Related papers: Exact Solution of the Einstein Field Equations for…
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…
We interpret the exact solutions previously obtained for spherically symmetric shells of liquid fluid in General Relativity in terms of the energies involved. We show that a certain parameter that was introduced into the solutions by the…
According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…
We study spherically symmetric spacetimes in Einstein-aether theory in three different coordinate systems, the isotropic, Painlev\`e-Gullstrand, and Schwarzschild coordinates, in which the aether is always comoving, and present both…
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 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…
It is well known that the Schwarzschild solution describes the gravitational field outside compact spherically symmetric mass distribution in General Relativity. In particular, it describes the gravitational field outside a point particle.…
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…
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}…
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…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…
1- It is shown that the upper bound for $\alpha$ in the general solutions of spherically symmetric vacuum field equations(gr-qc/9812081,$\Lambda$=0) is nearly 10^3.This has been obtained by comparing the theoretical prediction for bending…
Two new classes of exact interior static solutions of the Einstein equations in homogeneous coordinates for a gravitating ball filled by a Pascal perfect fluid are obtained. Schwarzschild's interior solution of is a special case of these…
This paper examines the inhomogeneous Einstein equation for a static spherically symmetric metric with a source term corresponding to a perfect fluid with p=-rho. By a careful treatment of the equation near the origin we find an analytic…
We study a static spherically symmetric problem with a black hole and radially directed geodesic flows of dark matter. The obtained solutions have the following properties. At large distances, the gravitational field produces constant…
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild(-Droste) solution, and into one specific stationary axially symmetric…
While it is known that any spherical fluid distribution may only source the spherically symmetric Schwarzschild space-time, the inverse is not true. Thus, in this manuscript, we find exact axially symmetric and static fluid (interior)…
We present spherically symmetric solutions to Einstein's equations which are equivalent to canonical Schwarzschild and Reissner-Nordstrom black holes on the exterior, but with singular (Planck-density) shells at their respective event and…
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 study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres are composed of a perfect fluid with a charge distribution that creates a…