume of the torus-like current structure, known in the continuum theory as a poloidal dipole or spherical vortex of Hill. The dipole magnetic resonance belongs to the excitation of axially symmetric differential rotations. These motions are described by the toroidal dipole field harmonic in time. The estimates of energies and PWBA-computed form-factors for these modes are presented. 28 refs., 3 figs.
Spontaneous spherical symmetry breaking in atomic confinement
NASA Astrophysics Data System (ADS)
Sveshnikov, Konstantin; Tolokonnikov, Andrey
2017-07-01
The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The most novel and nontrivial result, which has not been reported previously, is that such an effect takes place not only for attractive, but also for repulsive interactions of atomic electrons with the cavity environment. Moreover, in the limit of a large box size R ≫ aB the regime of an atom, soaring over a plane with boundary condition of "not going out", is reproduced, rather than a spherically symmetric configuration, which would be expected on the basis of the initial SO(3) symmetry of the problem.
Static spherical metrics: a geometrical approach
NASA Astrophysics Data System (ADS)
Tiwari, A. K.; Maharaj, S. D.; Narain, R.
2017-08-01
There exist several solution generating algorithms for static spherically symmetric metrics. Here we use the geometrical approach of Lie point symmetries to solve the condition of pressure isotropy by finding the associated five-dimensional Lie algebra of symmetry generators. For the non-Abelian subalgebras the underlying equation is solved to obtain a general solution. Contained within this class are vacuum models, constant density models, metrics with linear equations of state and the Buchdahl representation of the polytrope with index five. For a different particular symmetry generator the condition of pressure isotropy is transformed to a Riccati equation which admits particular solutions.
Symmetries of asymptotically flat axisymmetric space-times with null dust
NASA Astrophysics Data System (ADS)
Gönna, U. von der; Pravdová, A.
2000-05-01
Symmetries of space-times with null dust field as a source compatible with asymptotic flatness are studied by using the Bondi-Sachs-van der Burg formalism. It is shown that in an axially symmetric space-time with null dust field in which at least locally a smooth null infinity in the sense of Penrose exists, the only allowable additional Killing vector forming with the axial one a two-dimensional Lie algebra (the axial and the additional Killing vector are not assumed to be hypersurface orthogonal) is a supertranslational Killing vector and the gravitational field is then nonradiative (the Weyl tensor has a nonradiative character).
Stable black holes in shift-symmetric Horndeski theories
NASA Astrophysics Data System (ADS)
Tretyakova, Daria A.; Takahashi, Kazufumi
2017-09-01
In shift-symmetric Horndeski theories, a static and spherically symmetric black hole can support linearly time-dependent scalar hair. However, it was shown that such a solution generically suffers from ghost or gradient instability in the vicinity of the horizon. In the present paper, we explore the possibility to avoid the instability, and present a new example of theory and its black hole solution with a linearly time-dependent scalar configuration. We also discuss the stability of solutions with static scalar hair for a special case where nonminimal derivative coupling to the Einstein tensor appears.
Large displacement spherical joint
Bieg, Lothar F.; Benavides, Gilbert L.
2002-01-01
A new class of spherical joints has a very large accessible full cone angle, a property which is beneficial for a wide range of applications. Despite the large cone angles, these joints move freely without singularities.
The Precessing Spherical Pendulum.
ERIC Educational Resources Information Center
Olsson, M. G.
1978-01-01
Explains how the spherical pendulum could be used to observe nonreentrant orbits, and shows, using theoretical analysis, that for small displacements the elliptical orbit will precess at a rate proportional to its area. (GA)
Particle phenomenology on noncommutative spacetime
Joseph, Anosh
2009-05-01
We introduce particle phenomenology on the noncommutative spacetime called the Groenewold-Moyal plane. The length scale of spacetime noncommutativity is constrained from the CPT violation measurements in the K{sup 0}-K{sup 0} system and g-2 difference of {mu}{sup +}-{mu}{sup -}. The K{sup 0}-K{sup 0} system provides an upper bound on the length scale of spacetime noncommutativity of the order of 10{sup -32} m, corresponding to a lower energy bound E of the order of E > or approx. 10{sup 16} GeV. The g-2 difference of {mu}{sup +}-{mu}{sup -} constrains the noncommutativity length scale to be of the order of 10{sup -20} m, corresponding to a lower energy bound E of the order of E > or approx. 10{sup 3} GeV. We also present the phenomenology of the electromagnetic interaction of electrons and nucleons at the tree level on the noncommutative spacetime. We show that the distributions of charge and magnetization of nucleons are affected by spacetime noncommutativity. The analytic properties of electromagnetic form factors are also changed and it may give rise to interesting experimental signals.
Impact of curvature divergences on physical observers in a wormhole space-time with horizons
NASA Astrophysics Data System (ADS)
Olmo, Gonzalo J.; Rubiera-Garcia, D.; Sanchez-Puente, A.
2016-06-01
The impact of curvature divergences on physical observers in a black hole space-time, which, nonetheless, is geodesically complete is investigated. This space-time is an exact solution of certain extensions of general relativity coupled to Maxwell’s electrodynamics and, roughly speaking, consists of two Reissner-Nordström (or Schwarzschild or Minkowski) geometries connected by a spherical wormhole near the center. We find that, despite the existence of infinite tidal forces, causal contact is never lost among the elements making up the observer. This suggests that curvature divergences may not be as pathological as traditionally thought.
A multi-element cosmological model with a complex space-time topology
NASA Astrophysics Data System (ADS)
Kardashev, N. S.; Lipatova, L. N.; Novikov, I. D.; Shatskiy, A. A.
2015-02-01
Wormhole models with a complex topology having one entrance and two exits into the same space-time of another universe are considered, as well as models with two entrances from the same space-time and one exit to another universe. These models are used to build a model of a multi-sheeted universe (a multi-element model of the "Multiverse") with a complex topology. Spherical symmetry is assumed in all the models. A Reissner-Norström black-hole model having no singularity beyond the horizon is constructed. The strength of the central singularity of the black hole is analyzed.
Rome, J.A.; Harris, J.H.
1984-01-01
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
Feng, Huijuan; Ma, Jiayao; Peng, Rui
2016-01-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels. PMID:27436963
NASA Astrophysics Data System (ADS)
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Spherical null geodesics of rotating Kerr black holes
NASA Astrophysics Data System (ADS)
Hod, Shahar
2013-01-01
The non-equatorial spherical null geodesics of rotating Kerr black holes are studied analytically. Unlike the extensively studied equatorial circular orbits whose radii are known analytically, no closed-form formula exists in the literature for the radii of generic (non-equatorial) spherical geodesics. We provide here an approximate formula for the radii rph (a / M ; cos i) of these spherical null geodesics, where a / M is the dimensionless angular momentum of the black hole and cos i is an effective inclination angle (with respect to the black-hole equatorial plane) of the orbit. It is well-known that the equatorial circular geodesics of the Kerr spacetime (the prograde and the retrograde orbits with cos i = ± 1) are characterized by a monotonic dependence of their radii rph (a / M ; cos i = ± 1) on the dimensionless spin-parameter a / M of the black hole. We use here our novel analytical formula to reveal that this well-known property of the equatorial circular geodesics is actually not a generic property of the Kerr spacetime. In particular, we find that counter-rotating spherical null orbits in the range (3√{ 3} -√{ 59}) / 4 ≲ cos i < 0 are characterized by a non-monotonic dependence of rph (a / M ; cos i =const) on the dimensionless rotation-parameter a / M of the black hole. Furthermore, it is shown that spherical photon orbits of rapidly-rotating black holes are characterized by a critical inclination angle, cos i =√{ 4 / 7 }, above which the coordinate radii of the orbits approach the black-hole radius in the extremal limit. We prove that this critical inclination angle signals a transition in the physical properties of the spherical null geodesics: in particular, it separates orbits which are characterized by finite proper distances to the black-hole horizon from orbits which are characterized by infinite proper distances to the horizon.
N≥ 𝟐 symmetric superpolynomials
NASA Astrophysics Data System (ADS)
Alarie-Vézina, L.; Lapointe, L.; Mathieu, P.
2017-03-01
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N =1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where more than one independent anticommuting variable is attached to each ordinary variable. First, the N =2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, is constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N =2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N . Finally, for N =2 , the scalar product and the homogeneous functions are shown to have a one-parameter deformation, a result that prepares the ground for the yet-to-be-defined N =2 Jack superpolynomials.
Visibility of a spacetime singularity
Joshi, Pankaj S.
2007-02-15
We investigate here the causal structure of spacetime in the vicinity of a spacetime singularity. The particle and energy emission from such ultradense regions forming in gravitational collapse of a massive matter cloud is governed by the nature of nonspacelike paths near the same. These trajectories are examined to show that if a null geodesic comes out from the singularity, then there exist families of future-directed nonspacelike curves which also necessarily escape from the same. The existence of such families is crucial to the physical visibility of the singularity. We do not assume any underlying symmetries for the spacetime, and earlier considerations on the nature of causal trajectories emerging from a naked singularity are generalized and clarified.
Emergent geometry from quantized spacetime
Yang, Hyun Seok; Sivakumar, M.
2010-08-15
We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional flat spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.
The Historical Origins of Spacetime
NASA Astrophysics Data System (ADS)
Walter, Scott
The idea of spacetime investigated in this chapter, with a view toward understanding its immediate sources and development, is the one formulated and proposed by Hermann Minkowski in 1908. Until recently, the principle source used to form historical narratives of Minkowski's discovery of spacetime has been Minkowski's own discovery account, outlined in the lecture he delivered in Cologne, entitled Space and time [1]. Minkowski's lecture is usually considered as a bona fide first-person narrative of lived events. According to this received view, spacetime was a natural outgrowth of Felix Klein's successful project to promote the study of geometries via their characteristic groups of transformations. Or as Minkowski expressed the same basic thought himself, the theory of relativity discovered by physicists in 1905 could just as well have been proposed by some late-nineteenth-century mathematician, by simply reflecting upon the groups of transformations that left invariant the form of the equation of a propagating light wave. Minkowski's publications and research notes provide a contrasting picture of the discovery of spacetime, in which group theory plays no direct part. In order to relate the steps of Minkowski's discovery, we begin with an account of Poincaré's theory of gravitation, where Minkowski found some of the germs of spacetime. Poincaré's geometric interpretation of the Lorentz transformation is examined, along with his reasons for not pursuing a four-dimensional vector calculus. In the second section, Minkowski's discovery and presentation of the notion of a world line in spacetime is presented. In the third and final section, Poincaré's and Minkowski's diagrammatic interpretations of the Lorentz transformation are compared.
Radiation Transport in Dynamic Spacetimes
NASA Astrophysics Data System (ADS)
Schnittman, Jeremy; Baker, John G.; Etienne, Zachariah; Giacomazzo, Bruno; Kelly, Bernard J.
2017-08-01
We present early results from a new radiation transport calculation of gas accretion onto merging binary black holes. We use the Monte Carlo radiation transport code Pandurata, now generalized for application to dynamic spacetimes. The time variability of the metric requires careful numerical techniques for solving the geodesic equation, particularly with tabulated spacetime data from numerical relativity codes. Using a new series of general relativistic magneto-hydrodynamical simulations of magnetized flow onto binary black holes, we investigate the possibility for detecting and identifying unique electromagnetic counterparts to gravitational wave events.
Radiation Transport in Dynamic Spacetimes
NASA Astrophysics Data System (ADS)
Schnittman, Jeremy; Baker, John; Etienne, Zachariah; Giacomazzo, Bruno; Kelly, Bernard
2017-01-01
We present early results from a new radiation transport calculation of gas accretion onto merging binary black holes. We use the Monte Carlo radiation transport code Pandurata, now generalized for application to dynamic spacetimes. The time variability of the metric requires careful numerical techniques for solving the geodesic equation, particularly with tabulated spacetime data from numerical relativity codes. Using a new series of general relativistic magneto-hydrodynamical simulations of magnetized flow onto binary black holes, we investigate the possibility for detecting and identifying unique electromagnetic counterparts to gravitational wave events.
NASA Astrophysics Data System (ADS)
Agrawal, P. K.; Pawar, D. D.
2017-03-01
We studied plane symmetric cosmological model in the presence of quark and strange quark matter with the help of f( R, T) theory. To decipher solutions of plane symmetric space-time, we used power law relation between scale factor and deceleration parameter. We considered the special law of variation of Hubble's parameter proposed by Berman ( Nuovo Cimento B74, 182, 1983) which yields constant deceleration parameter. We also discussed the physical behavior of the solutions by using some physical parameters.
NASA Technical Reports Server (NTRS)
Peeples, Steven
2015-01-01
A three degree of freedom (DOF) spherical actuator is proposed that will replace functions requiring three single DOF actuators in robotic manipulators providing space and weight savings while reducing the overall failure rate. Exploration satellites, Space Station payload manipulators, and rovers requiring pan, tilt, and rotate movements need an actuator for each function. Not only does each actuator introduce additional failure modes and require bulky mechanical gimbals, each contains many moving parts, decreasing mean time to failure. A conventional robotic manipulator is shown in figure 1. Spherical motors perform all three actuation functions, i.e., three DOF, with only one moving part. Given a standard three actuator system whose actuators have a given failure rate compared to a spherical motor with an equal failure rate, the three actuator system is three times as likely to fail over the latter. The Jet Propulsion Laboratory reliability studies of NASA robotic spacecraft have shown that mechanical hardware/mechanism failures are more frequent and more likely to significantly affect mission success than are electronic failures. Unfortunately, previously designed spherical motors have been unable to provide the performance needed by space missions. This inadequacy is also why they are unavailable commercially. An improved patentable spherically actuated motor (SAM) is proposed to provide the performance and versatility required by NASA missions.
Outer trapped surfaces in Vaidya spacetimes
Ben-Dov, Ishai
2007-03-15
It is proven that in Vaidya spacetimes of bounded total mass, the outer boundary, in spacetime, of the region containing outer trapped surfaces, is the event horizon. Further, it is shown that the region containing trapped surfaces in these spacetimes does not always extend to the event horizon.
Cylindrically symmetric models of gravitational collapse to black holes: A short review
NASA Astrophysics Data System (ADS)
Mena, Filipe C.
2015-07-01
We survey results about exact cylindrically symmetric models of gravitational collapse in General Relativity. We focus on models which result from the matching of two spacetimes having collapsing interiors which develop trapped surfaces and vacuum exteriors containing gravitational waves. We collect some theorems from the literature which help to decide a priori about eventual spacetime matchings. We revise, in more detail, some toy models which include some of the main mathematical and physical issues that arise in this context, and compute the gravitational energy flux through the matching boundary of a particular collapsing region. Along the way, we point out several interesting open problems.
Spherical geodesic mesh generation
Fung, Jimmy; Kenamond, Mark Andrew; Burton, Donald E.; Shashkov, Mikhail Jurievich
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
NASA Astrophysics Data System (ADS)
Khan, Suhail; Hussain, Tahir; Khan, Gulzar Ali
The aim of this paper is to explore teleparallel conformal Killing vector fields (CKVFs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes in the context of teleparallel gravity and compare the obtained results with those of general relativity (GR). The general solution of teleparallel conformal Killing's equations is found in terms of some unknown functions of t and x, along with a set of integrability conditions. The integrability conditions are solved in some particular cases to get the final form of teleparallel CKVFs. It is observed that the LRS Bianchi type V spacetimes admit proper teleparallel CKVF in only one case, while in remaining cases the teleparallel CKVFs reduce to teleparallel Killing vector fields (KVFs). Moreover, it is shown that the LRS Bianchi type V spacetimes do not admit any proper teleparallel homothetic vector field (HVF).
NASA Technical Reports Server (NTRS)
Villarreal, James A.; Shelton, Robert O.
1992-01-01
Concept of space-time neural network affords distributed temporal memory enabling such network to model complicated dynamical systems mathematically and to recognize temporally varying spatial patterns. Digital filters replace synaptic-connection weights of conventional back-error-propagation neural network.
The hydrodynamics analysis for the underwater robot with a spherical hull
NASA Astrophysics Data System (ADS)
Lan, Xiaojuan; Sun, Hanxu; Jia, Qingxuan
2009-05-01
The underwater spherical robot has a spherical pressure hull which contains power modules, sensors, and so on. It lacks robot arms or end effectors but is highly maneuverable, for the simplest symmetrical geometry is the sphere. This paper analyzes the spherical robot's hydrodynamic model with CFD software, concludes the spherical robot's hydrodynamic characteristics, and compares these characteristics with the hydrodynamic model of another underwater robot which has a streamlined hull. The effect of sphere hydraulic resistance on the control of the robot is analyzed with some examples.
Preserving spherical symmetry in axisymmetric coordinates for diffusion problems
Brunner, T. A.; Kolev, T. V.; Bailey, T. S.; Till, A. T.
2013-07-01
Persevering symmetric solutions, even in the under-converged limit, is important to the robustness of production simulation codes. We explore the symmetry preservation in both a continuous nodal and a mixed finite element method. In their standard formulation, neither method preserves spherical solution symmetry in axisymmetric (RZ) coordinates. We propose two methods, one for each family of finite elements, that recover spherical symmetry for low-order finite elements on linear or curvilinear meshes. This is a first step toward understanding achieving symmetry for higher-order elements. (authors)
Construction of Aesthetic Spherical Patterns from Planar IFSs
NASA Astrophysics Data System (ADS)
Chen, Ning; Zhang, Yuting; Chung, K. W.
