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The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They provide a regularization of the standard…
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…
A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian…
A class of exact solutions for the Einstein-Maxwell field equations are obtained by assuming the erstwhile cosmological constant $ \Lambda $ to be a space-variable scalar, viz., $ \Lambda =\Lambda(r) $. The source considered here is static,…
The Newtonian theory of gravitation and electrostatics admit equilibrium configurations of charged fluids where the charge density can be equal to the mass density, in appropriate units. The general relativistic analog for charged dust…
We find the general behaviour of homogeneous and isotropic cosmological models in some fourth-order theories of gravity. Explicit, exact, general solutions are given for both empty universes and those filled with a perfect fluid. For the…
We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…
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 prove that the Einstein equations can be solved in a very general form for arbitrary spacetime dimensions and various types of vacuum and non-vacuum cases following a geometric method of anholonomic frame deformations for constructing…
Foundations of algebrodynamics based on earlier proposed equations of biquaternionic holomorphy are briefly expounded. Free Maxwell and Yang-Mills Eqs. are satisfied identically on the solutions of primary system which is also related to…
We present the complete family of higher dimensional spacetimes that admit a geodesic, shearfree, twistfree and expanding null congruence, thus extending the well-known D=4 class of Robinson-Trautman solutions. Einstein's equations are…
We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs system in the framework of Bondi coordinates. As a first step, the problem is reduced to a single first-order integro-differential equation by defining a generalized…
We construct the general spherically symmetric and self-similar solution of the Einstein-Vlasov system (collisionless matter coupled to general relativity) with massless particles, under certain regularity conditions. Such solutions have a…
We consider cosmological and black hole solutions in the Einstein and higher-derivative gravity in two dimensions where the theory is formulated first in $D$ dimensions. In the limit that $D$ tends to $2$ with simultaneous singular…
We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple…
The main purpose of this contribution is to determine physical and geometrical characterizations of whole classes of stationary cyclic symmetric gravitational fields coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional…
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such…
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…
We present solutions describing homogeneous and isotropic cosmologies in the massive gravity theory with two dynamical metrics recently proposed in arXiv:1109.3515 and claimed to be ghost free. These solutions can be spatially open, closed,…