Evolution of perturbations of squashed Kaluza-Klein black holes: escape from instability

TL;DR

This paper investigates the stability of squashed Kaluza-Klein black holes by analyzing scalar and gravitational perturbations, showing decay of perturbations and discussing quasinormal modes related to extra dimension size.

Contribution

It provides the first detailed analysis of perturbation evolution and stability for squashed KK black holes, including rotating cases and quasinormal frequency correlations.

Findings

Scalar perturbations decay in rotating black holes.

Gravitational zero mode perturbations decay, indicating stability.

Quasinormal frequencies relate to the size of extra dimensions.

Abstract

The squashed Kaluza-Klien (KK) black holes differ from the Schwarzschild black holes with asymptotic flatness or the black strings even at energies for which the KK modes are not excited yet, so that squashed KK black holes open a window in higher dimensions. Another important feature is that the squashed KK black holes are apparently stable and, thereby, let us avoid the Gregory-Laflamme instability. In the present paper, the evolution of scalar and gravitational perturbations in time and frequency domains is considered for these squashed KK black holes. The scalar field perturbations are analyzed for general rotating squashed KK black holes. Gravitational perturbations for the so called zero mode are shown to be decayed for non-rotating black holes, in concordance with the stability of the squashed KK black holes. The correlation of quasinormal frequencies with the size of extra dimension is discussed.