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In recent years higher-dimensional black holes have attracted much interest because of various developments in gravity and high energy physics. But whereas higher-dimensional charged static (Tangherlini) and uncharged rotating (Myers-Perry)…
After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…
We present a class of solutions to the Einstein-Maxwell equations in d-dimensions, all of which are asymptotically (anti)-de Sitter space-times. They describe electrically charged rotating solutions, which are generalizations of those found…
We get the general static, spherically symmetric solutions of the d-dimensional Einstein-Maxwell-Dilaton theories by dimensionally reducing them to a class of 2-dimensional dilaton gravity theories. By studying the symmetries of the actions…
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…
The Newtonian theory of gravitation and electrostatics admit equilibrium configurations of charged fluids where the charge density can be equal to the mass density, in appropriate units. The general relativistic analog for charged dust…
We construct stationary solutions to the Einstein-Maxwell-current system by using the Sasakian manifold for the three-dimensional space. Both the magnetic field and the electric current in the solution are specified by the contact form of…
We study Einstein-Maxwell (non-null) sourcefree configurations that can be extended to any conformally invariant non-linear electrodynamics (CINLE) by a constant rescaling of the electromagnetic field. We first obtain a criterion which…
We obtain a new class of exact solutions for the Einstein-Maxwell system in static spherically symmetric charged star in (2+1)-dimensional gravity. In order to obtain the analytical solutions we treat the matter distribution anisotropic in…
A three-dimensional slowly rotating black hole solution in the presence of negative cosmological constant in the Einstein-power-Maxwell theory is studied. It is shown that in the small rotation limit the electric field, diagonal metric…
We revisit the Ricci-flat metrics in four dimensions that are stationary and algebraically special, together with the locally asymptotically flat conditions in the generalized Bondi-Sachs framework. We show that the Einstein equation is…
We report on a new solution to the Einstein-Maxwell equations in 2+1 dimensions with a negative cosmological constant. The solution is static, rotationally symmetric and has a non-zero magnetic field. The solution can be interpreted as a…
A class of time dependent solutions to $(3+1)$ Einstein--Maxwell-dilaton theory with attractive electric force is found from Einstein--Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev--Petviashvili and…
In this report the exact rotating charged black hole solution to the Einstein--nonlinear electrodynamics theory with a cosmological constant is presented. This black hole is equipped with mass, rotation parameter, electric and magnetic…
Using a solution generating technique based on the symmetries of the dimensionally reduced Lagrangian we derive an exact solution of the Einstein-Maxwell-Dilaton field equations in five dimensions describing a system of two general…
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact solutions of Einstein equations for a scalar and massive field. The solutions have a permanent or transitory inflationary behavior.
We find a new class of exact solutions to the Einstein-Maxwell equations which can be used to model the interior of charged relativistic objects. These solutions can be written in terms of special functions in general; for particular…
In this paper, we present a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can…
We prove propagation of weighted Sobolev regularity for solutions of the hyperboloidal Cauchy problem for a class of quasi-linear symmetric hyperbolic systems, under structure conditions compatible with the Einstein-Maxwell equations in…
This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact $4$-manifolds that are $S^2$-bundles over compact Riemann surfaces of any genus. This generalizes the existence results by C. LeBrun in…