Related papers: The tetralogy of Birkhoff theorems
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…
We study static spherically symmetric solutions to the vacuum field equations of quadratic gravity in the presence of a cosmological constant $\Lambda$. Motivated by the trace no-hair theorem, we assume the Ricci scalar to be constant…
The analysis of the validity of Birkhoff's theorem about the uniqueness of the spherically symmetric solution of the gravitational field equations is extended to the framework of the Poincar\'e gauge gravity theory. The class of models with…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
Semiclassical gravity is investigated in a large class of asymptotically flat, static, spherically symmetric spacetimes including those containing static stars, black holes, and wormholes. Specifically the stress-energy tensors of massless…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
We demonstrate that generic two-dimensional Horndeski theories can arise from the reduction of pure gravities in $d \geq 4$ dimensions, and therefore generic onshell configurations for the two-dimensional metric and scalar field correspond…
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 in a very special case. When a canonical scalar field is…
The exact static spherically symmetric solutions for pure-aether theory and Einstein-aether theory are presented. It is shown that both theories can deliver the Schwarzschild metric, but only the Einstein-aether theory contains solutions…
It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason…
We introduce a two-parameter static, nonspherically-symmetric black hole solution in the Einstein theory of gravity coupled with a massless scalar field. The scalar field depends only on the polar coordinate $\theta$ in the spherical…
We study structure of solutions of the recently constructed minimal extensions of Einstein's gravity in four dimensions at the quartic curvature level. The extended higher derivative theory, just like Einstein's gravity, has only a massless…
We generalize the Tolman-Oppenheimer-Volkoff equations for space-times endowed with a Weyssenhoff like torsion field in the Einstein-Cartan theory. The new set of structure equations clearly show how the presence of torsion affects the…
We extend Birkhoff's theorem for almost LRS-II vacuum spacetimes to show that the rigidity of spherical vacuum solutions of Einstein's field equations continues even in the perturbed scenario.
We suggest that the vacuum field equation in Finsler spacetime is equivalent to vanishing of Ricci scalar. Schwarzschild metric can be deduced from a solution of our field equation if the spacetime preserve spherical symmetry. Supposing…
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically…
The validity conditions for the extended Birkhoff theorem in multidimensional gravity with $n$ internal spaces are formulated, with no restriction on space-time dimensionality and signature. Examples of matter sources and geometries for…
The double null form of the Schwarzschild metric is usually arrived at by demanding Eddington-Finkelstein (EF) conditions at the horizon. This leads to certain logarithmic fall-offs that are too slow along null directions at $\mathscr{I}$,…
Inserting a varying Lambda in Einstein's field equations can be made consistent with the Bianchi identities by allowing for torsion, without the need to add scalar field degrees of freedom. In the minimal such theory, Lambda is totally free…
Utilizing various gauges of the radial coordinate, we give a General Relativistic (GR) description of static spherically symmetric spacetimes with a massive point source and vacuum outside this singularity. We show that in GR there exists a…