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We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…
The staid subject of exact static spherically symmetric perfect fluid solutions of Einstein's equations has been reinvigorated in the last decade. We now have several solution generating techniques which give rise to new exact solutions.…
A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant $\Lambda$ and null fluid) in $2+1$ dimensions is given. This is a nonstatic generalization of the uncharged spinless BTZ metric. For…
In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D {\bf…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
Beginning with a special form of the Einstein-Rosen metric, we find new cosmological solutions of the Einstein equations, having two hypersurface-orthogonal Killing vectors , with ideal fluid. The equation of state is in the most cases of…
A class of exact spherically symmetric perturbations of retarding automodel solutions linearized around Friedman background of Einstein equations for an ideal fluid with an arbitrary barotrope value is obtained and investigated.
It is shown that different approaches towards the solution of the Einstein equations for a static spherically symmetric perfect fluid with a gamma-law equation of state lead to an Abel differential equation of the second kind. Its only…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, especially their properties from a chronological point of view. Each our spacetime is stationary cylindrically symmetric and it is filled…
We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to…
In this paper, we have searched the existence of the similarity solution for plane symmetric inhomogeneous cosmological models in general relativity. The matter source consists of perfect fluid with proportionality relation between…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
We consider the conformal Einstein equations for polytropic perfect fluid cosmologies which admit an isotropic singularity. For the polytropic index gamma strictly greater than 1 and less than or equal to 2 it is shown that the Cauchy…
We use a metric of the type Friedmann-Robertson-Walker to obtain new exact solutions of Einstein equations for a scalar and massive field. The solutions have a permanent or transitory inflationary behavior.
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 report a new symmetry of the Einstein-Friedmann equations for spatially flat Friedmann- Lema\^itre-Robertson-Walker universes. We discuss its application to barotropic perfect fluids and its use as a solution-generating technique for…
New exact solutions to the field equations in the Einstein--Gauss--Bonnet modified theory of gravity for a 5--dimensional spherically symmetric static distribution of a perfect fluid is obtained. The Frobenius method is used to obtain this…
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…
The general exact solution of the Einstein-matter field equations describing spherically symmetric shells satisfying an equation of state in closed form is discussed under general assumptions of physical reasonableness. The solutions split…