Properties of Kaluza-Klein black holes

TL;DR

This paper develops numerical methods to study 6-dimensional Kaluza-Klein black holes, revealing their geometric deformation with increasing mass and comparing them to non-uniform strings, raising questions about their maximum mass and potential topology changes.

Contribution

It introduces numerical techniques to analyze static vacuum black holes in 6D Kaluza-Klein theory and compares their properties to non-uniform strings, exploring their mass and geometry.

Findings

Black holes deform to prolate ellipsoids with increasing mass

Black holes can have horizon radii close to the compactification radius

Black holes achieve larger masses and volumes than non-uniform strings

Abstract

We detail numerical methods to compute the geometry of static vacuum black holes in 6 dimensional gravity compactified on a circle. We calculate properties of these Kaluza-Klein black holes for varying mass, while keeping the asymptotic compactification radius fixed. For increasing mass the horizon deforms to a prolate ellipsoid, and the geometry near the horizon and axis decompactifies. We are able to find solutions with horizon radii approximately equal to the asymptotic compactification radius. Having chosen 6-dimensions, we may compare these solutions to the non-uniform strings compactified on the same radius of circle found in previous numerical work. We find the black holes achieve larger masses and horizon volumes than the most non-uniform strings. This sheds doubt on whether these solution branches can merge via a topology changing solution. Further work is required to resolve whether there is a maximum mass for the black holes, or whether the mass can become arbitrarily large.