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The Einstein Equation on 4-dimensional Lorentzian manifolds admitting recurrent null vector fields is discussed. Several examples of a special form are constructed. The holonomy algebras, Petrov types and the Lie algebras of Killing vector…
We derive an asymptotic solution of the Einstein field equations which describes the propagation of a thin, large amplitude gravitational wave into a curved space-time. The resulting equations have the same form as the colliding plane wave…
The problem of cylindrically symmetric vacuum solutions of Brans-Dicke scalar fields has been studied. Exact solutions have been obtained for the vacuum B-D field equations for the cylindrically symmetric Einstein-Rosen metric. The…
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…
A four-parameter class of exact asymptotically flat solutions of the Einstein-Maxwell equations involving only rational functions is presented. It is able to describe the exterior field of a slowly or rapidly rotating neutron star with…
We demonstrate how plane fronted waves with colliding wave fronts are the asymptotic limit of spherical electromagnetic and gravitational waves. In the case of the electromagnetic waves we utilize Bateman's representation of radiative…
McVittie's spacetime is a spherically symmetric solution to Einstein's equation with an energy-momentum tensor of a perfect fluid. It describes the external field of a single quasi-isolated object with vanishing electric charge and angular…
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 algebraically classify some higher dimensional spacetimes, including a number of vacuum solutions of the Einstein field equations which can represent higher dimensional black holes. We discuss some consequences of this work.
A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations…
We consider a D dimensional Kasner type diagonal spacetime where metric functions depend only on a single coordinate and electromagnetic field shares the symmetries of spacetime. These solutions can describe static cylindrical or…
In classical electrodynamics for rotating with variable angular velocity charged rigid sphere are found: the exact values of electromagnetic fields, the flux of radiating energy and the exact integral equation of rotation including the…
We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in $N$-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based…
Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov…
We study the special class of the exact solutions in cosmological models based on the Generalized Scalar-Tensor Gravity with non-minimal coupling of a scalar field to the Ricci scalar and to the Gauss-Bonnet scalar in 4D Friedmann universe…
In this manuscript we review the theoretical foundations of gravitational waves in the framework of Albert Einstein's theory of general relativity. Following Einstein's early efforts we first derive the linearised Einstein field equations…
The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that…
Multidimensional cosmological model describing the evolution of n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane Ansatz is adopted the field equations are…