Related papers: On a Static Solution to Einstein Equations with in…
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…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
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…
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…
We present a spherically symmetric and static exact solution of Quantum Einstein Equations. This solution is asymptotically (for large $r$) identical with the black hole solution on the anti--De Sitter background and, for some range of…
We obtain an exact solution for the Einstein's equations with cosmological constant coupled to a scalar, static particle in static, "spherically" symmetric background in 2+1 dimensions.
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…
We analyze the stability of the Einstein static closed and open universe in two types of exponential $f(T)$ gravity theories. We show that the stable solutions exist in these two models. In particular, we find that large regions of…
Solutions to the Einstein equation that represent the superposition of static isolated bodies with axially symmetry are presented. The equations nonlinearity yields singular structures (strut and membranes) to equilibrate the bodies. The…
Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the…
Perfect-fluid, static, cylindrically symmetric solutions of Einstein's field equations are obtained for the equations of state $\rho+3p=0$ and $\rho=p$. In the former case, the density and the pressure turn out to be constant while in the…
In this note we examine some recently proposed solutions of the linearized vacuum Einstein equations. We show that such solutions are {\it not} symmetries of the Einstein equations, because of a crucial integrability condition.
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
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…
We construct spherically symmetric solutions to the Einstein-Euler equations, which contains a positive cosmological constant, say, the Einstein-Euler-de Sitter equations. We assume a realistic barotropic equation of state. Equilibria of…
The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
We shall in the framework of Bohmian quantum gravity show that it is possible to find a {\it pure} quantum state which leads to the static Einstein universe whose classical counterpart is flat space--time. We obtain the solution not only in…
We ask the following question: Of the exact solutions to Einstein's equations extant in the literature, how many could represent the field associated with an isolated static spherically symmetric perfect fluid source? The candidate…
We give a modified derivation of the Einstein equation of state by considering the Clausius relation $T\delta S-\delta N =\delta Q$ on a null hypersurface with a non-vanishing expansion ($\theta \neq 0$), i.e. not in the equilibrium. The…