2012/07/23 by Shahar Hod
Physics and Astronomy · #astro-ph.HE #gr-qc #hep-th
paper · pdf · doi:10.1016/j.physletb.2012.08.001
published as Physics Letters B 715, 348 (2012) · 11 pages. arXiv admin note: substantial text overlap with arXiv:0909.0314, arXiv:0811.3806
arxiv created 2012/07/23 · arxiv updated 2015/06/05
The fundamental resonances of rapidly rotating Kerr black holes in the eikonal limit are derived analytically. We show that there exists a critical value, μc=√15-√(193)\over2, for the dimensionless ratio μ≡ 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 μc the imaginary parts of the quasinormal frequencies scale like the black-hole temperature: ωI(n;μ>μc)=2πTBH(n+1\over 2). This implies that for perturbations modes in the interval μc<μ≤ 1, the relaxation period τ∼ 1/ωI of the black hole becomes extremely long as the extremal limit TBH→ 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 MΩ≥ 2\over 5, where M and Ω are the black-hole mass and angular velocity, respectively) possess this family of remarkably long-lived perturbation modes.