Related papers: On the link between the Maxwell and linearised Ein…
Spherically symmetric static topological black hole solutions associated with some extended higher order gravitational models in the presence of a Maxwell-field are derived by means of simple Lagrangian method, based on spherically…
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…
We investigate perturbations of a class of spherically symmetric solutions in massive gravity and bi-gravity. The background equations of motion for the particular class of solutions we are interested in reduce to a set of the Einstein…
We present a short introduction to the M{\o}ller gravity theory and study the Schwarzschild solution and self-consistent spontaneous compactification solutions in Kaluza-Klein theories, which can be obtained in the framework of this…
From the Einstein field equations, in a weak-field approximation and for speeds small compared to the speed of light in vacuum, the following system is obtained \begin{align*} \nabla \times \overrightarrow{E_g} & = -\frac{1}{c}…
We study which geometric structure can be constructed from the vierbein (frame/coframe) variables and which field models can be related to this geometry. The coframe field models, alternative to GR, are known as viable models for gravity,…
No positive result has been obtained on the magnetic monopoles search. This allows to consider different theoretical approaches as the proposed in this paper, developed in the framework of the Einstein General Relativity. The properties of…
A reformulation of the Schwarzschild solution of the linearised Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the…
An electric monopole solution to the equations of Maxwell and Einstein's general relativity is displayed. It differs from the usual one in that all components of the metric vanish at large spatial distances from the charge rather than…
Using recently developed efficient symbolic manipulations tools, we present a general gauge-invariant formalism to study arbitrary radiative $(l\geq 2)$ second-order perturbations of a Schwarzschild black hole. In particular, we construct…
On the basis of the first principle -- the law of probability conservation and the Helmholtz decomposition theorem the authors have succeeded to construct the Schr\"odinger, Pauli, Dirac equation, the Hamilton-Jacobi equation and the…
A mathematical derivation of Maxwell's equations for gravitation, based on a mathematical proof of Faraday's Law, is presented. The theory provides a linear, relativistic Lagrangian field theory of gravity in a weak field, and paves the way…
The Einstein-Maxwell (E-M) equations in a curved spacetime that admits at least one Killing vector are derived, from a Lagrangian density adapted to symmetries. In this context, an auxiliary space of potentials is introduced, in which, the…
A gauge-invariant treatment of the monopole- ($l=0$) and dipole ($l=1$) modes in linear perturbations of the Schwarzschild background spacetime is proposed. Through this gauge-invariant treatment, we derived the solutions to the linearized…
The metric-affine Lagrangian of Ponomarev and Obukhov for the unified gravitational and electromagnetic field is linear in the Ricci scalar and quadratic in the tensor of homothetic curvature. We apply to this Lagrangian the variational…
We develop the General Theory of Relativity in a formalism with extended causality that describes physical interaction through discrete, transversal and localized pointlike fields. The homogeneous field equations are then solved for a…
On vacuum spacetimes of general dimension, we study the linearized Einstein vacuum equations with a spatially compactly supported and (necessarily) divergence-free source. We prove that the vanishing of appropriate charges of the source,…
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…
In this paper, we present a formalism to generate a family of interior solutions to the Einstein-Maxwell system of equations for a spherically symmetric relativistic charged fluid sphere matched to the exterior Reissner-Nordstr\"om…
An analytical solution of Einstein-Maxwell equations with a static fluid as a source is presented. The spacetime is represented by the axially symmetric Weyl metric and the energy-momentum tensor describes a coupling of a fluid with an…