Related papers: Relativistic Spheres
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
The stability of static uncharged spheres with anisotropic internal stresses is studied in general relativity. It has been noticed that pressure anisotropy plays an important role for stability of stellar structure. It is shown that radial…
In case of a spherically symmetric non-linear scalar field (SF) in flat space, besides singularity at the center, spherical singularities can occur for non-zero values of radial variable $r>0$. We show that in the General Relativity the…
In this work, a spherically symmetric and static relativistic anisotropic fluid sphere solution of the Einstein field equations is provided. To build this particular model, we have imposed metric potential $e^{2\lambda(r)}$ and an equation…
We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are…
In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be related to orientation, and its…
A static spherically symmetric metric in Einstein-scalar-tensor gravity theory with a scalar field potential $V[\phi]$ is non-singular for all real values of the coordinates. It does not have a black hole event horizon and there is no…
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 study the behaviour of a specific system of relativistic elasticity in its own gravitational field: a static, spherically symmetric shell whose wall is of arbitrary thickness consisting of hyperelastic material. We give the system of…
The existence and stability conditions of Einstein static universe against homogeneous scalar perturbations in the context of Lyra geometry is investigated. The stability condition is obtained in terms of the constant equation of state…
It is proven that the relativistic charged ball with its charge less than its mass (in natural units) cannot have a non-singular static configuration while its radius approaches its external horizon size. This conclusion does not depend on…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an…
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…
Considering Vaidya-Tikekar metric, we obtain a class of solutions of the Einstein-Maxwell equations for a charged static fluid sphere. The physical 3-space (t=constant) here is described by pseudo-spheroidal geometry. The relativistic…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
The existence of static and axially symmetric regions in a Friedman-Lemaitre cosmology is investigated under the only assumption that the cosmic time and the static time match properly on the boundary hypersurface. It turns out that the…
We describe a novel class of geometrical models of relativistic stars. Our approach to the static spherically symmetric solutions of Einstein equations is based on a careful physical analysis of radial gauge conditions. It brings us to a…
We discuss the physical features of two recent classes of analytical solutions of the Einstein equations sourced by an exotic perfect fluid with equation of state $ P=-\rho/5$. These geometries depend on up to four parameters and are static…