2016-07-01
To construct symmetrical patterns on the unit sphere from the planar iterative function systems (IFSs), we present a method of constructing IFSs with D3 symmetry which is composed of three-fold rotational symmetries together with reflections. An algorithm is developed to generate strange attractors with D3 symmetry on a triangular face and then project it onto the surface of the unit sphere to form aesthetics patterns with spherical symmetry. As an illustrative example, we consider the regular inscribed icosahedron in the unit sphere which contains 20 triangular faces. This method is valid to randomly generate aesthetic spherical patterns using planar IFSs.
Quantifying Departures from Equilibrium with the Spherical Jeans Equation
NASA Astrophysics Data System (ADS)
Evslin, Jarah; Del Popolo, Antonino
2017-06-01
Proper motions of collisionless, pointlike objects in a spherically symmetric system—for example, stars in a galaxy—can be used to test whether that system is in equilibrium, with no assumptions regarding isotropy. In particular, the fourth-order spherical Jeans equation yields expressions for two observable quantities characterizing the departure from equilibrium, both of which can be expressed in terms of time derivatives of first and third moments of the velocities. As illustrations, we compute these quantities for tracer distributions drawn from an exact equilibrium configuration, and also from near-equilibrium configurations generated using the N-body code GALIC.
A vacuum spacetime with closed null geodesics
Sarma, Debojit Patgiri, Mahadev Ahmed, Faiz Uddin
2013-02-15
Here we present a vacuum spacetime with closed null geodesics (CNGs). These CNGs are obtained by analytically solving the geodesic equations. This spacetime is locally isometric to the plane wave spacetime and has very different global properties from metrics of the latter type. - Highlights: Black-Right-Pointing-Pointer Closed null geodesics are found in a vacuum spacetime. Black-Right-Pointing-Pointer These are obtained by analytically solving the geodesic equations. Black-Right-Pointing-Pointer The nature of the spacetime is fully analysed.
Analytical solution of the geodesic equation in Kerr-(anti-) de Sitter space-times
Hackmann, Eva; Laemmerzahl, Claus; Kagramanova, Valeria; Kunz, Jutta
2010-02-15
The complete analytical solutions of the geodesic equations in Kerr-de Sitter and Kerr-anti-de Sitter space-times are presented. They are expressed in terms of Weierstrass elliptic p, {zeta}, and {sigma} functions as well as hyperelliptic Kleinian {sigma} functions restricted to the one-dimensional {theta} divisor. We analyze the dependency of timelike geodesics on the parameters of the space-time metric and the test-particle and compare the results with the situation in Kerr space-time with vanishing cosmological constant. Furthermore, we systematically can find all last stable spherical and circular orbits and derive the expressions of the deflection angle of flyby orbits, the orbital frequencies of bound orbits, the periastron shift, and the Lense-Thirring effect.
Detecting internally symmetric protein structures.
Kim, Changhoon; Basner, Jodi; Lee, Byungkook
2010-06-03
Many functional proteins have a symmetric structure. Most of these are multimeric complexes, which are made of non-symmetric monomers arranged in a symmetric manner. However, there are also a large number of proteins that have a symmetric structure in the monomeric state. These internally symmetric proteins are interesting objects from the point of view of their folding, function, and evolution. Most algorithms that detect the internally symmetric proteins depend on finding repeating units of similar structure and do not use the symmetry information. We describe a new method, called SymD, for detecting symmetric protein structures. The SymD procedure works by comparing the structure to its own copy after the copy is circularly permuted by all possible number of residues. The procedure is relatively insensitive to symmetry-breaking insertions and deletions and amplifies positive signals from symmetry. It finds 70% to 80% of the TIM barrel fold domains in the ASTRAL 40 domain database and 100% of the beta-propellers as symmetric. More globally, 10% to 15% of the proteins in the ASTRAL 40 domain database may be considered symmetric according to this procedure depending on the precise cutoff value used to measure the degree of perfection of the symmetry. Symmetrical proteins occur in all structural classes and can have a closed, circular structure, a cylindrical barrel-like structure, or an open, helical structure. SymD is a sensitive procedure for detecting internally symmetric protein structures. Using this procedure, we estimate that 10% to 15% of the known protein domains may be considered symmetric. We also report an initial, overall view of the types of symmetries and symmetric folds that occur in the protein domain structure universe.
Detecting internally symmetric protein structures
2010-01-01
Background Many functional proteins have a symmetric structure. Most of these are multimeric complexes, which are made of non-symmetric monomers arranged in a symmetric manner. However, there are also a large number of proteins that have a symmetric structure in the monomeric state. These internally symmetric proteins are interesting objects from the point of view of their folding, function, and evolution. Most algorithms that detect the internally symmetric proteins depend on finding repeating units of similar structure and do not use the symmetry information. Results We describe a new method, called SymD, for detecting symmetric protein structures. The SymD procedure works by comparing the structure to its own copy after the copy is circularly permuted by all possible number of residues. The procedure is relatively insensitive to symmetry-breaking insertions and deletions and amplifies positive signals from symmetry. It finds 70% to 80% of the TIM barrel fold domains in the ASTRAL 40 domain database and 100% of the beta-propellers as symmetric. More globally, 10% to 15% of the proteins in the ASTRAL 40 domain database may be considered symmetric according to this procedure depending on the precise cutoff value used to measure the degree of perfection of the symmetry. Symmetrical proteins occur in all structural classes and can have a closed, circular structure, a cylindrical barrel-like structure, or an open, helical structure. Conclusions SymD is a sensitive procedure for detecting internally symmetric protein structures. Using this procedure, we estimate that 10% to 15% of the known protein domains may be considered symmetric. We also report an initial, overall view of the types of symmetries and symmetric folds that occur in the protein domain structure universe. PMID:20525292
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
1982-01-01
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
Affine conformal vectors in space-time
NASA Astrophysics Data System (ADS)
Coley, A. A.; Tupper, B. O. J.
1992-05-01
All space-times admitting a proper affine conformal vector (ACV) are found. By using a theorem of Hall and da Costa, it is shown that such space-times either (i) admit a covariantly constant vector (timelike, spacelike, or null) and the ACV is the sum of a proper affine vector and a conformal Killing vector or (ii) the space-time is 2+2 decomposable, in which case it is shown that no ACV can exist (unless the space-time decomposes further). Furthermore, it is proved that all space-times admitting an ACV and a null covariantly constant vector (which are necessarily generalized pp-wave space-times) must have Ricci tensor of Segré type {2,(1,1)}. It follows that, among space-times admitting proper ACV, the Einstein static universe is the only perfect fluid space-time, there are no non-null Einstein-Maxwell space-times, and only the pp-wave space-times are representative of null Einstein-Maxwell solutions. Otherwise, the space-times can represent anisotropic fluids and viscous heat-conducting fluids, but only with restricted equations of state in each case.
NASA Technical Reports Server (NTRS)
Meyer, Jay L. (Inventor); Messick, Glenn C. (Inventor); Nardell, Carl A. (Inventor); Hendlin, Martin J. (Inventor)
2011-01-01
A spherical mounting assembly for mounting an optical element allows for rotational motion of an optical surface of the optical element only. In that regard, an optical surface of the optical element does not translate in any of the three perpendicular translational axes. More importantly, the assembly provides adjustment that may be independently controlled for each of the three mutually perpendicular rotational axes.
Raine, D.J.; Heller, M.
1981-01-01
Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics Copernican kinematics Newtonian dynamics the space-time of classical dynamics classical space-time in the presence of gravity the space-time of special relativity the space-time of general relativity solutions and problems in general relativity Mach's principle and the dynamics of space-time theories of inertial mass the integral formation of general relativity and the frontiers of relativity (e.g., unified field theories and quantum gravity).
NASA Astrophysics Data System (ADS)
Raine, D. J.; Heller, M.
Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics; Copernican kinematics; Newtonian dynamics; the space-time of classical dynamics; classical space-time in the presence of gravity; the space-time of special relativity; the space-time of general relativity; solutions and problems in general relativity; Mach's principle and the dynamics of space-time; theories of inertial mass; the integral formation of general relativity; and the frontiers of relativity (e.g., unified field theories and quantum gravity).
Spherical colloidal photonic crystals.
