Kerr quasinormal modes and Hod's time-temperature bound

Understand

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, $\lim \sup \omega_{IS}/T\leq \pi / \hbar$, 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 $\lim \inf \omega_{IS}/T< \pi /\hbar$ is a strict inequality.
• {\it It remains unclear} whether the bound is saturated in the sense that $\lim \sup \omega_{IS}/T= \pi /\hbar$.