General Relativity and Gravitation最新文献

We examine the black-hole limits of the family of static and spherically symmetric solutions of the Einstein field equations for polytropic matter, that was presented in a previous paper. This exploration is done in the asymptotic sub-regions of the allowed regions of the parameter planes of that family of solutions, for a few values of the polytropic index n, with the limitation that (n>1). These allowed regions were determined and discussed in some detail in another previous paper. The characteristics of these limits are examined and analyzed. We find that there are different types of black-hole limits, with specific characteristics involving the local temperature of the matter. We also find that the limits produce a very unexpected but specific type of spacetime geometry in the interior of the black holes, which we analyze in detail. Regarding the spatial part of the interior geometry, we show that in the black-hole limits there is a general collapse of all spatial distances to zero. Regarding the temporal part, there results an infinite overall red shift in the limits, with respect to the flat space at radial infinity, over the whole interior region. The analysis of the interior geometry leads to a very surprising connection with quantum-mechanical studies in the background metric of a naked Schwarzschild black hole. The nature of the solutions in the black-hole limits leads to the definition of a new type of singularity in General Relativity. We argue that the black-hole limits cannot actually be taken all the way to their ultimate conclusion, due to the fact that this would lead to the violation of some essential physical and mathematical conditions. These include questions of consistency of the solutions, questions involving infinite energies, and questions involving violations of the quantum behavior of matter. However, one can still approach these limiting situations to a very significant degree, from the physical standpoint, so that the limits can still be considered, at least for some purposes, as useful and simpler approximate representations of physically realizable configurations with rather extreme properties.

Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications.

This paper is the initial part of a comprehensive study of spacetimes that admit the canonical forms of Killing tensor in General Relativity. The general scope of the study is to derive either new exact solutions of Einstein’s equations that exhibit hidden symmetries or to identify the hidden symmetries in already known spacetimes that may emerge during the resolution process. In this preliminary paper, we first introduce the canonical forms of Killing tensor, based on a geometrical approach to classify the canonical forms of symmetric 2-rank tensors, as postulated by R. V. Churchill. Subsequently, the derived integrability conditions of the canonical forms serve as additional equations transforming the under-determined system of equations, comprising of Einstein’s Field Equations and the Bianchi Identities (in vacuum with (Lambda )), into an over-determined one. Using a null rotation around the null tetrad frame we manage to simplify the system of equations to the point where the geometric characterization (Petrov Classification) of the extracted solutions can be performed and their null congruences can be characterized geometrically. Therein, we obtain multiple special algebraic solutions according to the Petrov classification (D, III, N, O) where some of them appeared to be new. The latter becomes possible since our analysis is embodied with the usage of the Newman-Penrose formalism of null tetrads.

We discuss the problem of singularity crossing in isotropic and anisotropic universes. We study at which conditions singularities can disappear in quantum cosmology and how quantum particles behave in the vicinity of singularities. Some attempts to develop general approach to the connection between the field reparametrization and the elimination of singularities is presented as well.

We give a family of exact solutions of (N=1) supergravity field equations in (D=4) dimensions that describe the collision of plane-fronted gravitino waves.

The late-time behaviour of the solutions of the Fackerell–Ipser equation (which is a wave equation for the spin-zero component of the electromagnetic field strength tensor) on the closure of the domain of outer communication of sub-extremal Kerr spacetime is studied numerically. Within the Kerr family, the case of Schwarzschild background is also considered. Horizon-penetrating compactified hyperboloidal coordinates are used, which allow the behaviour of the solutions to be observed at the event horizon and at future null infinity as well. For the initial data, pure multipole configurations that have compact support and are either stationary or non-stationary are taken. It is found that with such initial data the solutions of the Fackerell–Ipser equation converge at late times either to a known static solution (up to a constant factor) or to zero. As the limit is approached, the solutions exhibit a quasinormal ringdown and finally a power-law decay. The exponents characterizing the power-law decay of the spherical harmonic components of the field variable are extracted from the numerical data for various values of the parameters of the initial data, and based on the results a proposal for a Price’s law relevant to the Fackerell–Ipser equation is made. Certain conserved energy and angular momentum currents are used to verify the numerical implementation of the underlying mathematical model. In the construction of these currents a discrete symmetry of the Fackerell–Ipser equation, which is the product of an equatorial reflection and a complex conjugation, is also taken into account.

We derive the equation governing the axial-perturbations in the space-time of a non-rotating uncharged primordial black hole (PBH), produced in early Universe, whose metric has been taken as the generalized McVittie metric. The generalized McVittie metric is a cosmological black hole metric, proposed by Faraoni and Jacques in 2007 (Phys. Rev. D 76:063510, 2007). This describes the space-time of a Schwarzschild black hole embedded in FLRW-Universe, while allowing its mass-change. Our derivation has basic similarities with the procedure of derivation of Chandrasekhar, for deriving the Regge-Wheeler equation for Schwarzschild metric (Chandrasekhar The Mathematical Theory of Black holes, Oxford University Press, New York, 1983); but it has some distinct differences with that due to the complexity and time-dependency of the generalized McVittie metric. We show that after applying some approximations which are very well valid in the early radiation-dominated Universe, the overall equation governing the axial perturbations can be separated into radial and angular parts, among which the radial part is the intended one, as the angular part is identical to the case of Schwarzschild metric as expected. We identify the potential from the Schrödinger-like format of the equation and draw some physical interpretation from it.

The gravitational interaction of (classical and quantum) spinning bodies is currently the focus of many works using a variety of approaches. This note is a comment on a short paper by Jean-Marie Souriau, now reprinted in the GRG Golden Oldies collection. Souriau’s short 1970 note was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. We explain the specificity of Souriau’s approach and emphasize its potential interest within the current flurry of activity on the gravitational interaction of spinning particles.

This paper was a pioneering contribution to a symplectic description of the dynamics of spinning particles in general relativity which remained somewhat unnoticed. In particular, it introduced the pre-symplectic 2-form (sigma ) describing the dynamics of spinning particles coupled to an Einsteinian curved background. The method throws light on approaches to spinning black holes and neutron stars.

It is often argued that the Planck length (or mass) is the scale of quantum gravity, as shown by comparing the Compton length with the gravitational radius of a particle. However, the Compton length is relevant in scattering processes but does not play a significant role in bound states. We will derive a possible ground state for a dust ball composed of a large number of quantum particles entailing a core with the size of a fraction of the horizon radius. This suggests that quantum gravity becomes physically relevant for systems with compactness of order one for which the nonlinearity of General Relativity cannot be discarded. A quantum corrected geometry can then be obtained from the effective energy-momentum tensor of the core or from quantum coherent states for the effective gravitational degrees of freedom. These descriptions replace the classical singularity of black holes with integrable structures in which tidal forces remain finite and there is no inner Cauchy horizon. The extension to rotating systems is briefly mentioned.