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 and black hole spins a/M, we numerically determine the quasinormal frequencies for various orbital, 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 1. For =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) c 0. 3704981 and (a/M) c 0. 9994660.