Related papers: Solution of the vacuum Kerr-Schild problem
A new framework for analysing the gravitational fields in a stationary, axisymmetric configuration is introduced. The method is used to construct a complete set of field equations for the vacuum region outside a rotating source. These…
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…
In this note the Schwarzschild and Kerr solutions are constructed for 3 space and $N$ time dimensions. Solutions, by construction, possesses symmetry with respect to rotations in time volume.
Making use of the Kerr theorem for shear-free null congruences and of Newman's representation for a virtual charge ``moving'' in complex space-time, we obtain an axisymmetric time-dependent generalization of the Kerr congruence, with a…
The metric of a spacetime can be greatly simplified if the spacetime is circular. We prove that in generic effective theories of gravity, the spacetime of a stationary, axisymmetric and asymptotically flat solution must be circular if the…
We have recently discovered a smooth vacuum-wormhole solution of the first-order equations of general relativity. Here, we obtain the corresponding multiple-vacuum-wormhole solution. Assuming that our world is essentially Minkowski…
We present interesting relationship between what are called stationary axisymmetric black hole solutions for the vacuum Einstein equations in the ordinary four-dimensions and exact solutions for self-dual Yang-Mills fields in flat $2+2$…
In the Kerr-Schild double copy, static and spherically symmetric black hole solutions of general relativity are mapped to purely electric solutions of Maxwell's theory in flat spacetime. We demonstrate that, for these configurations, the…
We prove that there are no restrictions on the spatial topology of asymptotically flat solutions of the vacuum Einstein equations in (n+1)-dimensions. We do this by gluing a solution of the vacuum constraint equations on an arbitrary…
We consider the linearised vacuum Einstein equations around a Kerr exterior solution and present a scheme to prove elliptic $L^2(\mathbb{S}^2)$-estimates for the linearised curvature quantities in the equations. The scheme employs the…
We consider null bosonic p-branes in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null membrane in general stationary, axially symmetrical, four dimensional, gravity background…
We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism,…
A new solution to the Einstein-Maxwell field equations is presented describing a cylindrically symmetric homogeneous cosmology. The solution is conformally flat, it possesses seven Killing vectors of which the timelike one is rotating and…
In this work, we construct a modified version of the Einstein field equations for a vacuum and spherically symmetric spacetime in terms of the Riemann-Louville fractional derivative. The main difference between our approach and other works…
In this paper, we prove a series of results concerning the uniqueness of Kerr-de Sitter as a family of smooth stationary black hole solutions to the nonlinear Einstein vacuum equations with positive cosmological constant $\Lambda$. The…
We obtain static, spherically symmetric, and asymptotically flat numerical solutions of massive gravity with a source. Those solutions show, for the first time explicitly, a recovery of the Schwarzschild solution of General Relativity via…
The separated radial part of a sourceless massive complex scalar field equation on the Kerr-Newman black hole background is shown to be a generalized spin-weighted spheroidal wave equation of imaginary number order. While the separated…
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…
In this thesis four separate problems in general relativity are considered, divided into two separate themes: coordinate conditions and perfect fluid spheres. Regarding coordinate conditions we present a pedagogical discussion of how the…