Black hole in closed spacetime with an anisotropic fluid

Abstract

We study spherically symmetric geometries made of anisotropic perfect fluid based on general relativity. The purpose of the work is to find and classify black hole solutions in closed spacetime. In a general setting, we find that a static and closed space exists only when the radial pressure is negative but its size is smaller than the density. The Einstein equation is eventually casted into a first order autonomous equation on two-dimensional plane of scale-invariant variables, which are equivalent to the Tolman-Oppenheimer-Volkoff (TOV) equation in general relativity. Then, we display various solution curves numerically. An exact solution describing a black hole solution in a closed spacetime was known in Ref. [1], which solution bears a naked singularity and negative energy era. We find that the two deficits can be remedied when ρ + 3p1 > 0 and ρ + p1 + 2p2 < 0, where the second violates the strong energy condition.

Entropy of self-gravitating anisotropic matter

“…Recently, in Ref. [34] the author suggested conditions to avoid naked singularities for a system with an anisotropic fluid. One of the conditions is ρ + p 1 + 2p 2 < 0, which indicates a violation of the strong energy condition.…”

Entropy of a Wormhole from the Constituent

“…Most of the results in this section are brief summaries of Refs. [24,25], up to some tweaks to the notation to simplify writing and discussion.…”

Numerical Study of Instability of Fluid Black Holes

“…Gravitating fluid has been a hot issue for a long time. Lots of works have been focussed on the time dependent situation such as the Friedmann universe in the literature, while gravity of static fluid has also been studied quite intensively [1][2][3][4][5][6][7][8][9][10][11]. For static fluid, the gravitating solutions have been obtained recently in Refs.…”