Related papers: Field Line Solutions of the Einstein-Maxwell Equat…
We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell--Minkowski equations, complementing a variety of other representations…
In (3 + 1) spacetime dimensions the Rainich conditions are a set of equations expressed solely in terms of the metric tensor which are equivalent to the Einstein-Maxwell equations for non-null electromagnetic fields. Here we provide the…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial…
A class of solutions in $d$-dimensional Einstein gravity minimally coupled to a massless scalar field is studied, where the spacetime metric is of a generalized Weyl form with $d-2$ commuting Killing vectors. In addition to the procedure to…
We report a new class of rotating charged solutions in 2+1 dimensions. These solutions are obtained for Einstein-Maxwell gravity coupled to a dilaton field with selfdual electromagnetic fields. The mass and the angular momentum of these…
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,…
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…
We study modified $f(R,(\nabla R)^2,\square R)$ gravity and show in detail how it can be reduced to Einstein gravity with a few scalar fields and then represented in the form of chiral self-gravitating model of the special type. In further…
Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field,…
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…
The field equations of the recent nonlocal generalization of Einstein's theory of gravitation are presented in a form that is reminiscent of general relativity. The implications of the nonlocal field equations are studied in the case of…
We derive a local curvature estimate for four-dimensional stationary solutions to the inheriting Einstein-Maxwell-Klein-Gordon equations. In particular, it implies that any such stationary geodesically complete solution with vanishing…
This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to…
A unification of Klein--Gordon, Dirac, Maxwell, Rarita--Schwinger and Einstein equations exact solutions (for the massless fields cases) is presented. The method is based on writing all of the relevant dynamical fields in terms of products…
We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to…
Translation by S. Antoci and A. Loinger of the fundamental memoir, that contains the ORIGINAL form of the solution of Schwarzschild's problem. The solution is regular in the whole space-time, with the only exception of the origin of the…
We study series of the stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent with the exterior solutions in some class of the scalar-tensor theories of…
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…
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.