Related papers: Exact solutions of Einstein equations for anisotro…
The asymptotic properties of conformally static metrics in Einstein-aether theory with a perfect fluid source and a scalar field are analyzed. In case of perfect fluid, some relativistic solutions are recovered such as: Minkowski spacetime,…
Einstein equations for several matter sources in homogeneous, isotropic metric are shown to reduce to a second order nonlinear ordinary differential equation. An analysis of its solutions is made in an important case.
The coupled system of the spherically symmetric Einstein--Maxwell differential equations is solved under two different source conditions: non-zero electric charge and pressure anisotropy. Expressions for the metric functions, and pressures…
In this article, an exact solution of Einstein's field equations for spherically symmetric anisotropic matter distributions in isotropic coordinates is obtained. For this, the solution has been obtained by using a generalized physically…
In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is…
The results on local existence and continuation criteria obtained by G. Rein in [4] are extended to the case with a non-zero cosmological constant. It is also shown that for the spherically symmetric case and a positive cosmological…
We study Einstein's equations with an isotropic but inhomogeneous metric in the cosmic rest frame. The equations are solved perturbatively in the late Universe. The leading plus next-to-leading order results agree with observations without…
Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities.…
The special conformal transformation (composed by inversion - translation - inversion) is used to generate a time dependent conformally flat spacetime. In order to be an exact solution of Einstein's equations, we need as a source a stress…
In the field equations of Einstein-Cartan theory with cosmological constant a static spherically symmetric perfect fluid with spin density satisfying the Weyssenhoff restriction is considered. This serves as a rough model of space filled…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
We obtain the magnetic counterpart of the BTZ solution, i.e., the rotating spacetime of a point source generating a magnetic field in three dimensional Einstein gravity with a negative cosmological constant. The static (non-rotating)…
The Einstein-Maxwell (or Einstein) system of field equations plays a substantial role in the modeling of compact stars. Although due to its non-linearity getting an exact solution for the system of field equations is a difficult task, the…
A, recently presented, general procedure to find static and axially symmetric, interior solutions to the Einstein equations, is extended to the stationary case, and applied to find an interior solution for the Kerr metric. The solution,…
We show that any magnetostatic axially symmetric solution of the Einstein-Maxwell equations can be endowed with a specific charged fluid source of the Polanco et al type via a simple procedure requiring the knowledge of exclusively the…
Starting with a static, spherically symmetric spacetime incorporating critical (unstable) closed null geodesics, a family of models for equilibrium states of non-isolated compact objects is obtained by solving the Einstein equations for an…
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…
Recent results on solutions of the Einstein equations with matter are surveyed and a number of open questions are stated. The first group of results presented concern asymptotically flat spacetimes, both stationary and dynamical. Then there…
We have solved the Einstein-Maxwell equations for a class of isotropic metrics with constant spatial curvature in the presence of magnetic fields. We consider a slight modification of the Tolman averaging relations so that the…