Zhao, Yuanjin; Shang, Luoran; Cheng, Yao; Gu, Zhongze
2014-12-16
CONSPECTUS: Colloidal photonic crystals (PhCs), periodically arranged monodisperse nanoparticles, have emerged as one of the most promising materials for light manipulation because of their photonic band gaps (PBGs), which affect photons in a manner similar to the effect of semiconductor energy band gaps on electrons. The PBGs arise due to the periodic modulation of the refractive index between the building nanoparticles and the surrounding medium in space with subwavelength period. This leads to light with certain wavelengths or frequencies located in the PBG being prohibited from propagating. Because of this special property, the fabrication and application of colloidal PhCs have attracted increasing interest from researchers. The most simple and economical method for fabrication of colloidal PhCs is the bottom-up approach of nanoparticle self-assembly. Common colloidal PhCs from this approach in nature are gem opals, which are made from the ordered assembly and deposition of spherical silica nanoparticles after years of siliceous sedimentation and compression. Besides naturally occurring opals, a variety of manmade colloidal PhCs with thin film or bulk morphology have also been developed. In principle, because of the effect of Bragg diffraction, these PhC materials show different structural colors when observed from different angles, resulting in brilliant colors and important applications. However, this angle dependence is disadvantageous for the construction of some optical materials and devices in which wide viewing angles are desired. Recently, a series of colloidal PhC materials with spherical macroscopic morphology have been created. Because of their spherical symmetry, the PBGs of spherical colloidal PhCs are independent of rotation under illumination of the surface at a fixed incident angle of the light, broadening the perspective of their applications. Based on droplet templates containing colloidal nanoparticles, these spherical colloidal PhCs can be
NASA Astrophysics Data System (ADS)
Ma, Xiaojun; Tang, Xing; Wang, Zongwei; Gao, Dangzhong; Tang, Yongjian
2016-12-01
An analytical model of surface acoustic waves on the surface of a hollow spherical shell generated by a pulsed laser source is proposed using the Legendre polynomials expansion and contour integration method. The model predicts two interesting phenomena. The dispersive characteristic of thick spherical shells is mainly determined by the spherical Rayleigh waves, but the corresponding characteristic of thin spherical shells is dominated by zero-order anti-symmetric plate waves; The hollow spherical spheres with the same ratio of thickness to radius have the same dispersive characteristic. Using laser ultrasound technique, the proposed model is confirmed experimentally on a hollow polymer sphere of mm-sized diameter.
NASA Astrophysics Data System (ADS)
McNutt, David D.; Page, Don N.
2017-04-01
We construct a scalar polynomial curvature invariant that transforms covariantly under a conformal transformation from any spherically symmetric metric. This invariant has the additional property that it vanishes on the event horizon of any black hole that is conformal to a static spherical metric.
Symmetric Waveguide Orthomode Junctions
NASA Technical Reports Server (NTRS)
Wollack, E. J.; Grammer, W.
2003-01-01
Imaging applications at millimeter and submillimeter wavelengths demand precise characterization of the amplitude, spectrum, and polarization of the electromagnetic radiation. The use of a waveguide orthomode transducer (OMT) can help achieve these goals by increasing spectral coverage and sensitivity while reducing exit aperture size, optical spill, instrumental polarization offsets, and lending itself to integration in focal plane arrays. For these reasons, four-fold symmetric OMTs are favored over a traditional quasi-optical wire grid for focal plane imaging arrays from a systems perspective. The design, fabrication, and test of OMTs realized with conventional split-block techniques for millimeter wave-bands are described. The design provides a return loss is -20 dB over a full waveguide band (40% bandwidth), and the cross-polarization and isolation are greater than -40 dB for tolerances readily achievable in practice. Prototype examples realized in WR10.0 and WR3.7 wavebands will be considered in detail.
Symmetric Waveguide Orthomode Junctions
NASA Technical Reports Server (NTRS)
Wollack, E. J.; Grammer, W.
2003-01-01
Imaging applications at millimeter and submillimeter wavelengths demand precise characterization of the amplitude, spectrum, and polarization of the electromagnetic radiation. The use of a waveguide orthomode transducer (OMT) can help achieve these goals by increasing spectral coverage and sensitivity while reducing exit aperture size, optical spill, instrumental polarization offsets, and lending itself to integration in focal plane arrays. For these reasons, four-old symmetric OMTs are favored over a traditional quasi-optical wire grid for focal plane imaging arrays from a systems perspective. The design, fabrication, and test of OMTs realized with conventional split-block techniques for millimeter wave-bands are described. The design provides a return loss is -20 dB over a full waveguide band (40% bandwidth), and the cross-polarization and isolation are greater than -40 dB for tolerances readily achievable in practice. Prototype examples realized in WR10.0 and WR3.7 wavebands will be considered in detail.
Minimally symmetric Higgs boson
Low, Ian
2015-06-17
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized SU(2)(L) x U(1)(Y) electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective Lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal among all models where the Higgs arises as a pseudo-Nambu-Goldstone boson. Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.
Optimal symmetric flight studies
NASA Technical Reports Server (NTRS)
Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.
1985-01-01
Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.
Stability of thin-shell wormholes with spherical symmetry
Eiroa, Ernesto F.
2008-07-15
In this article, the stability of a general class of spherically symmetric thin-shell wormholes is studied under perturbations preserving the symmetry. For this purpose, the equation of state at the throat is linearized around the static solutions. The formalism presented here is applied to dilaton wormholes, and it is found that there is a smaller range of possible stable configurations for them than in the case of Reissner-Nordstroem wormholes with the same charge.
Spherical coordinate descriptions of cylindrical and spherical Bessel beams.
Poletti, M A
2017-03-01
This paper derives a generalized spherical harmonic description of Bessel beams. The spherical harmonic description of the well-known cylindrical Bessel beams is reviewed and a family of spherical Bessel beams are introduced which can provide a number of azimuthal phase variations for a single beam radial amplitude. The results are verified by numerical simulations.
Trumpet solution from spherical gravitational collapse with puncture gauges
Thierfelder, Marcus; Bernuzzi, Sebastiano; Hilditch, David; Bruegmann, Bernd; Rezzolla, Luciano
2011-03-15
We investigate the stationary end state obtained by evolving a collapsing spherical star with the gauges routinely adopted to study puncture black holes. We compare the end state of the collapse with the trumpet solution found in the evolution of a single wormhole slice and show that the two solutions closely agree. We demonstrate that the agreement is caused by the use of the Gamma-driver shift condition, which allows the matter to fall inwards into a region of spacetime that is not resolved by the numerical grid, and which simultaneously finds the stationary coordinates of the trumpet outside the matter.
Dark energy from discrete spacetime.
Trout, Aaron D
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, [Formula: see text] in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.
Dark Energy from Discrete Spacetime
Trout, Aaron D.
2013-01-01
Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies. PMID:24312502
Gravitational energy in spherical symmetry
NASA Astrophysics Data System (ADS)
Hayward, Sean A.
1996-02-01
Various properties of the Misner-Sharp spherically symmetric gravitational energy E are established or reviewed. In the Newtonian limit of a perfect fluid, E yields the Newtonian mass to leading order and the Newtonian kinetic and potential energy to the next order. For test particles, the corresponding Hájíček energy is conserved and has the behavior appropriate to energy in the Newtonian and special-relativistic limits. In the small-sphere limit, the leading term in E is the product of volume and the energy density of the matter. In vacuo, E reduces to the Schwarzschild energy. At null and spatial infinity, E reduces to the Bondi-Sachs and Arnowitt-Deser-Misner energies, respectively. The conserved Kodama current has charge E. A sphere is trapped if E>1/2r, marginal if E=1/2r, and untrapped if E<1/2r, where r is the areal radius. A central singularity is spatial and trapped if E>0, and temporal and untrapped if E<0. On an untrapped sphere, E is nondecreasing in any outgoing spatial or null direction, assuming the dominant energy condition. It follows that E>=0 on an untrapped spatial hypersurface with a regular center, and E>=1/2r0 on an untrapped spatial hypersurface bounded at the inward end by a marginal sphere of radius r0. All these inequalities extend to the asymptotic energies, recovering the Bondi-Sachs energy loss and the positivity of the asymptotic energies, as well as proving the conjectured Penrose inequality for black or white holes. Implications for the cosmic censorship hypothesis and for general definitions of gravitational energy are discussed.
Gauge Transformations as Spacetime Symmetries
Angeles, Rene; Napsuciale, Mauro
2009-04-20
Weinberg has shown that massless fields of helicity {+-}1(vector fields) do not transform homogeneously under Unitary Lorentz Transformations (LT). We calculate explicitly the inhomogeneous term. We show that imposing strict invariance of the Lagrangian under LT for an iteracting Dirac field requires the fermion field to transform with a space-time (and photon creation and annihilation operators) dependent phase and dictates the interaction terms as those arising from the conventional gauge principle.
Spacetimes containing slowly evolving horizons
Kavanagh, William; Booth, Ivan
2006-08-15
Slowly evolving horizons are trapping horizons that are ''almost'' isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes.
A Novel View of Spacetime Permitting Faster-Than-Light Travel
NASA Astrophysics Data System (ADS)
Meholic, Gregory V.
