Kaluza-Klein Black Holes with Squashed Horizons

TL;DR

This paper investigates five-dimensional charged static black holes with squashed horizons, revealing their unique geometric and asymptotic structures, bridging five-dimensional and four-dimensional spacetime behaviors.

Contribution

It introduces a detailed analysis of black holes with squashed ${ m S}^3$ horizons in Einstein-Maxwell theory, highlighting their geometric and asymptotic properties.

Findings

Black holes have horizons as squashed ${ m S}^3$

Asymptotic structure is a twisted ${ m S}^1$ bundle over flat spacetime

Spacetime transitions from five-dimensional near the horizon to four-dimensional at infinity

Abstract

We study geometrical structures of charged static black holes in the five-dimensional Einstein-Maxwell theory. The black holes we study have horizons in the form of squashed $ {\rm S}^3$, and their asymptotic structure consists of a twisted ${\rm S}^1$ bundle over the four-dimensional flat spacetime at the spatial infinity. The spacetime we consider is fully five-dimensional in the vicinity of the black hole and four-dimensional with a compact extra dimension at infinity.