Massive scalar perturbations in Kerr black holes: Near extremal analysis
João Paulo Cavalcante, Maurício Richartz, Bruno Carneiro da Cunha
Abstract
We study quasinormal modes of massive scalar perturbations in Kerr black holes using the isomonodromic method. For arbitrary scalar masses $M\ensuremath{\mu}$ and black hole spins $a/M$, we numerically determine the quasinormal frequencies for various orbital $\ensuremath{\ell}$, azimuthal $m$, and overtone $n$ numbers. In particular, we derive an analytic expression for frequencies of the zero-damping modes near the extremal limit $a/M\ensuremath{\rightarrow}1$. For $\ensuremath{\ell}=m=1$, 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 $(M\ensuremath{\mu}{)}_{c}\ensuremath{\simeq}0.3704981$ and $(a/M{)}_{c}\ensuremath{\simeq}0.9994660$.