2004-02-01
Recent discoveries across many disciplines of physics have supported a driving need for a ``new'' science to explain the apparent relationship between phenomenon at cosmological scales and those at the quantum, subatomic level while still supporting the classical mechanics of motion, electromagnetism and relativity. A novel view of both the spacetime continuum and the universe is postulated that not only connects these fields of interest, but proposes a method to travel at superluminal speeds by examining the underlying equations of special relativity. The governing mathematics of special relativity describe a symmetrical continuum that supports not just one, but three, independent spacetimes each with a unique set of physical laws founded on the speed of light, c. These spacetimes are the subluminal (where v/c < 1), the luminal (where v/c = 1), and the superluminal (where v/c > 1) comprising a `tri-space' universe. Relativistic symmetry illustrates that there can be up to three velocities (one for each spacetime) for a given absolute energy state. The similar characteristics of mass and energy in each spacetime may permit faster-than-light (FTL) travel through a quantum transformation/exchange of energy and mass (at the quark level or beyond) between the subluminal and superluminal realms. Based on the suggested characteristics of superluminal spacetime, the `trans-space' method of FTL travel would allow a particle to traverse sublight space by traveling through the superlight continuum without incurring the penalties of special relativity or causal relations. In addition, the spacetime construct and superluminal realm of the `tri-space' universe may offer a different perspective than the current ideologies that could better represent physical phenomena including universal expansion, the zero-point field, dark matter, and the source of inertia.
Spherical torus fusion reactor
Peng, Yueng-Kay M.
1989-01-01
A fusion reactor is provided having a near spherical-shaped plasma with a modest central opening through which straight segments of toroidal field coils extend that carry electrical current for generating a toroidal magnet plasma confinement fields. By retaining only the indispensable components inboard of the plasma torus, principally the cooled toroidal field conductors and in some cases a vacuum containment vessel wall, the fusion reactor features an exceptionally small aspect ratio (typically about 1.5), a naturally elongated plasma cross section without extensive field shaping, requires low strength magnetic containment fields, small size and high beta. These features combine to produce a spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost.
Spherical torus fusion reactor
Peng, Yueng-Kay M.
1989-04-04
A fusion reactor is provided having a near spherical-shaped plasma with a modest central opening through which straight segments of toroidal field coils extend that carry electrical current for generating a toroidal magnet plasma confinement fields. By retaining only the indispensable components inboard of the plasma torus, principally the cooled toroidal field conductors and in some cases a vacuum containment vessel wall, the fusion reactor features an exceptionally small aspect ratio (typically about 1.5), a naturally elongated plasma cross section without extensive field shaping, requires low strength magnetic containment fields, small size and high beta. These features combine to produce a spherical torus plasma in a unique physics regime which permits compact fusion at low field and modest cost.
NASA Technical Reports Server (NTRS)
Lee, M. C.; Kendall, J. M., Jr.; Bahrami, P. A.; Wang, T. G.
1986-01-01
Fluid-dynamic and capillary forces can be used to form nearly perfect, very small spherical shells when a liquid that can solidify is passed through an annular die to form an annular jet. Gravity and certain properties of even the most ideal materials, however, can cause slight asymmetries. The primary objective of the present work is the control of this shell formation process in earth laboratories rather than space microgravity, through the development of facilities and methods that minimize the deleterious effects of gravity, aerodynamic drag, and uncontrolled cooling. The spherical shells thus produced can be used in insulation, recyclable filter materials, fire retardants, explosives, heat transport slurries, shock-absorbing armor, and solid rocket motors.
Noncommuting spherical coordinates
Bander, Myron
2004-10-15
Restricting the states of a charged particle to the lowest Landau level introduces a noncommutativity between Cartesian coordinate operators. This idea is extended to the motion of a charged particle on a sphere in the presence of a magnetic monopole. Restricting the dynamics to the lowest energy level results in noncommutativity for angular variables and to a definition of a noncommuting spherical product. The values of the commutators of various angular variables are not arbitrary but are restricted by the discrete magnitude of the magnetic monopole charge. An algebra, isomorphic to angular momentum, appears. This algebra is used to define a spherical star product. Solutions are obtained for dynamics in the presence of additional angular dependent potentials.
Hollow spherical shell manufacture
O'Holleran, Thomas P.
1991-01-01
A process for making a hollow spherical shell of silicate glass composition in which an aqueous suspension of silicate glass particles and an immiscible liquid blowing agent is placed within the hollow spherical cavity of a porous mold. The mold is spun to reduce effective gravity to zero and to center the blowing agent, while being heated so as to vaporize the immiscible liquid and urge the water carrier of the aqueous suspension to migrate into the body of the mold, leaving a green shell compact deposited around the mold cavity. The green shell compact is then removed from the cavity, and is sintered for a time and a temperature sufficient to form a silicate glass shell of substantially homogeneous composition and uniform geometry.
NASA Technical Reports Server (NTRS)
Lee, M. C.; Kendall, J. M., Jr.; Bahrami, P. A.; Wang, T. G.
1986-01-01
Fluid-dynamic and capillary forces can be used to form nearly perfect, very small spherical shells when a liquid that can solidify is passed through an annular die to form an annular jet. Gravity and certain properties of even the most ideal materials, however, can cause slight asymmetries. The primary objective of the present work is the control of this shell formation process in earth laboratories rather than space microgravity, through the development of facilities and methods that minimize the deleterious effects of gravity, aerodynamic drag, and uncontrolled cooling. The spherical shells thus produced can be used in insulation, recyclable filter materials, fire retardants, explosives, heat transport slurries, shock-absorbing armor, and solid rocket motors.
Hollow spherical shell manufacture
O'Holleran, T.P.
1991-11-26
A process is disclosed for making a hollow spherical shell of silicate glass composition in which an aqueous suspension of silicate glass particles and an immiscible liquid blowing agent is placed within the hollow spherical cavity of a porous mold. The mold is spun to reduce effective gravity to zero and to center the blowing agent, while being heated so as to vaporize the immiscible liquid and urge the water carrier of the aqueous suspension to migrate into the body of the mold, leaving a green shell compact deposited around the mold cavity. The green shell compact is then removed from the cavity, and is sintered for a time and a temperature sufficient to form a silicate glass shell of substantially homogeneous composition and uniform geometry. 3 figures.
Spacetime Singularities in Quantum Gravity
NASA Astrophysics Data System (ADS)
Minassian, Eric A.
2000-04-01
Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.
Thermal dimension of quantum spacetime
NASA Astrophysics Data System (ADS)
Amelino-Camelia, Giovanni; Brighenti, Francesco; Gubitosi, Giulia; Santos, Grasiele
2017-04-01
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of "dynamical dimensional reduction" which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the "spectral dimension", which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the "thermal dimension" which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.
Lorentz violations in multifractal spacetimes
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca
2017-05-01
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E_{*}>10^{14} {GeV} (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E_{*}> 10^{17} {GeV} or greater.
Spherical nitroguanidine process
Sanchez, John A.; Roemer, Edward L.; Stretz, Lawrence A.
1990-01-01
A process of preparing spherical high bulk density nitroguanidine by dissing low bulk density nitroguanidine in N-methyl pyrrolidone at elevated temperatures and then cooling the solution to lower temperatures as a liquid characterized as a nonsolvent for the nitroguanidine is provided. The process is enhanced by inclusion in the solution of from about 1 ppm up to about 250 ppm of a metal salt such as nickel nitrate, zinc nitrate or chromium nitrate, preferably from about 20 to about 50 ppm.
NASA Astrophysics Data System (ADS)
Nichols, David A.; Owen, Robert; Zhang, Fan; Zimmerman, Aaron; Brink, Jeandrew; Chen, Yanbei; Kaplan, Jeffrey D.; Lovelace, Geoffrey; Matthews, Keith D.; Scheel, Mark A.; Thorne, Kip S.
