Kerr quasinormal modes and Hod's time-temperature bound

Abstract

We give an explicit expression for the frequencies of slowly damped quasinormal modes of near-extreme Kerr black holes. It follows from this expression that the near-extreme Kerr holes obey the Hod's bound: in the limit of maximal rotation, $\lim \sup {\omega }_{IS}/T\le \pi /\hslash$, where ${\omega }_{IS}$ is the decay rate of the slowest decaying quasinormal mode, $T$ is the black hole temperature. On the other hand, the bound is not saturated in the sense that $\lim \inf {\omega }_{IS}/T<\pi /\hslash$ is a strict inequality. {\it It remains unclear} whether the bound is saturated in the sense that $\lim \sup {\omega }_{IS}/T=\pi /\hslash$.

5 pages