The general solution of the system of General Relativity equations has been found for isotropic Universe with the flat spatial distribution and synchronized time taking into account a perfect dust and the cosmological constant. Schwarzschild, Friedmann and Einstein-de Sitter solutions (as well as all of their fusion with each other) are special cases of the found general solution. A method of generating an infinite number of Tolman's like solutions has been found. Exact solutions has been found for the spherically symmetric gravitational field of perfect dust clouds in the expanding Universe filled with radiation. A system of ordinary differential equations has been obtained for the spherically symmetric gravitational field of perfect dust clouds in the expanding Universe filled with radiation and nonrelativistic gas. A system of equations has been obtained for the spherically symmetric gravitational field of ultrarelativistic celestial body explosion (supernova, quasar). The problem of a negative density of a perfect dust cloud in General Relativity has been considered.
It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential $V(ψ^2)$ 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.
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.
Metric Reconstruction and Second Order Perturbation for Generic Spherically Symmetric spacetime
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（杭州高等研究院基础物理与数学学院，UCAS）；University of Chinese Academy of Sciences（中国科学院大学）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
It is proved that spherically symmetric asymptotically flat neutral black holes cannot support spatially regular static configurations made of massive scalar fields with non-minimal coupling to gravity. Interestingly, our compact no-hair theorem is valid for generic values of the dimensionless physical parameter $ξ$ which quantifies the strength of coupling between the scalar field and the spacetime curvature.
We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the sense that linear time-dependent perturbations cannot exist, and we can conclude that these solutions are stable. Possible reasons for this inconsistency are discussed.
We study collapse of evaporating spherically-symmetric thin dust shells and dust balls assuming that quantum effects are encapsulated in a spherically-symmetric metric that satisfied mild regularity conditions. The evaporation may accelerate collapse, but for a generic metric the Schwarzschild radius is not crossed. Instead the shell (or the layer in the ball of dust) is always at a certain sub-Planckian distance from it.
The possibility to distinguish Dirac from Majorana fermion by gravitational interaction and torsion coupling is discussed. The scattering of both Dirac and Majorana particles are the same in the spherically symmetric gravitational field up to the first order perturbation of the fermion-gravity interaction. The scattering behaviors of Dirac and Majorana fermion are also the same by axial vector torsion but different by vector torsion. We get the conclusion that the scattering by vector torsion field can distinguish the Dirac from Majorana neutrino.
A recent paper promises new constructions that may make it possible to achieve covariance in spherically symmetric models of loop quantum gravity. This claim is contrary to the discovery of several stubborn obstacles to covariance uncovered in the same models during the last few years. As the authors point out in their abstract, new progress is supposedly possible if one takes into account crucial features of a certain partial Abelianization of the gauge transformations of spherically symmetric gravity, published by the same authors. In canonical form, these gauge transformations are given by …
We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master equation, the solution of which leads to the specification of all other unknown functions. We first obtained an exact solution which represents a new wormhole-like solution dressed with a regular scalar field. Then, we found large distance linearized spherically symmetric solutions in which the space asymptotically is AdS.
In this work, we study the implications of nonlinearity in general relativistic spherically symmetric inviscid irrotational accretion flow in a stationary non-rotating spacetime. It has been found that the perturbation scheme leads to a differential equation of the form of general Li{é}nard's equation. We discuss the equilibrium conditions of this system and its implications for globally subsonic accretion flows in the spherically symmetric stationary background. It is found that the stable solution predicted by linear stability analysis may become unstable under inclusion of lowest order nonl…
We numerically simulate gravitational collapse in asymptotically anti-de Sitter spacetimes away from spherical symmetry. Starting from initial data sourced by a massless real scalar field, we solve the Einstein equations with a negative cosmological constant in five spacetime dimensions and obtain a family of non-spherically symmetric solutions, including those that form two distinct black holes on the axis. We find that these configurations collapse faster than spherically symmetric ones of the same mass and radial compactness. Similarly, they require less mass to collapse within a fixed time…
We consider the new horizon first law in $f(R)$ theory with general spherically symmetric black hole. We derive the general formulas to computed the entropy and energy of the black hole. For applications, some nontrivial black hole solutions in some popular $f(R)$ theories are investigated, the entropies and the energies of black holes in these models are first calculated.
We consider spherically symmetric linear perturbations of static spherically symmetric spacetimes where the matter content is ellectrically counterpoised dust. We show that the evolution equation for the fluid perturbation implies that the fluid elements move with constant velocities. Therefore there are neither oscillations nor exponential departure from the background solution. We present an explicit example that shows that the perturbation could lead to the formation of a black hole.
We determine the conditions under which a static spherically symmetric spacetime metric is equivalent to a perturbed Friedman-Robertson-Walker metric. We construct the correspondence between the two metrics and discuss a simple application.
Einstein, Landau-Lifshitz, Papapetrou, Weinberg, and Møller energy-momentum prescriptions in general spherically symmetric space-times are investigated. It is shown that for two special but not unusual classes of general spherically symmetric space-times several energy-momentum prescriptions in Schwarzschild Cartesian coordinates lead to some coincidences in energy distribution. It is also obtained that for a special class of spherically symmetric metrics Møller and Einstein energy-momentum prescriptions give the same result for energy distribution if and only if it has a specific dependence o…
The purpose of this article is to obtain the periastron precession of a free particle moving around an extremal spherically symmetric dilaton black hole. To get the formulae for the periastron precession we use the phase-plane analysis of the general relativistic equations of motion.
