Kerr quasinormal modes and Hod's time-temperature bound

Details Kerr quasinormal modes and Hod's time-temperature bound Kerr quasinormal modes and Hod's time-temperature bound

2007-05-11

arxiv.org/abs/0705.1725v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

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 $\lim \sup \omega_{IS}/T= \pi /\hbar$.

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