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arXiv · 1901.04586

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

Marc Casals·Luís F. Longo Micchi
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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.

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Marc Casals, Luís F. Longo Micchi. 2019-01-14. Spectroscopy of Extremal (and Near-Extremal) Kerr Black Holes. https://doi.org/10.1103/physrevd.99.084047

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