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We investigate shock-wave solutions of the Einstein equations in the case when the speed of propagation is equal to the speed of light. The work extends the shock matching theory of Smoller and Temple, which characterizes solutions of the…
A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…
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…
Some of the most interesting results on the global dynamics of solutions of the vacuum Einstein equations concern the Gowdy spacetimes whose spatial topology is that of a three-dimensional torus. In this paper certain of these ideas are…
We set up an Einstein-Gauss-Bonnet theory in four dimensions, based on the recent formulation of pure gravity with extra dimensions of vanishing metrical length [1]. In absence of torsion, the effective field equations depend only on the…
Motivated by the Extremal Vanishing Horizon (EVH) black holes, their near horizon geometry and the EVH/CFT proposal, we construct and classify solutions with (local) SO(2,2) symmetry to four and five dimensional Einstein-Maxwell-Dilaton…
Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…
We present an explicit three-parameter class of $p=\gamma \varrho$, ($-1/3\leq\gamma<1$), cosmological models admitting a two-dimensional group $G_{2}$ of isometries acting on spacelike surfaces. The family is self-similar in the sense that…
We give an alternative description of the physical content of general relativity that does not require a Lorentz invariant spacetime. Instead, we find that gravity admits a dual description in terms of a theory where local size is…
We present and describe an exact solution of Einstein's equations which represents a snapping cosmic string in a vacuum background with a cosmological constant $\Lambda$. The snapping of the string generates an impulsive spherical…
We consider the existence and stability of the Einstein static universe under the Generalized Uncertainty Principle (GUP) effects. We show that this solution in the presence of perfect fluid with a minimal length is cyclically stable around…
For the study of cosmological backreacktion an avaragng procedure is required. In this work a covariant and gauge invariant averaging formalism for finite volumes will be developed. This averaging will be applied to the scalar parts of…
The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free…
We present a strategy to obtain equations of general relativity for an irrotational dust continuum within a flow-orthogonal foliation of spacetime from the equations of Newtonian gravitation, and vice versa, without employing a weak field…
Smooth Cauchy data for the Einstein-Lambda-vacuum field equations with positive cosmological constant Lambda that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary Scri+ in its future.…
A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…
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…
We study four-dimensional Einstein-Maxwell fields for which any higher-order corrections to the field equations effectively reduces to just a rescaling of the gravitational and the cosmological constant. These configurations are thus…
The general class of Robinson-Trautman metrics that describe gravitational radiation in the exterior of bounded sources in four space-time dimensions is shown to admit zero curvature formulation in terms of appropriately chosen…
In this paper, we give a new proof to a past stability result established in Fournodavlos-Rodnianski-Speck (arXiv:2012.05888), for Kasner solutions of the $(3+1)$-dimensional Einstein vacuum equations under polarized $U(1)$-symmetry. Our…