Related papers: Spherical Universes with Anisotropic Pressure
The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical…
We provide new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is…
A spherically symmetric charged ideal fluid solution of Einstein field equation is given in the presence of the cosmological constant and two well known example of this type of solution is presented. If the matter is confined in a region,…
The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
We explore the gravitational collapse of a spherically symmetric dust cloud in the Einstein-Gauss-Bonnet gravity without a cosmological constant, and obtain three families of LTB-like solutions. It is shown that the Gauss-Bonnet term has a…
In this paper Einstein's field equations, for static spherically symmetric perfect fluid models with a linear barotropic equation of state, are recast into a 3-dimensional regular system of ordinary differential equations on a compact state…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
Cylindrically symmetric inhomogeneous string cosmological models are investigated in presence of string fluid as a source of matter. To get the three types of exact solutions of Einstein's field equations we assume $A = f(x)k(t)$, $B =…
We provide exact solutions to the Einstein equations when the Universe contains vacuum energy plus a uniform arrangements of magnetic fields, strings, or domain walls. Such a universe has planar symmetry, i. e., it is homogeneous but, not…
We investigate the vacuum and charged spherically symmetric static solutions of the Einstein equations on cosmological background. The background metric is not flat, but curved, with constant - curvature spatial sections. Both vacuum and…
We show that equations of Newtonian hydrodynamics and gravity with Einstein's cosmological constant included admit gravitostatic wave solutions propagating in the background of Einstein's static Universe. In the zero pressure limit these…
We consider a system representing self-gravitating balls of dust in an expanding Universe. It is demonstrated that one can prescribe data for such a system at infinity and evolve it backward in time without the development of shocks or…
The collapse of marginally bound, inhomogeneous, pressureless (dust) matter, in spherical symmetry, is considered. The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions.…
Exact solutions of Einstein equations with null Riemman-Christoffel curvature tensor everywhere, except on a hypersurface, are studied using quantum particles obeying the Klein-Gordon equation. We consider the particular cases when the…
Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.
Introducing $f(\mathcal{R})$ term in the five-dimensional bulk action we derive effective Einstein's equation on the brane using Gauss-Codazzi equation. This effective equation is then solved for different conditions on dark radiation and…
An expanding spherically symmetric dust cloud is considered in a framework of general relativity. Initial conditions leading to a shell-crossing singularity are chosen. The way to construct a weak solution for such a case is proposed.…
We construct exact static inhomogeneous solutions to Einstein's equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an…
f(R) gravity is a well-known modification of General Relativity, that can be reduced to a scalar-tensor theory by a conformal transformation (Einstein frame). We study static spherically symmetric (SSS) asymptotically flat vacuum…