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The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model $E^3$ for this…
It is argued that, in order for the gravitational field to be propagated as a wave, it is necessary for it to satisfy a further set of field equations, in addition to those of Einstein and Hilbert, and these equations mean there is a…
We show that certain solutions to the linearized Einstein equation can---by the application of a particular type of linearized gauge transformation---be straightforwardly transformed into solutions of the exact Einstein equation. In cases…
The Einstein equation in D dimensions, if restricted to the class of space-times possessing n = D - 2 commuting hypersurface-orthogonal Killing vectors, can be equivalently written as metric-dilaton gravity in 2 dimensions with n scalar…
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 Einstein equations, apart from being the classical field equations of General Relativity, are also the classical field equations of two other theories of gravity. As the experimental tests of General Relativity are done using the…
We study a noncommutative theory of gravity in the framework of torsional spacetime. This theory is based on a Lagrangian obtained by applying the technique of dimensional reduction of noncommutative gauge theory and that the yielded…
In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively.…
In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds…
By using Bianchi I type of homogenous and anisotropic background metric having cylindrical symmetry in $x$ direction of a local cartesian coordinates system, we solve metric field equations for a non-minimally coupled Einstein-Maxwell…
We discuss dynamical aspects of gravitational plane waves in Einstein theory with massless scalar fields. The general analytic solution describes colliding gravitational waves with constant polarization, which interact with scalar waves…
Non-linear special relativity (or doubly special relativity) is a simple framework for encoding properties of flat quantum space-time. In this paper we show how this formalism may be generalized to incorporate curvature (leading to what…
The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We…
We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and…
We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein-like equation.…
One of the longstanding problems of modern gravitational physics is the detection of gravitational waves, for which the standard theoretical analysis relies upon the split of the space-time metric into a background metric plus perturbation.…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
We start by analysing the Lie algebra of Hermitian vector fields of a Hermitian line bundle. Then, we specify the base space of the above bundle by considering a Galilei, or an Einstein spacetime. Namely, in the first case, we consider, a…
We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any…