Static-Fluid Black Holes

TL;DR

This paper explores static black hole solutions formed by a perfect fluid with specific pressure-density relation in different spatial geometries, revealing multiple classes with unique singularity structures and related cosmological solutions.

Contribution

It classifies and analyzes static black hole solutions with a perfect fluid in $S_3$ and $H_3$ geometries, identifying new solution types and their singularity properties.

Findings

Three classes of black-hole solutions identified.

The $S_3$ type solution has two singularities, one behind the horizon and one naked.

Existence of nonstatic cosmological solutions in $S_3$ and $H_3$.

Abstract

We investigate black holes formed by static perfect fluid with $p=-\rho/3$. These represent the black holes in $S_3$ and $H_3$ spatial geometries. There are three classes of black-hole solutions, two $S_3$ types and one $H_3$ type. The interesting solution is the one of $S_3$ type which possesses two singularities. The one is at the north pole behind the horizon, and the other is naked at the south pole. The observers, however, are free from falling to the naked singularity. There are also nonstatic cosmological solutions in $S_3$ and $H_3$, and a singular static solution in $H_3$.