2011-12-01
When one splits spacetime into space plus time, the Weyl curvature tensor (vacuum Riemann tensor) gets split into two spatial, symmetric, and trace-free tensors: (i) the Weyl tensor’s so-called electric part or tidal field Ejk, which raises tides on the Earth’s oceans and drives geodesic deviation (the relative acceleration of two freely falling test particles separated by a spatial vector ξk is Δaj=-Ejkξk), and (ii) the Weyl tensor’s so-called magnetic part or (as we call it) frame-drag field Bjk, which drives differential frame dragging (the precessional angular velocity of a gyroscope at the tip of ξk, as measured using a local inertial frame at the tail of ξk, is ΔΩj=Bjkξk). Being symmetric and trace-free, Ejk and Bjk each have three orthogonal eigenvector fields which can be depicted by their integral curves. We call the integral curves of Ejk’s eigenvectors tidal tendex lines or simply tendex lines, we call each tendex line’s eigenvalue its tendicity, and we give the name tendex to a collection of tendex lines with large tendicity. The analogous quantities for Bjk are frame-drag vortex lines or simply vortex lines, their vorticities, and their vortexes. These concepts are powerful tools for visualizing spacetime curvature. We build up physical intuition into them by applying them to a variety of weak-gravity phenomena: a spinning, gravitating point particle, two such particles side-by-side, a plane gravitational wave, a point particle with a dynamical current-quadrupole moment or dynamical mass-quadrupole moment, and a slow-motion binary system made of nonspinning point particles. We show that a rotating current quadrupole has four rotating vortexes that sweep outward and backward like water streams from a rotating sprinkler. As they sweep, the vortexes acquire accompanying tendexes and thereby become outgoing current-quadrupole gravitational waves. We show similarly that a rotating mass quadrupole has four rotating, outward
Stability of thick spherical shells
NASA Astrophysics Data System (ADS)
Liu, I.-Shih
1995-06-01
The pressure-radius relation of spherical rubber balloons has been derived and its stability behavior investigated before. In this work, we show that similar results remain valid for thick spherical shells of Mooney-Rivlin materials. In addition, we show that eversion of a spherical shell is possible for any incompressible isotropic materials if the shell is not too thick.
Representation of Fuzzy Symmetric Relations
1986-03-19
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
{PT}-symmetric optical superlattices
NASA Astrophysics Data System (ADS)
Longhi, Stefano
2014-04-01
The spectral and localization properties of {PT}-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are derived. The analysis is applied to the case of superlattices describing a complex ( {PT}-symmetric) extension of the Harper Hamiltonian in the rational case.
Wake control with permeable multilayer structures: The spherical symmetry case
NASA Astrophysics Data System (ADS)
Bowen, Patrick T.; Smith, David R.; Urzhumov, Yaroslav A.
2015-12-01
We explore the possibility of controlling the wake and drag of a spherical object independently of each other, using radial distributions of permeability in the Brinkman-Stokes formalism. By discretizing a graded-permeability shell into discrete, macroscopically homogeneous layers, we are able to sample the entire functional space of spherically-symmetric permeabilities and observe quick convergence to a certain manifold in the wake-drag coordinates. Monte Carlo samplings with 104-105 points have become possible thanks to our new algorithm, which is based on exact analytical solutions for the Stokes flow through an arbitrary multilayer porous sphere. The algorithm is not restricted to the Brinkman-Stokes equation and can be modified to account for other types of scattering problems for spherically-symmetric systems with arbitrary radial complexity. Our main practical finding for Stokes flow is that it is possible to reduce a certain measure of wake of a spherical object without any energy penalty and without active (power-consuming) force generation.
Tensor species and symmetric functions.
Méndez, M
1991-01-01
An equivariant representation of the symmetric group Sn (equivariant representation from here on) is defined as a particular type of tensor species. For any tensor species R the characteristic generating function of R is defined in a way that generalizes the Frobenius characters of representations of the symmetric groups. If R is an equivariant representation, then the characteristic is a homogeneous symmetric function. The combinatorial operations on equivariant representations correspond to formal operations on the respective characteristic functions. In particular, substitution of equivariant representations corresponds to plethysm of symmetric functions. Equivariant representations are constructed that have as characteristic the elementary, complete, and Schur functions. Bijective proofs are given for the formulas that connect them with the monomial symmetric functions. PMID:11607233
Mapping curved spacetimes into Dirac spinors
Sabín, Carlos
2017-01-01
We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions. PMID:28074908
Vacuum Spacetimes with Constant Weyl Eigenvalues
NASA Astrophysics Data System (ADS)
Barnes, A.
2015-04-01
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant Λ) with constant non-zero Weyl eigenvalues are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated eigenvalue necessarily has the value 2Λ/3 and it turns out that the only possible spacetimes are some Kundt-waves considered by Lewandowski which are type II and a Robinson-Bertotti solution of type D. For Petrov type I the only solution turns out to be a homogeneous pure vacuum solution found long ago by Petrov using group theoretic methods. These results can be summarised by the statement that the only vacuum spacetimes with constant Weyl eigenvalues are either homogeneous or are Kundt spacetimes. This result is similar to that of Coley et al. who proved their result for general spacetimes under the assumption that all scalar invariants constructed from the curvature tensor and all its derivatives were constant.
Gravitational Lensing from a Spacetime Perspective.
Perlick, Volker
2004-01-01
The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.
Mapping curved spacetimes into Dirac spinors.
Sabín, Carlos
2017-01-11
We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions.
NASA Astrophysics Data System (ADS)
Lake, Kayll
2010-12-01
The title immediately brings to mind a standard reference of almost the same title [1]. The authors are quick to point out the relationship between these two works: they are complementary. The purpose of this work is to explain what is known about a selection of exact solutions. As the authors state, it is often much easier to find a new solution of Einstein's equations than it is to understand it. Even at first glance it is very clear that great effort went into the production of this reference. The book is replete with beautifully detailed diagrams that reflect deep geometric intuition. In many parts of the text there are detailed calculations that are not readily available elsewhere. The book begins with a review of basic tools that allows the authors to set the notation. Then follows a discussion of Minkowski space with an emphasis on the conformal structure and applications such as simple cosmic strings. The next two chapters give an in-depth review of de Sitter space and then anti-de Sitter space. Both chapters contain a remarkable collection of useful diagrams. The standard model in cosmology these days is the ICDM model and whereas the chapter on the Friedmann-Lemaître-Robertson-Walker space-times contains much useful information, I found the discussion of the currently popular a representation rather too brief. After a brief but interesting excursion into electrovacuum, the authors consider the Schwarzschild space-time. This chapter does mention the Swiss cheese model but the discussion is too brief and certainly dated. Space-times related to Schwarzschild are covered in some detail and include not only the addition of charge and the cosmological constant but also the addition of radiation (the Vaidya solution). Just prior to a discussion of the Kerr space-time, static axially symmetric space-times are reviewed. Here one can find a very interesting discussion of the Curzon-Chazy space-time. The chapter on rotating black holes is rather brief and, for
Vacuum spacetimes that admit no maximal slice
NASA Astrophysics Data System (ADS)
Witt, Donald M.
1986-09-01
Every closed three-manifold occurs as a spacelike hypersurface of a vacuum spacetime. For most of these three-manifolds, however, the vacuum spacetimes that contain them have no maximal slice. For asymptotically flat manifolds there are no restrictions on which three-manifolds can occur obeying the local energy conditions ρ>=(JaJa)1/2, and the spacetimes that contain them in most cases have no maximal slice.
Dynamical spacetimes in conformal gravity
NASA Astrophysics Data System (ADS)
Zhang, Hongsheng; Zhang, Yi; Li, Xin-Zhou
2017-08-01
The conformal gravity remarkably boosts our prehension of gravity theories. We find a series of dynamical solutions in the W2-conformal gravity, including generalized Schwarzschild-Friedmann-Robertson-Walker (GSFRW), charged generalized Schwarzschild-Friedmann-Robertson-Walker (CGSFRW), especially rotating Friedmann-Robertson-Walker (RFRW), charged rotating Friedmann-Robertson-Walker (CRFRW), and a dynamical cylindrically symmetric solutions. The RFRW, CRFRW and the dynamical cylindrically symmetric solutions are never found in the Einstein gravity and modified gravities. The GSFRW and CGSFRW solutions take different forms from the corresponding solutions in the Einstein gravity.
Spherical boson stars as black hole mimickers
Guzman, F. S.; Rueda-Becerril, J. M.
2009-10-15
We present spherically symmetric boson stars as black hole mimickers based on the power spectrum of a simple accretion disk model. The free parameters of the boson star are the mass of the boson and the fourth-order self-interaction coefficient in the scalar field potential. We show that even if the mass of the boson is the only free parameter, it is possible to find a configuration that mimics the power spectrum of the disk due to a black hole of the same mass. We also show that for each value of the self-interaction a single boson star configuration can mimic a black hole at very different astrophysical scales in terms of the mass of the object and the accretion rate. In order to show that it is possible to distinguish one of our mimickers from a black hole, we also study the deflection of light.
Quantum singularity of Levi-Civita spacetimes
NASA Astrophysics Data System (ADS)
Konkowski, D. A.; Helliwell, T. M.; Wieland, C.
2004-01-01
Quantum singularities in general relativistic spacetimes are determined by the behaviour of quantum test particles. A static spacetime is quantum mechanically singular if the spatial portion of the wave operator is not essentially self-adjoint. Here Weyl's limit point limit circle criterion is used to determine whether a wave operator is essentially self-adjoint. This test is then applied to scalar wave packets in Levi-Civita spacetimes to help elucidate the physical properties of the spacetimes in terms of their metric parameters.
Probing spacetime foam with extragalactic sources.
