Resonance spectrum of near-extremal Kerr black holes in the eikonal limit

Shahar Hod

doi:10.1016/j.physletb.2012.08.001

paper

Resonance spectrum of near-extremal Kerr black holes in the eikonal limit

arXiv:1207.5282 · doi:10.1016/j.physletb.2012.08.001

Abstract

The fundamental resonances of rapidly rotating Kerr black holes in the eikonal limit are derived analytically. We show that there exists a critical value, $μ_{c} = \frac{15 - 193}{2}$ , for the dimensionless ratio $μ \equiv m / l$ between the azimuthal harmonic index $m$ and the spheroidal harmonic index $l$ of the perturbation mode, above which the perturbations become long lived. In particular, it is proved that above $μ_{c}$ the imaginary parts of the quasinormal frequencies scale like the black-hole temperature: $ω_{I} (n; μ > μ_{c}) = 2 π T_{B H} (n + \frac{1}{2})$ . This implies that for perturbations modes in the interval $μ_{c} < μ \leq 1$ , the relaxation period $τ \sim 1/ ω_{I}$ of the black hole becomes extremely long as the extremal limit $T_{B H} \to 0$ is approached. A generalization of the results to the case of scalar quasinormal resonances of near-extremal Kerr-Newman black holes is also provided. In particular, we prove that only black holes that rotate fast enough (with $M Ω \geq \frac{2}{5}$ , where $M$ and $Ω$ are the black-hole mass and angular velocity, respectively) possess this family of remarkably long-lived perturbation modes.

11 pages. arXiv admin note: substantial text overlap with arXiv:0909.0314, arXiv:0811.3806

Resonance spectrum of near-extremal Kerr black holes in the eikonal limit

Abstract

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