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We discuss and prove an extended version of the Kerr theorem which allows one to construct exact solutions of the Einstein-Maxwell field equations from a holomorphic generating function $F$ of twistor variables. The exact multiparticle…
We derive and discuss the physical interpretation of a conformally flat, static solution of the Einstein-Maxwell equations. It is argued that it describes a conformally flat, static spacetime outside a charged spherically symmetric domain…
We study inverse problems for the Einstein-Maxwell equations. We prove that it is possible to generate gravitational waves from the nonlinear interactions of electromagnetic waves. By sending electromagnetic waves from a neighborhood of a…
In this summary article, we review and discuss the non-existence of stationary black hole solutions for the Einstein-Dirac-Maxwell equations.
We consider rotating wormhole solutions in general relativity supported by a complex non-phantom spinor field (which provides a nontrivial spacetime topology) and electromagnetic fields. The solutions are asymmetric, regular, asymptotically…
We obtain charged rotating black hole solutions to the theory of Einstein-Maxwell gravity with cosmological constant in five dimensions. Some of the physical properties of these black holes are discussed.
In this paper, we develop a new method to find the exact solutions of the Einstein's field equations by using which we construct time-periodic solutions. The singularities of the time-periodic solutions are investigated and some new…
A novel method to derive stationary solutions of the Vlasov-Maxwell system is established. This method is based on the assumption that the deviation of the velocity distribution from the Maxwell-Boltzmann distribution can be expanded by the…
We discuss a new analytic solution to the Einstein-Maxwell field equations that describes electrically charged black holes with a slow rotation and with a single angular momentum in all higher dimensions. We also compute the gyromagnetic…
The existence of stationary solutions of the Einstein-Vlasov-Maxwell system which are axially symmetric but not spherically symmetric is proven by means of the implicit function theorem on Banach spaces. The proof generalises the methods of…
The Einstein-Maxwell fields of rotating stationary sources are represented by the SU(2,1) spinor potential $\Psi_A$ satisfying \[ \nabla \cdot [\Theta ^{-1}(\Psi_A\nabla \Psi_B-\Psi_B\nabla \Psi_A)]=-2\Theta ^{-2}\vec{C}\cdot (\Psi_A\nabla…
Uniqueness results are established for time-independent finite-energy electromagnetic fields which solve the nonlinear Maxwell--Born--Infeld equations in boundary-free space under the condition that either the charge or current density…
We present and discuss a 4-parameter stationary axisymmetric solution of the Einstein-Maxwell equations able to describe the exterior field of a rotating magnetized deformed mass. The solution arises as a system of two overlapping…
Following the technique of M\"uller-zum-Hagen, refs [1,2], we show that strictly static and strictly stationary solutions of the Einstein-Maxwell equations are analytic in harmonic coordinates. This holds whether or not the Maxwell field…
The regularized Maxwell theory is a recently discovered theory of non-linear electrodynamics that admits many important gravitating solutions within the Einstein theory. Namely, it was originally derived as the unique non-linear…
Non stationary cylindrically symmetric exact solutions of the Einstein-Maxwell equations are derived as single soliton perturbations of a Levi-Civita metric, by an application of Alekseev inverse scattering method. We show that the metric…
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…
The Geroch/Stephani transformation is a solution-generating transformation, and may generate spiky solutions. The spikes in solutions generated so far are either early-time permanent spikes or transient spikes. We want to generate a…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
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…