Stability of Squashed Kaluza-Klein Black Holes

TL;DR

This paper investigates the stability of squashed Kaluza-Klein black holes, which resemble five-dimensional black holes near the horizon and four-dimensional spacetime at infinity, providing evidence for their stability in Kaluza-Klein models.

Contribution

The study derives master equations for metric perturbations using symmetry properties, offering the first strong evidence of stability for squashed Kaluza-Klein black holes.

Findings

Master equations indicate stability of these black holes.

Strong evidence supports their stability in Kaluza-Klein spacetime.

Black holes are viable models in higher-dimensional theories.

Abstract

The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for the stability of squashed Kaluza-Klein black holes. Hence, the squashed Kaluza-Klein black holes deserve to be taken seriously as realistic black holes in the Kaluza-Klein spacetime.