Kerr quasinormal modes and Hod's time-temperature bound

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, $\lim \sup {\omega }_{IS}\mathrm{/}T\le \pi \mathrm{/}\mathrm{\hslash }$, where $\omega {IS}$isthedecayrateoftheslowestdecayingquasinormalmode,$T$ is the black hole temperature. On the other hand, the bound is not saturated in the sense that $\lim \inf {\omega }_{IS}\mathrm{/}T<\pi \mathrm{/}\mathrm{\hslash }$ is a strict inequality. {\it It remains unclear} whether the bound is saturated in the sense that $\lim \sup \omega{IS}/T= \pi /\hbar$.