From Black Strings to Black Holes

TL;DR

This paper investigates the connection between non-uniform black strings and black holes using numerical methods, providing evidence for a topology change and analyzing the geometric and singularity properties of these solutions.

Contribution

It offers new numerical evidence supporting the conjecture that non-uniform black strings connect to black hole solutions through a topology-changing transition.

Findings

Potential connection between black strings and black holes.

Evidence of a naked singularity at the topology change point.

All solutions can be expressed in Harmark and Obers' coordinates.

Abstract

Using recently developed numerical methods, we examine neutral compactified non-uniform black strings which connect to the Gregory-Laflamme critical point. By studying the geometry of the horizon we give evidence that this branch of solutions may connect to the black hole solutions, as conjectured by Kol. We find the geometry of the topology changing solution is likely to be nakedly singular at the point where the horizon radius is zero. We show that these solutions can all be expressed in the coordinate system discussed by Harmark and Obers.