Related papers: Birkhoffs Theorem and Lie Symmetry Analysis

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 prove there is a unique vacuum solution in split-signature spacetimes with Kleinian SO(2,1) spherical symmetry. We extend our analysis to accommodate a positive or negative cosmological constant and we prove the Kleinian spherically…

All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual…

According to general relativity, black holes are incomplete, which prevents developing a complete physical description of their dynamical formation and evolution once quantum effects are taken into account. Theories beyond general…

The paper deals with phantom scalar field cosmology in Einstein gravity. At first using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter…

It is known that the Jebsen-Birkhoff theorem is valid for vacuum solutions to Einstein's equation, as well as some of its generalizations. Using symmetry inheritance properties we investigate in detail the additional constraints that fields…

We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild…

The well-known Schwarzschild black hole was first obtained as a stationary, spherically symmetric solution of the Einstein's vacuum field equations. But until thirty years later, efforts were made for the analytic extension from the…

We seek exact solutions to the Einstein field equations which arise when two spacetime geometries are conformally related. Whilst this is a simple method to generate new solutions to the field equations, very few such examples have been…

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…

We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum…

Motivated by the newest progress in geometric flows both in mathematics and physics, we apply the geometric evolution equation to study some black-hole problems. Our results show that, under certain conditions, the geometric evolution…

We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential.…

We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both…

The geometry of three-dimensional space guides the search for a better model than the blackhole with its unwelcome singularity. An elementary construction produces on the 4-manifold of 2-spheres in a Riemannian 3-space a space-time metric…

The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…

We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution be static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of…

We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…

We establish a new uniqueness theorem for the three dimensional Schwarzschild-de Sitter metrics. For this some new or improved tools are developed. These include a reverse Lojasiewicz inequality, which holds in a neighborhood of the…