Superradiant instability of a massive scalar on the Kerr spacetime

TL;DR

This paper analyzes the superradiant instability of Kerr black holes caused by a massive scalar field, deriving conditions for quasibound and bound states through potential analysis.

Contribution

It introduces a novel potential expansion approach to determine conditions for superradiant instability and bound states in Kerr black holes with massive scalar perturbations.

Findings

Conditions for trapping wells leading to quasibound states

Identification of tiny wells causing asymptotic bound states

Application to ultralight boson potentials

Abstract

We investigate the superradiant instability of Kerr black holes under a massive scalar perturbation. We obtain a potential $V_i(r)$ when expanding the scalar potential $V_K(r)$ for large $r$. The Newton potential $V_1(r)$ and the far-region potential $V_2(r)$ are used to explore the superradiant instability, while $V_3(r)$ matches a geodesic potential $V_{gK}(r)$ for a neutral particle moving around the Kerr black hole. Thus, $V_{gK}(r)$ is employed to fix the separation constant. We obtain a condition for a trapping well to possess a quasibound state in the Kerr black holes by analyzing the Newton potential $V_1(r)$and far-region wave functions obtained from $V_2(r)$. The other condition for no trapping well (a tiny well) is found to generate an asymptotic bound state. Finally, we discuss an ultralight boson whose potential has a tiny well located at asymptotic region.