paper

Slow relaxation of rapidly rotating black holes

arXiv:0811.3806 · doi:10.1103/PhysRevD.78.084035

Abstract

We study analytically the relaxation phase of perturbed, rapidly rotating black holes. In particular, we derive a simple formula for the fundamental quasinormal resonances of near-extremal Kerr black holes. The formula is expressed in terms of the black-hole physical parameters: omega=m Omega-i2 pi T(n+1/2), where T and Omega are the temperature and angular velocity of the black hole, and m is the azimuthal harmonic index of a co-rotating equatorial mode. This formula implies that the relaxation period tau sim 1/Im(omega) of the black hole becomes extremely long as the extremal limit T to 0 is approached. The analytically derived formula is shown to agree with direct numerical computations of the black-hole resonances. We use our results to demonstrate analytically the fact that near-extremal Kerr black holes saturate the recently proposed universal relaxation bound.

5 pages

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