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Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
We study gravitational theory in 1+2 spacetime dimensions which is determined by the Lagrangian constructed as a sum of the Einstein-Hilbert term plus the two (translational and rotational) gravitational Chern-Simons terms. When the…
We give the Lagrangian formulation of a generic non-minimally extended Einstein-Maxwell theory with an action that is linear in the curvature and quadratic in the electromagnetic field. We derive the coupled field equations by a first order…
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…
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
We examine the motion of charged particles in gravitational and electro-magnetic background fields. We study in particular the deviation of world lines, describing the relative acceleration between particles on different space-time…
The possibility that the strength of gravitational interactions might slowly increase with distance, is explored by formulating a set of effective field equations, which incorporate the gravitational, vacuum-polarization induced, running of…
Mathematical modeling of gravitating configurations of physical fields is one of the priority directions of the modern theory of gravity. Most of the exact solutions constructed within the framework of the general relativity are static or…
We consider a theory of gravity with a hidden extra-dimension and metric-dependent torsion. A set of physically motivated constraints are imposed on the geometry so that the torsion stays confined to the extra-dimension and the…
A model is proposed for the classical electron as a point charge with finite electromagnetic self-energy. Modifications of the Reissner-Nordstr{\o}m (spin 0) and Kerr-Newman (spin 1/2) solutions of the Einstein-Maxwell equations are…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
An axially symmetric exact solution of the Einstein-Maxwell equations is obtained and is interpreted to give the gravitational and electromagnetic fields of a charged tachyon. Switching off the charge parameter yields the solution for the…
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a…
The classical Einstein--Maxwell field equations admit static horizonless wormhole solutions with only a circular cosmic string singularity. We show how to extend these static solutions to exact rotating asymptotically flat solutions. For a…
The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincar\'e…
We first investigate the form the General Relativity Theory would have taken had the gravitational mass and the inertial mass of material objects been different. We then extend this analysis to electromagnetism and postulate an equivalence…
We give a derivation of the Einstein equation for gravity which employs a definition of the local energy density of the gravitational field as a symmetric second rank tensor whose value for each observer gives the trace of the spatial part…
We consider the metrics of the General Relativity, whose energy-momentum tensor has a bounded support where it is continuous except for a finite step across the corresponding boundary surface. As a consequence, the first derivative of the…
The gravitational description given for an electric on the basis of exact solution of the Einstein-Maxwell equations eliminates Coulomb divergence. The internal pulsating semiconfined world formed by neutral dust is smoothly joined with…