Dynamics of localized Kaluza-Klein black holes in a collapsing universe

TL;DR

This paper investigates the behavior of localized charged Kaluza-Klein black holes in a collapsing deSitter universe, providing evidence that they remain localized and do not merge into a black string, contrary to naive expectations.

Contribution

The study offers analytic and numerical evidence that localized Kaluza-Klein black holes do not undergo a topological transition during universe collapse, preserving their localized nature.

Findings

Black holes remain localized despite collapsing universe.

No transition to black string state observed.

DeSitter horizon changes topology between spherical and cylindrical.

Abstract

The Clayton Antitrust Act of 1914 prohibits corporate mergers that would result in certain highly undesired end states. We study an exact solution of the Einstein equations describing localized, charged Kaluza-Klein black holes in a collapsing deSitter universe and seek to demonstrate that a similar effect holds, preventing a potentially catastrophic black hole merger. As the collapse proceeds, it is natural to expect that the black hole undergoes a topological transition, wrapping around the shrinking compact dimension to merge with itself and form a black string. However, the putative uniform charged black string end state is singular and such a transition would violate (a reasonable notion of) cosmic censorship. We present analytic and numerical evidence that strongly suggests the absence of such a transition. Based on this evidence, we expect that the Kaluza-Klein black hole horizon stays localized, despite the increasingly constraining size of the compact dimension. On the other hand, the deSitter horizon does change between spherical and cylindrical topologies in a simple way.