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We show under the assumption of small data that solutions to the Einstein-Vlasov system with a pure magnetic field and Bianchi I symmetry isotropise and tend to dust solutions. We also obtain the decay rates for the main variables. This…
The universe is viewed as a dust gas filling a sphere and floating in infinite empty space. Einstein's gravitational equations are applied to this case together with appropriate boundary values. The equations are solved for initial…
We present a simple method to obtain vacuum solutions of Einstein's equations in parabolic coordinates starting from ones with cylindrical symmetries. Furthermore, a generalization of the method to a more general situation is given together…
The cosmological constant problem is seen as a symptom of the ambiguity of the Riemann curvature in general relativity. The solution of that ambiguity provided by Nash's theorem on gravitational perturbations along extra dimensions…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…
We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails and we discuss the reasons of this…
A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
We present an exact analytical solution of the Einstein equations with cosmological constant in a spatially flat Robertson-Walker metric. This is interpreted as an isotropic Lemaitre-type version of the cosmological Friedmann model.…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
It is proved that the only geodesically complete stationary vacuum solution of the Einstein equations is the empty Minkowski space, or a quotient of it by a discrete group of isometries, generalizing a classical result of Lichnerowicz. In…
The purpose of this work is to investigate spatially homogeneous and flat cosmological solutions of the Einstein equations coupled to a non-variational ``near-minimal'' scalar field. This coupling model represents a minimal departure from…
In this thesis we consider several aspects of general relativity relating to exact solutions of the Einstein equations. In the first part gravitational plane waves in the Rosen form are investigated, and we develop a formalism for writing…
A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
We study time-dependent compactification of extra dimensions. We assume that the spacetime is spatially homogeneous, and solve the vacuum Einstein equations without cosmological constant in more than three dimensions. We consider globally…
We present a systematic study of static solutions of the vacuum Einstein equations with negative cosmological constant which asymptotically approach the generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within (mainly) a…
The accelerating expansion of the Universe points to a small positive vacuum energy density and negative vacuum pressure. A strong candidate is the cosmological constant in Einstein's equations of General Relativity. The vacuum dark energy…
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…