Related papers: The standard "static" spherically symmetric ansatz…
Spherically symmetric static solutions of the Einstein equations with a positive cosmological constant for the energy-momentum tensor of a barotropic perfect fluid are governed by the Tolman-Oppenheimer-Volkoff-de Sitter equation. Existence…
This diploma thesis analyses static, spherically symmetric perfect fluid solutions to Einstein's field equations with cosmological constant. Constant density solutions are derived for different values of the cosmological constant. Eleven…
We discuss spherically symmetric perfect fluid solutions of Einstein's equations which have equation of state ($p=\alpha \mu$) and which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. For each…
Static and spherically symmetric perfect fluid solutions of Einstein's field equations with cosmological constant are analysed. After showing existence and uniqueness of a regular solution at the centre the extension of this solution is…
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic…
We present the explicit form for all the four dimensional, static, spherically symmetric solutions in $(4+n)$-d Abelian Kaluza-Klein theory by performing a subset of $SO(2,n)$ transformations corresponding to four $SO(1,1)$ boosts on the…
An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular}…
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius $r$ is either a constant or has a null gradient in the $(t,x)$ subspace orthogonal to the symmetry spheres (i.e., $(\partial…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
Spatially homogeneous but totally anisotropic and non-flat Bianchi type II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical…
We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…
Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot…
We investigate the existence of analytic solutions for the field equations in the Einstein-\ae ther theory for a static spherically symmetric spacetime and provide a detailed dynamical system analysis of the field equations. In particular,…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
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 obtain a two-parameter set of solutions, which represents a spherically symmetric space-time with a superposition of a neutral fluid and an electric field. The electromagnetic four-potential of this Einstein-Maxwell space-time is taken…
Following a solution generating technique introduced recently by one of us, we transform the Einstein static Universe into a two - fold infinity class of physically acceptable exact perfect fluid solutions of Einstein's equations. Whereas…
We study static spherically symmetric solutions of Einstein gravity plus an action polynomial in the Ricci scalar, $R$, of arbitrary degree, $n$, in arbitrary dimension, $D$. The global properties of all such solutions are derived by…
We investigate static axially symmetric black hole solutions in a four-dimensional Einstein-Yang-Mills-SU(2) theory with a negative cosmological constant $\Lambda$. These solutions approach asymptotically the anti-de Sitter spacetime and…
Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity…