Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes

Abstract

We investigate linear, spin-field perturbations of Kerr black holes in the extremal limit throughout the complex-frequency domain. We calculate quasi-normal modes of extremal Kerr, as well as of near-extremal Kerr, via a novel approach: using the method of Mano, Suzuki and Takasugi (MST). 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 quasi-normal 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.

32 pages, 13 figures. In version 2, we included QNMs in extremal Kerr for spin=-2, l=m=2 and 3

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• Fundamental Tone and Overtones of Quasinormal Modes in Ringdown Gravitational Waves: A Detailed Study in Black Hole Perturbation
• Massive scalar perturbations in Kerr Black Holes: near extremal analysis
• Connecting scattering, monodromy, and MST's renormalized angular momentum for the Teukolsky equation in Kerr spacetime
• Complete quasinormal modes of Type-D black holes
• Quasinormal modes of Kerr-Newman black holes: revisiting the Dudley-Finley approximation
• Quasinormal mode frequencies of Kerr black holes from Regge trajectories
• Ergodic Hysteresis of the Kerr black hole spectrum