Charged Black Holes in a Five-dimensional Kaluza-Klein Universe

TL;DR

This paper studies an exact five-dimensional charged black hole solution in a Kaluza-Klein universe, revealing unique horizon geometry and near-horizon properties within Einstein-Maxwell theory.

Contribution

It presents a new exact solution describing a charged black hole with a squashed horizon in a five-dimensional Kaluza-Klein spacetime.

Findings

The spacetime approaches a Kasner universe at large distances.

The horizon is a squashed three-sphere with constant size.

The metric is approximately static near the horizon.

Abstract

We examine an exact solution which represents a charged black hole in a Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The spacetime approaches to the five-dimensional Kasner solution that describes expanding three dimensions and shrinking an extra dimension in the far region. The metric is continuous but not smooth at the black hole horizon. There appears a mild curvature singularity that a free-fall observer can traverse the horizon. The horizon is a squashed three-sphere with a constant size, and the metric is approximately static near the horizon.