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

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 de Sitter 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 de Sitter horizon does change between spherical and cylindrical topologies in a simple way.