Christiansen, W A; Ng, Y Jack; van Dam, H
2006-02-10
Because of quantum fluctuations, spacetime is probably "foamy" on very small scales. We propose to detect this texture of spacetime foam by looking for halo structures in the images of distant quasars. We find that the Very Large Telescope interferometer will be on the verge of being able to probe the fabric of spacetime when it reaches its design performance. Our method also allows us to use spacetime foam physics and physics of computation to infer the existence of dark energy or matter, independent of the evidence from recent cosmological observations.
A Model of Classical Space-Times.
ERIC Educational Resources Information Center
Maudlin, Tim
1989-01-01
Discusses some historically important reference systems including those by Newton, Leibniz, and Galileo. Provides models illustrating space-time relationship of the reference systems. Describes building models. (YP)
A Model of Classical Space-Times.
ERIC Educational Resources Information Center
Maudlin, Tim
1989-01-01
Discusses some historically important reference systems including those by Newton, Leibniz, and Galileo. Provides models illustrating space-time relationship of the reference systems. Describes building models. (YP)
Multiple scattering of light in a spherical cometary atmosphere with an axisymmetric dust jet
NASA Technical Reports Server (NTRS)
Chick, Kenneth M.; Gombosi, Tamas I.
1992-01-01
A numerical solution has been developed for the anisotropic multiple scattering of light in a spherical shell comet atmosphere. The code has been run for a spherically symmetric coma distribution, benchmarked against past studies, and then run for the conditions of an axisymmetric dust jet at the subsolar point of the comet. The radiant flux impinging on the nucleus surface and the mean intensity of light throughout the coma were investigated.
Geodesics dynamics in the Linet-Tian spacetime with
NASA Astrophysics Data System (ADS)
Brito, Irene; Da Silva, M. F. A.; Mena, Filipe C.; Santos, N. O.
2014-03-01
We investigate the geodesics' kinematics and dynamics in the Linet-Tian metric with and compare with the results for the Levi-Civita metric, when . This is used to derive new stability results about the geodesics' dynamics in static vacuum cylindrically symmetric spacetimes with respect to the introduction of . In particular, we find that increasing always increases the minimum and maximum radial distances to the axis of any spatially confined planar null geodesic. Furthermore, we show that, in some cases, the inclusion of any breaks the geodesics' orbit confinement of the metric, for both planar and non-planar null geodesics, which are therefore unstable. Using the full system of geodesics' equations, we provide numerical examples which illustrate our results.
NASA Astrophysics Data System (ADS)
de Rham, Claudia; Motohashi, Hayato
2017-03-01
We study the development of caustics in shift-symmetric scalar field theories by focusing on simple waves with an S O (p )-symmetry in an arbitrary number of space dimensions. We show that the pure Galileon, the DBI-Galileon, and the extreme-relativistic Galileon naturally emerge as the unique set of caustic-free theories, highlighting a link between the caustic-free condition for simple S O (p )-waves and the existence of either a global Galilean symmetry or a global (extreme-)relativistic Galilean symmetry.
Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
Einstein Revisited - Gravity in Curved Spacetime Without Event Horizons
NASA Astrophysics Data System (ADS)
Leiter, Darryl
2000-04-01
In terms of covariant derivatives with respect to flat background spacetimes upon which the physical curved spacetime is imposed (1), covariant conservation of energy momentum requires, via the Bianchi Identity, that the Einstein tensor be equated to the matter energy momentum tensor. However the Einstein tensor covariantly splits (2) into two tensor parts: (a) a term proportional to the gravitational stress energy momentum tensor, and (b) an anti-symmetric tensor which obeys a covariant 4-divergence identity called the Freud Identity. Hence covariant conservation of energy momentum requires, via the Freud Identity, that the Freud tensor be equal to a constant times the matter energy momentum tensor. The resultant field equations (3) agree with the Einstein equations to first order, but differ in higher orders (4) such that black holes are replaced by "red holes" i.e., dense objects collapsed inside of their photon orbits with no event horizons. (1) Rosen, N., (1963), Ann. Phys. v22, 1; (2) Rund, H., (1991), Alg. Grps. & Geom. v8, 267; (3) Yilmaz, Hl, (1992), Nuo. Cim. v107B, 946; (4) Roberstson, S., (1999),Ap.J. v515, 365.
Casimir effect in the Kerr spacetime with quintessence
NASA Astrophysics Data System (ADS)
Bezerra, V. B.; Cunha, M. S.; Freitas, L. F. F.; Muniz, C. R.; Tahim, M. O.
2017-01-01
We calculate the Casimir energy of a massless scalar field in a cavity formed by nearby parallel plates orbiting a rotating spherical body surrounded by quintessence, investigating the influence of the gravitational field on that energy, at zero temperature. This influence includes the effects due to the spacetime dragging caused by the source rotation as well as those ones due to the quintessence. We show that the energy depends on all the involved parameters, as source mass, angular momentum and quintessence state parameter, for any radial coordinate and polar angle. We show that at the north pole the Casimir energy is not influenced by the quintessential matter. At the equatorial plane, when the quintessence is canceled, the result obtained in the literature is recovered. Finally, constraints in the quintessence parameters are obtained from the uncertainty in the current measurements of Casimir effect.
General Relativity and Spacetime Relationism.
NASA Astrophysics Data System (ADS)
Hoefer, Carl
1992-01-01
This dissertation takes up the project of showing that, in the context of the general theory of relativity (GTR), spacetime relationism is not a refuted or hopeless view, as many in the recent literature have maintained (John Earman, Michael Friedman, and others). Most of the challenges to the relationist view in General Relativity can be satisfactorily answered; in addition, the opposing absolutist and substantivalist views of spacetime can be shown to be problematic. The crucial burden for relationists concerned with GTR is to show that the realistic cosmological models, i.e. those that may be roughly accurate representations of our universe, satisfy Mach's ideas about the origin of inertia. This dissertation clears the way for and begins such a demonstration. After a brief discussion of the problem of the nature of spacetime and its history in the Introduction, chapters 2 and 3 provide conceptual analysis and criticism of contemporary philosophical arguments about relationism, absolutism, and particularly substantivalism. The current best arguments in favor of substantivalism are shown to be flawed, with the exception of the argument from inertial and metrical structure; and on this issue, it is shown that both relationism and substantivalism need to argue for modifications of GTR (restriction of its models to those with certain features) in order to have a non-trivial explanation of inertial and metrical structure. For relationists, a Machian account of the origin of inertia in some models of GTR is required. Chapter 4 demonstrates that such a Machian account is equivalent to the demand for a truly general relativity of motion. Chapter 5 explores the history of Einstein's commitment to Mach's ideas in his work on GTR. Through an examination of the history of Einstein's attempts to impose Machian constraints on the models of General Relativity, further insight into the nature of this problem is obtained, as are reasons to believe that the project is by no means
Quantization of spacetime based on a spacetime interval operator
NASA Astrophysics Data System (ADS)
Chiang, Hsu-Wen; Hu, Yao-Chieh; Chen, Pisin
2016-04-01
Motivated by both concepts of Adler's recent work on utilizing Clifford algebra as the linear line element d s =⟨γμ⟩ d Xμ and the fermionization of the cylindrical worldsheet Polyakov action, we introduce a new type of spacetime quantization that is fully covariant. The theory is based on the reinterpretation of Adler's linear line element as d s =γμ⟨λ γμ⟩ , where λ is the characteristic length of the theory. We name this new operator the "spacetime interval operator" and argue that it can be regarded as a natural extension to the one-forms in the U (s u (2 )) noncommutative geometry. By treating Fourier momentum as the particle momentum, the generalized uncertainty principle of the U (s u (2 )) noncommutative geometry, as an approximation to the generalized uncertainty principle of our theory, is derived and is shown to have a lowest order correction term of the order p2 similar to that of Snyder's. The holography nature of the theory is demonstrated and the predicted fuzziness of the geodesic is shown to be much smaller than conceivable astrophysical bounds.
Trumpet slices in Kerr spacetimes.
Dennison, Kenneth A; Baumgarte, Thomas W; Montero, Pedro J
2014-12-31
We introduce a new time-independent family of analytical coordinate systems for the Kerr spacetime representing rotating black holes. We also propose a (2+1)+1 formalism for the characterization of trumpet geometries. Applying this formalism to our new family of coordinate systems we identify, for the first time, analytical and stationary trumpet slices for general rotating black holes, even for charged black holes in the presence of a cosmological constant. We present results for metric functions in this slicing and analyze the geometry of the rotating trumpet surface.
