Formation of Higher-dimensional Topological Black Holes

TL;DR

This paper explores the formation of higher-dimensional topological black holes through gravitational collapse, constructing new solutions and analyzing their global properties, including the potential for naked singularities and wormholes.

Contribution

It introduces new (n+2)-dimensional collapsing solutions, including generalized Lemaitre-Tolman-Bondi models, and studies their matching to exterior spacetimes, advancing understanding of higher-dimensional black hole formation.

Findings

Constructed (n+2)-dimensional collapsing solutions.

Matched collapsing interiors to static and radiating exterior spacetimes.

Identified conditions for black hole, naked singularity, and wormhole formation.

Abstract

We study higher dimensional gravitational collapse to topological black holes in two steps. Firstly, we construct some (n+2)-dimensional collapsing space-times, which include generalised Lemaitre-Tolman-Bondi-like solutions, and we prove that these can be matched to static $\Lambda$-vacuum exterior space-times. We then investigate the global properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. Secondly, we consider as interiors classes of 5-dimensional collapsing solutions built on Riemannian Bianchi IX spatial metrics matched to radiating exteriors given by the Bizon-Chmaj-Schmidt metric. In some cases, the data at the boundary for the exterior can be chosen to be close to the data for the Schwarzschild solution.