Related papers: Energetic Stability of the Solutions of the Einste…
We determine the exact solution of the Einstein field equations for the case of a spherically symmetric shell of liquid matter, characterized by an energy density which is constant with the Schwarzschild radial coordinate $r$ between two…
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…
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 provide all basic equations and concepts required to carry out a general study on axially symmetric static sources. The Einstein equations and the conservation equations are written down for a general anisotropic static fluid endowed…
Spacetimes with a thin shell offer a framework where both the dynamical stability and the thermodynamical stability of the matter comprising the shell can be consistently studied. In the present work, we consider the dynamical and…
We analyze the thermodynamics of spherically symmetric thin-shell solutions to Einstein's equations, including solutions with negative interior mass. We show the inclusion of such solutions is essential for the thermodynamic consistency of…
We examine various well known exact solutions available in the literature to investigate the recent criterion obtained in ref. [20] which should be fulfilled by any static and spherically symmetric solution in the state of hydrostatic…
We numerically study the stability of collisionless equilibria in the context of general relativity. More precisely, we consider the spherically symmetric, asymptotically flat Einstein-Vlasov system in Schwarzschild and in maximal areal…
We construct models of static spherical distributions of perfect fluid in trace--free Einstein gravity theory. The equations governing the gravitational field are equivalent to the standard Einstein's equations however, their presentation…
We present a simple spherically symmetric and regular solution of Einstein's equations with two parameters $k$ and $M$, which matches to Schwarzschild's solution, satisfies the weak energy conditions in the interior region and for small $r$…
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…
We present new results concerning the existence of static, electrically charged, perfect fluid spheres that have a regular interior and are arbitrarily close to a maximally charged black-hole state. These configurations are described by…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(d\theta ^2 +\sin ^2 \theta d\phi ^2)$ with $f(r) = 1…
We propose two models for constant density relativistic perfect-fluid spheres supported by thin shell configurations. These models are obtained from the Schwarzschild constant density star solution: the first via the collapse of the…
We construct a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system bifurcating from the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter…
We construct, by numerical means, static solutions of the spherically symmetric Einstein-Vlasov-Maxwell system and investigate various features of the solutions. This extends a previous investigation \cite{AR1} of the chargeless case. We…
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match…
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…