Massive scalar perturbations in Kerr Black Holes: near extremal analysis

TL;DR

This paper analyzes quasinormal modes of massive scalar fields in Kerr black holes, deriving analytic expressions near extremality and revealing mode behavior changes with scalar mass and black hole spin.

Contribution

It provides the first analytic formula for zero-damping modes near extremality and uncovers mode transitions and level-crossings in the parameter space.

Findings

Analytic expression for near-extremal zero-damping modes

Heavy scalar fields cause fundamental modes to become damped

Numerical evidence of level-crossing at specific parameters

Abstract

We study quasinormal modes of massive scalar perturbations in Kerr black holes using the isomonodromic method. For arbitrary scalar masses $M \mu$ and black hole spins $a/M$, we numerically determine the quasinormal frequencies for various orbital $\ell$, azimuthal $m$, and overtone $n$ numbers. In particular, we derive an analytic expression for frequencies of the zero-damping modes near the extremal limit $a/M \rightarrow 1$. For $\ell=m=1$, we reveal that the fundamental mode becomes a damped mode (rather than a zero-damping mode) if the scalar field is sufficiently heavy. By exploring the parameter space, we find numerical evidence for level-crossing between the longest-living mode and the first overtone at an exceptional point $(M\mu)_c \simeq 0.3704981$ and $(a/M)_c\simeq 0.9994660$.