Stability and quasinormal modes of the massive scalar field around Kerr black holes

TL;DR

This paper analyzes the quasinormal modes of a massive scalar field around Kerr black holes, demonstrating stability for certain mass ranges and showing that high damping behavior is unaffected by the field's mass.

Contribution

It provides the first detailed computation of the quasinormal spectrum for massive scalar fields in Kerr backgrounds, extending stability analysis beyond previous bounds.

Findings

All modes are damped for moderate masses, indicating stability.

High damping modes are unaffected by the scalar field's mass, matching the massless case.

The stability region aligns with the Beyer inequality for large masses.

Abstract

We find quasinormal spectrum of the massive scalar field in the background of the Kerr black holes. We show that all found modes are damped under the quasinormal modes boundary conditions when $\mu M$ is not large, thereby implying stability of the massive scalar field. This complements the region of stability determined by the Beyer inequality for large masses of the field. We show that, similar to the case of a non-rotating black holes, the massive term of the scalar field does not contribute in the regime of high damping. Thereby, the high damping asymptotic should be the same as for the massless scalar field.