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Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data.…
We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection…
We construct a 4-parameter family of inhomogeneous cosmological models, which contains two recently derived 3-parameter families as special cases. The corresponding exact vacuum solution to Einstein's field equations is obtained with…
We consider the relativistic Vlasov-Maxwell system (RVM) on a general axisymmetric spatial domain with perfect conducting boundary which reflects particles specularly, assuming axisymmetry in the problem. We construct continuous global…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…
In this paper we perform a systematic study of vacuum spatially flat ((3+D)+1)-dimensional Einstein-Gauss-Bonnet cosmological models. We consider models which topologically are the product of two flat isotropic subspaces with different…
We present the 3+1 decomposition of the Simon-Mars tensor, which has the property of being identically zero for a vacuum and asymptotically flat spacetime if and only if the latter is locally isometric to the Kerr spacetime. Using this…
Matrix models and their connections to String Theory and noncommutative geometry are discussed. Various types of matrix models are reviewed. Most of interest are IKKT and BFSS models. They are introduced as 0+0 and 1+0 dimensional reduction…
Rigidly rotating stationary matter in general relativity has been investigated by Kramer by the Ernst coordinate method. A weakness of this approach is that the Ernst potential does not exist for differential rotation. We now generalize the…
Gauge bosons associated to new gauge symmetries under which the standard model particles are not charged are predicted in many extensions of the standard model of particles and interactions. We show that under very general conditions, the…
In this manuscript, we develop a class of inhomogeneous relativistic cosmological models with the following properties: (i) They contain cosmological observers to whom the spatial geometry and the expansion are homogeneous and isotropic;…
Stationary rotating matter configurations in general relativity are considered. A formalism for general stationary space times is developed. Axisymmetric systems are discussed by the use of a nonholonomic and nonrigid frame in the…
We present the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves) that are of algebraic type III and for which the cosmological constant ($\Lambda_c$) is non-zero.…
The Null Surface Formulation of General Relativity is developed for 2+1 dimensional gravity. The geometrical meaning of the metricity condition is analyzed and two approaches to the derivation of the field equations are presented. One…
A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…
In this paper, we revisit the no black hole theorem in three dimensional (3D) gravity in the Newman-Penrose formalism in a generalized Newman-Unti gauge. After adapting the well established 4D NP formalism and its gauge and coordinates…
This paper concerns the well-posedness theory of the motion of physical vacuum for the compressible Euler equations with or without self-gravitation. First, a general uniqueness theorem of classical solutions is proved for the three…
We apply the method of moving anholonomic frames in order to construct new classes of solutions of the Einstein equations on (2+1)-dimensional pseudo-Riemannian spaces. There are investigated black holes with deformed horizons and…
We explicitly compute the dynamics of closed homogeneous and isotropic universes permeated by a single perfect fluid with a constant equation of state parameter $w$ in the context of a recent reformulation of general relativity, proposed in…
We establish the future nonlinear stability of a large class of FLRW models as solutions to the Einstein-Dust system. We consider the case of a vanishing cosmological constant, which in particular implies that the expansion rate of the…