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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,…
General static solutions of effectively 2-dimensional Einstein-Dilaton-Maxwell-Scalar theories are obtained. Our model action includes a class of 2-d dilaton gravity theories coupled with a $U(1)$ gauge field and a massless scalar field.…
In this paper we construct a new kind of solutions of the Einstein's field equations with non-vanishing cosmological constant, which possess some interesting physical properties. The singularities of this kind of solutions are investigated.…
The system of Einstein-Maxwell equations for fields mentioned in the title is simplified. Known pure radiation solutions are systematized and new solutions are given by separating the variables.
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…
We study symmetry properties of the Einstein-Maxwell theory nonminimaly coupled to the dilaton field. We consider a static case with pure electric (magnetic) Maxwell field and show that the resulting system becomes a nonlinear sigma-model…
We propose a numerical method to solve the three-dimensional static Maxwell equations in a singular axisymmetric domain, generated by the rotation of a singular polygon around one of its sides. The mathematical tools and an in-depth study…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
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…
The purpose of the present work is to extend the earlier results for asymptotically flat vacuum space-times to asymptotically flat solutions of the Einstein-Maxwell equations. Once again, in this case, we get a class of asymptotically…
In this paper we provide a method capable of producing an infinite number of solutions for Einstein's equation on static spacetimes with perfect fluid as a matter field. All spacetimes of this type which are symmetric with respect to a…
We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein-Maxwell space-times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the…
Classes of exact static solutions in four-dimensional Einstein-Maxwell-Dilaton gravity are found. Besides of the well-known solutions previously found in the literature, new solutions are presented.It's shown that spherically symmetric…
An Electrodynamics solver for moving sources is introduced. The main challenges and formulation are highlighted. The solver enables the simulation of fields for sources undergoing arbitrary motion. Two examples of uniformly moving current…
I use the Newtonian equation of hydrostatic equilibrium for an isotropic fluid sphere to generate exact anisotropic solutions of Einstein's equations. The input function is simply the density. An infinite number of regular solutions are…
Applications of the monodromy transform approach to construction of exact solutions of electrovacuum Einstein - Maxwell field equations are considered. Examples of new solutions are given.
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact solutions of Einstein equations for a scalar and massive field. The solutions have a permanent or transitory inflationary behavior.
We consider $5$ dimensional electrostatic solutions to Einstein-Maxwell gravity with $2$ commuting spacelike Killing fields. Taking two distinct reductions from $5$ dimensions to a $3$ dimensional base space, we write the Einstein-Maxwell…