Spectroscopy of extremal and near-extremal Kerr black holes

We investigate linear, spin-field perturbations of Kerr black holes in the extremal limit throughout the complex-frequency domain. We calculate quasinormal modes of extremal Kerr as well as of near-extremal Kerr, via a novel approach: using the method of Mano, Suzuki, and Takasugi. We also show how, in the extremal limit, a branch cut is formed at the superradiant-bound frequency, omega(SR), via a simultaneous accumulation of quasinormal modes and totally reflected modes. For real frequencies, we calculate the superradiant amplification factor, which yields the amount of rotational energy that can be extracted from a black hole. In the extremal limit, this factor is the largest, and it displays a discontinuity at omega(SR) for some modes. Finally, we find no exponentially growing modes nor branch points on the upper-frequency plane in extremal Kerr after a numerical investigation, thus providing evidence of the mode stability of this space-time away from the horizon.