Probing Gravity with Spacetime Sirens
NASA Astrophysics Data System (ADS)
Deffayet, Cédric; Menou, Kristen
2007-10-01
A gravitational observatory such as LISA will detect coalescing pairs of massive black holes, accurately measure their luminosity distance, and help identify a host galaxy or an electromagnetic counterpart. If dark energy is a manifestation of modified gravity on large scales, gravitational waves from cosmologically distant spacetime sirens are direct probes of this new physics. For example, a gravitational Hubble diagram based on black hole pair luminosity distances and host galaxy redshifts could reveal a large distance extradimensional leakage of gravity. Various additional signatures may be expected in a gravitational signal propagated over cosmological scales.
On spacetime structure and electrodynamics
NASA Astrophysics Data System (ADS)
Ni, Wei-Tou
2016-10-01
Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell-Lorentz electrodynamics. Introducing the metric gij as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the
Dirac's aether in curved spacetime.
Oliveira; Teixeira
2000-06-01
Proca's equations for two types of fields in a Dirac's aether with electric conductivity sigma are solved exactly. The Proca electromagnetic fields are assumed with cylindrical symmetry. The background is a static, curved spacetime whose spatial section is homogeneous and has the topology of either the three-sphere S 3 or the projective three-space P 3. Simple relations between the range of Proca field lambda, the Universe radius R, the limit of photon rest mass mgamma and the conductivity sigma are written down.
Binary black hole spacetimes with a helical Killing vector
Klein, Christian
2004-12-15
Binary black hole spacetimes with a helical Killing vector, which are discussed as an approximation for the early stage of a binary system, are studied in a projection formalism. In this setting the four-dimensional Einstein equations are equivalent to a three-dimensional gravitational theory with a SL(2,R)/SO(1,1) sigma model as the material source. The sigma model is determined by a complex Ernst equation. 2+1 decompositions of the three-metric are used to establish the field equations on the orbit space of the Killing vector. The two Killing horizons of spherical topology which characterize the black holes, the cylinder of light where the Killing vector changes from timelike to spacelike, and infinity are singular points of the equations. The horizon and the light cylinder are shown to be regular singularities, i.e., the metric functions can be expanded in a formal power series in the vicinity. The behavior of the metric at spatial infinity is studied in terms of formal series solutions to the linearized Einstein equations. It is shown that the spacetime is not asymptotically flat in the strong sense to have a smooth null infinity under the assumption that the metric tends asymptotically to the Minkowski metric. In this case the metric functions have an oscillatory behavior in the radial coordinate in a nonaxisymmetric setting, the asymptotic multipoles are not defined. The asymptotic behavior of the Weyl tensor near infinity shows that there is no smooth null infinity.
Gravitational geons in asymptotically anti-de Sitter spacetimes
NASA Astrophysics Data System (ADS)
Martinon, Grégoire; Fodor, Gyula; Grandclément, Philippe; Forgács, Peter
2017-06-01
We report on numerical constructions of fully non-linear geons in asymptotically anti-de Sitter (AdS) spacetimes in four dimensions. Our approach is based on 3 + 1 formalism and spectral methods in a gauge combining maximal slicing and spatial harmonic coordinates. We are able to construct several families of geons seeded by different families of spherical harmonics. We can reach unprecedentedly high amplitudes, with mass of order ∼1/2 of the AdS length, and with deviations of the order of 50% compared to third order perturbative approaches. The consistency of our results with numerical resolution is carefully checked and we give extensive precision monitoring techniques. All global quantities, such as mass and angular momentum, are computed using two independent frameworks that agree with each other at the 0.1% level. We also provide strong evidence for the existence of ‘excited’ (i.e. with one radial node) geon solutions of Einstein equations in asymptotically AdS spacetimes by constructing them numerically.
Compressible inviscid instability of rapidly expanding spherical material interfaces
NASA Astrophysics Data System (ADS)
Mankbadi, Mina R.; Balachandar, S.
2012-03-01
A high-order weighted essentially non-oscillatory scheme is employed to investigate the stability of a rapidly expanding material interface produced by a spherical shock tube. The flow structure is characterized by a forward moving primary shock, a backward moving secondary shock, and a spherical contact interface in-between. We consider herein the linear inviscid regime and focus on the development of the three-dimensional perturbations around the contact interface by solving a one-dimensional system of partial differential equations. Numerical simulations are performed to illustrate the effects of the contact interface's density discontinuity on the growth of the disturbances for various spherical wave numbers. In a spherical shock tube the instability is influenced by various mechanisms which include classical Rayleigh-Taylor (RT) effects, Bell-Plesset or geometry/curvature effects, the effects of impulsively accelerating the interface, and compressibility effects. Henceforth, the present instability will be referred to as non-classical RT instability to distinguish it from classical RT instability. For an extended intermediate time period, it can be shown that the small disturbances grow exponentially as in the classical RT instability. During this stage, the exponential growth rate increases with the spherical wave number, until it saturates for very large wave numbers due to the finite thickness limitation of the numerical representation of the contact interface. The results compare favorably with previous theoretical models; but indicate that in addition to compressibility, the space-time evolution of the contact interface's thickness plays a significant role. A parametric study is performed that varies the pressure and density ratios of the initial spherical container. The characteristics of the contact interface and the applicability of various instability theories is investigated for these regimes. Furthermore, varying the pressure and density ratios aids
From noncommutative spacetimes to Lorentz symmetry violation
NASA Astrophysics Data System (ADS)
Schreck, M.
2014-11-01
The current article provides a brief review on noncommutative spacetimes in light of Lorentz invariance violation and especially on how these models are linked to the Lorentz- violating Standard-Model Extension. By embedding a general noncommutative spacetime with a constant background tensor into the Standard-Model Extension, a couple of implications are drawn on Lorentz violation in such models.
Emission coordinates in Minkowski space-time
Coll, Bartolome; Ferrando, Joan J.; Morales, Juan A.
2009-05-01
The theory of relativistic positioning systems and their natural associated emission coordinates are essential ingredients in the analysis of navigation systems and astrometry. Here we study emission coordinates in Minkowski space-time. For any choice of the four emitters (arbitrary space-time trajectories) the relation between the corresponding emission coordinates and the inertial ones are explicitly given.
Entanglement and the architecture of spacetime
NASA Astrophysics Data System (ADS)
Bianchi, Eugenio
2017-01-01
I discuss the role of entanglement in the reconstruction of a spacetime geometry in loop quantum gravity. In particular I show that semiclassical solutions of the Hamiltonian constraint are highly-entangled superpositions of spin-network states. Quantum squeezing of the Ashtekar-Lewandowski vacuum provides a new variational tool for solving the constraints and describing a semiclassical spacetime with graviton fluctuations.
NASA Astrophysics Data System (ADS)
Field, F.; Goodbun, J.; Watson, V.
Architects have a role to play in interplanetary space that has barely yet been explored. The architectural community is largely unaware of this new territory, for which there is still no agreed method of practice. There is moreover a general confusion, in scientific and related fields, over what architects might actually do there today. Current extra-planetary designs generally fail to explore the dynamic and relational nature of space-time, and often reduce human habitation to a purely functional problem. This is compounded by a crisis over the representation (drawing) of space-time. The present work returns to first principles of architecture in order to realign them with current socio-economic and technological trends surrounding the space industry. What emerges is simultaneously the basis for an ecological space architecture, and the representational strategies necessary to draw it. We explore this approach through a work of design-based research that describes the construction of Ocean; a huge body of water formed by the collision of two asteroids at the Translunar Lagrange Point (L2), that would serve as a site for colonisation, and as a resource to fuel future missions. Ocean is an experimental model for extra-planetary space design and its representation, within the autonomous discipline of architecture.
NASA Technical Reports Server (NTRS)
Braverman, Amy; Nguyen, Hai; Olsen, Edward; Cressie, Noel
2011-01-01
Space-time Data Fusion (STDF) is a methodology for combing heterogeneous remote sensing data to optimally estimate the true values of a geophysical field of interest, and obtain uncertainties for those estimates. The input data sets may have different observing characteristics including different footprints, spatial resolutions and fields of view, orbit cycles, biases, and noise characteristics. Despite these differences all observed data can be linked to the underlying field, and therefore the each other, by a statistical model. Differences in footprints and other geometric characteristics are accounted for by parameterizing pixel-level remote sensing observations as spatial integrals of true field values lying within pixel boundaries, plus measurement error. Both spatial and temporal correlations in the true field and in the observations are estimated and incorporated through the use of a space-time random effects (STRE) model. Once the models parameters are estimated, we use it to derive expressions for optimal (minimum mean squared error and unbiased) estimates of the true field at any arbitrary location of interest, computed from the observations. Standard errors of these estimates are also produced, allowing confidence intervals to be constructed. The procedure is carried out on a fine spatial grid to approximate a continuous field. We demonstrate STDF by applying it to the problem of estimating CO2 concentration in the lower-atmosphere using data from the Atmospheric Infrared Sounder (AIRS) and the Japanese Greenhouse Gasses Observing Satellite (GOSAT) over one year for the continental US.