The scalar perturbation of the higher-dimensional rotating black holes

TL;DR

This paper investigates scalar field perturbations in higher-dimensional Kerr black holes, demonstrating separability of the field equations and providing evidence for stability in five dimensions through numerical analysis of quasi-normal modes.

Contribution

It shows that the scalar field equation is separable in arbitrary dimensions and numerically analyzes quasi-normal modes in five dimensions, revealing stability and new time scale characteristics.

Findings

Scalar field equations are separable in higher-dimensional Kerr black holes.

Numerical evidence supports stability of scalar perturbations in five dimensions.

Resonant oscillation time scale depends on black hole mass and Planck mass, not horizon crossing time.

Abstract

The massless scalar field in the higher-dimensional Kerr black hole (Myers- Perry solution with a single rotation axis) has been investigated. It has been shown that the field equation is separable in arbitrary dimensions. The quasi-normal modes of the scalar field have been searched in five dimensions using the continued fraction method. The numerical result shows the evidence for the stability of the scalar perturbation of the five-dimensional Kerr black holes. The time scale of the resonant oscillation in the rapidly rotating black hole, in which case the horizon radius becomes small, is characterized by (black hole mass)^{1/2}(Planck mass)^{-3/2} rather than the light-crossing time of the horizon.