Slow relaxation of rapidly rotating black holes

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: ω=mΩ-i2πTBH(n+1/2), where TBH and Ω are the temperature and angular velocity of the black hole, and m is the azimuthal harmonic index of a corotating equatorial mode. This formula implies that the relaxation period τ~1/Iω of the black hole becomes extremely long as the extremal limit TBH→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.