Related papers: How can exact and approximate solutions of Einstei…
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 discuss the linear gravitoelectromagnetic approach used to solve Einstein equations in the weak-field and slow-motion approximation, which is a powerful tool to explain, by analogy with electromagnetism, several gravitational effects in…
It is known that B\"acklund transformations can be used to generate stationary axisymmetric solutions of Einstein's vacuum field equations with any number of constants. We will use this class of exact solutions to describe the exterior…
We present exact solutions in Einstein-aether theory in a static spherically symmetric background space with a spacelike aether field, as a difference with the usual selection of timelike aether field. We assume a coupling between the…
In this work, we have obtained exact solutions of Einstein equations for static and axially symmetric magnetized matter, specifically in plane-symmetric and almost-plane symmetric cases. Although these solutions impose constraints on the…
Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of…
We present a spherically symmetric and static exact solution of Quantum Einstein Equations. This solution is asymptotically (for large $r$) identical with the black hole solution on the anti--De Sitter background and, for some range of…
Using a new ansatz for solving the Einstein equations with a scalar field with the sign of the kinetic term inverted, I find a series of formulae to derive axial symmetric stationary exact solutions of the Phantom scalar field in general…
It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar…
We apply the energy-momentum tensor which is coordinate independent to calculate the energy content of the axisymmetric solutions. Our results are compared with what have been obtained before within the framework of Einstein general…
We present the Ernst potential and the line element of an exact solution of Einstein's vacuum field equations that contains as arbitrary parameters the total mass, the angular momentum, and the quadrupole moment of a rotating mass…
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 $2+2$…
The non-linear superposition of the stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field on the basis of the method of variation of parameters was constructed. Stationary soliton solution of the…
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass…
The problem of cylindrically symmetric vacuum solutions of Brans-Dicke scalar fields has been studied. Exact solutions have been obtained for the vacuum B-D field equations for the cylindrically symmetric Einstein-Rosen metric. The…
We present new exact solutions for the Einstein-Maxwell system in static spherically symmetric interior spacetimes. For a particular form of the gravitational potentials and the electric field intensity, it is possible to integrate the…
An idea which has been around in general relativity for more than forty years is that in the approach to a big bang singularity solutions of the Einstein equations can be approximated by the Kasner map, which describes a succession of…
We show that the exact solution of Einstein's equations describing a system of two aligned identical Kerr black holes separated by a massless strut follows straightforwardly from the extended 2-soliton solution possessing equatorial…
This paper explores the Kerr-Schild double copy, a duality relating gravity and electromagnetism. We show how Einstein's vacuum solutions in four dimensions can be converted into Maxwell's solutions via a double copy procedure, employing…
For the plane symmetry we have found the electro-vacuum exact solutions of the Einstein-Maxwell equations and we have shown that one of them is equivalent to the McVittie solution of a charged infinite thin plane. The analytical extension…