Massive scalar perturbations in Kerr black holes: Near extremal analysis

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 $(a/M{)}_{c}\ensuremath{\simeq}0.9994660$.