Related papers: The tetralogy of Birkhoff theorems
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…
We provide a set of general tools to study the problem of stellar equilibrium in any gravitational theory in which spherically symmetric spacetimes satisfy master field equations taking the form of an equality between an identically…
Exact solutions of spherically symmetric black hole and gravitational wave are explored in $f(R)$ gravity in arbitrary dimension. We find two exact solutions for the radiation and absorption of null dust. In the framework of general…
We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded…
We study spinoptics equations in the Schwarzschild spacetime. We demonstrate that using the explicit and hidden symmetries of this metric one can explicitly solve the equations for complex null tetrad associated with null rays representing…
This work is a purely syntactic geometric exploration of some few elements, which are our axioms, that in last instance it is the set of differential equations whose solutions give the geodesic lines of the Schwarzschild spacetime. We…
Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the…
Within the scalar-tensor theory of gravity with Higgs mechanism without Higgs particles, we prove that the excited Higgs potential (the scalar field) vanishs inside and outside of the stellar matter for static spherically symmetric…
Based on perturbation theory, we present the exact first-order solution to the Einstein equations for the exterior static gravitational field of an isolated non-rotating star in a spatially finite universe having the topology of a flat…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes. But its power lies in being able to handle…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…
The Born-Infeld theory of the gravitational field formulated in Weitzenbock spacetime is studied in detail. The action, constructed quadratically upon the torsion two-form, reduces to Einstein gravity in the low field limit where the…
The $\cal{N}=4$ supersymmetric spinning particle admits several consistent quantizations, related to the gauging of different subgroups of the $SO(4)$ $R$-symmetry on the worldline. We construct the background independent BRST quantization…
In the spherically symmetric case the requirements of regularity of density and pressures and finiteness of the ADM mass $m$, together with the weak energy condition, define the family of asymptotically flat globally regular solutions to…
The topos theory is a theory which is used for deciding a number of problems of theory of relativity, gravitation and quantum physics. In the article spherically symmetric solution of the vacuum Einstein equations in the Intuitionistic…
The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen…
We prove Birkhoff-type results showing that $L^2$ solutions of the linearized Einstein equations around Riemannian Kottler ("Schwarzschild-anti de Sitter") metrics in arbitrary dimension and horizon topology, which are not controlled by…
We present a tetrad-based method for solving the Einstein field equations for spherically-symmetric systems and compare it with the widely-used Lema\^itre-Tolman-Bondi (LTB) model. In particular, we focus on the issues of gauge ambiguity…