Slow relaxation of rapidly rotating black holes

TL;DR

This paper derives an analytical formula for the relaxation times of rapidly rotating, near-extremal Kerr black holes, showing they can have extremely long relaxation periods as they approach extremality, and confirms this with numerical results.

Contribution

It provides a simple analytical expression for quasinormal modes of near-extremal Kerr black holes, linking relaxation times to black hole parameters and confirming the universal relaxation bound.

Findings

Relaxation time diverges as black hole approaches extremality.

Analytical formula matches numerical computations.

Near-extremal Kerr black holes saturate the universal relaxation bound.

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.