Related papers: Direct generation of spinning Einstein--Maxwell fi…
We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the…
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…
We revisit the problem of the rotating generalization of the Fisher-Janis-Newman-Winicour solution of the minimal Einstein-scalar theory proving that the two previously proposed solutions do not satisfy the equations of motion. We also…
We establish, for the first time, an exact correspondence between Einstein-scalar-Maxwell theory and gauged Skyrme-Maxwell-Einstein models in (3+1) dimensions. By constructing the simplest consistent ansatz within the gauged Skyrme-Maxwell…
A formulation for stationary axisymmetric electromagnetic fields in general relativity is derived by casting them into the form of an anisotropic fluid. Several simplifications of the formalism are carried out in order to analyze different…
The inverse scattering problem is applied to 2-dimensional partial differential equations called soliton equations such as the KdV equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse…
We construct new supersymmetric solutions to the Euclidean Einstein-Maxwell theory with a non-vanishing cosmological constant, and for which the Maxwell field strength is neither self-dual or anti-self-dual. We find that there are three…
We generate from the static charged BTZ black hole a family of spinning charged solutions to the Einstein-Maxwell equations in 2+1 dimensions. These solutions go over, in a suitable limit, to self-dual spinning charged solutions, which are…
For stationary cylindrically symmetric solutions of the Einstein-Maxwell equation we have shown that the "charged" solutions of McCrea, Chitre et al.(CGN), Van den Bergh and Wils (VW) can be obtained from the seed metrics using generating…
We establish an algorithm that produces a new solution to the Einstein field equations, with an anisotropic matter distribution, from a given seed isotropic solution. The new solution is expressed in terms of integrals of known functions,…
In this paper, we study new exact solutions of Einstein's field equations with the motivation of the relativistic elasticity theory. We construct the static conformal elastic solution by applying conformal transformations to the…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…
The action of the isometry subgroup which preserves the trivial values of the fields is studied for the stationary D=4 Einstein--Maxwell--Dilaton--Axion theory. The technique for generation of charges and the corresponding procedure for…
New exact solutions of the Einstein-Maxwell field equations that describe $pp$-waves are presented.
Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to…
A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
We consider a class of Einstein-Maxwell-dilaton theories in general dimensions and construct both static and dynamic charged black holes. We adopt the reverse engineering procedure and make a specific ansatz for the scalar field and then…
A new formulation of electromagnetism based on linear differential commutator brackets is developed. Maxwell equations are derived, using these commutator brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and the…