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An Exact solution of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources is study. In this context, effective potential are studied in order to understand the dynamics of the magnetic field in galaxies.…
The uniqueness theorem for static, spherically symmetric, asymptotically flat, higher dimensional phantom black holes, with non-degenerate event horizon , being the solutions of Einstein phantom/dilaton Maxwell/anti-Maxwell gravity systems…
Einstein originally proposed a nonsymmetric tensor field, with its symmetric part associated with the spacetime metric and its antisymmetric part associated with the electromagnetic field, as an approach to a unified field theory. Here we…
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,…
Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
We use Moeller's energy-momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein-Maxwell equations. The magnetic spacetime under…
In the framework of Einstein-Maxwell-axion theory we consider static spherically symmetric solutions, which describe a magnetic monopole in the axionic environment. These solutions are interpreted as the solutions for an axionic dyon, the…
Based on the conformal energy theorem we prove the uniqueness theorem for static higher dimensional electrically and magnetically charged black holes being the solution of Einstein (n-2)-gauge forms equations of motion. Black hole spacetime…
We construct three families of general magnetostatic axisymmetric exact solutions of Einstein-Maxwell equations in spherical coordinates, prolate, and oblates. The solutions obtained are then presented in the system of generalized…
We consider the existence of Einstein-Maxwell-dilaton plus fluid system for the case of stationary cylindrically symmetric spacetimes. An exact inhomogeneous $ \epsilon$-order solution is found, where the parameter $\epsilon$ parametrizes…
The exact relativistic treatment of a rotating disk surrounded by a magnetized material halo is presented. The features of the halo and disk are described by the distributional energy-momentum tensor of a general fluid in canonical form.…
The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic…
A class of exact static spherically symmetric solutions of the Einstein-Maxwell gravity coupled to a massless scalar field has been obtained in harmonic coordinates of the Minkowski space-time. For each value of the coupling constant $a$,…
We present new static spherically-symmetric exact solutions of Einstein equations with the quintessential matter surrounding a black hole charged or not as well as for the case without the black hole. A condition of additivity and linearity…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at…
A formalism for analyzing the complete set of field equations describing Macroscopic Gravity is presented. Using this formalism, a cosmological solution to the Macroscopic Gravity equations is determined. It is found that if a particular…
The energy density of the gravitational field is a full-fledged source of the gravitational field. This principle of Einstein was not implemented by him in the Einstein equation. Not long ago it was possible to find an energy-momentum…
An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsk\'y-Mitskievitch generating conjecture.…