Topological Charged Black Holes in High Dimensional Spacetimes and Their Formation from Gravitational Collapse of a Type II Fluid

TL;DR

This paper investigates topological charged black holes in high-dimensional spacetimes, analyzing their structure and formation via gravitational collapse of a Type II fluid, revealing conditions for black hole or naked singularity formation.

Contribution

It derives the most general solutions for Type II fluid collapse in high dimensions and explores the global structure and formation outcomes of such black holes.

Findings

Black holes form from Type II fluid collapse in certain high-dimensional spacetimes.

Collapse always results in black holes for specific topologies ($k=0, -1$).

Naked singularities can form when $k=1$, depending on conditions.

Abstract

Topological charged black holes coupled with a cosmological constant in $R^{2}\times X^{D-2}$ spacetimes are studied, where $X^{D-2}$ is an Einstein space of the form ${}^{(D-2)}R_{AB} = k(D-3) h_{AB}$. The global structure for the four-dimensional spacetimes with $k = 0$ is investigated systematically. The most general solutions that represent a Type $II$ fluid in such a high dimensional spacetime are found, and showed that topological charged black holes can be formed from the gravitational collapse of such a fluid. When the spacetime is (asymptotically) self-similar, the collapse always forms black holes for $k = 0, -1$, in contrast to the case $k = 1$, where it can form either balck holes or naked singularities.