Highly damped quasinormal modes of Kerr black holes

Motivated by recent suggestions that highly damped black hole quasinormal modes (QNM's) may provide a link between classical general relativity and quantum gravity, we present an extensive computation of highly damped QNM's of Kerr black holes. We do not limit our attention to gravitational modes, thus filling some gaps in the existing literature. The frequency of gravitational modes with $l=m=2$ tends to $\omega_R=2 \Omega$, $\Omega$ being the angular velocity of the black hole horizon. If Hod's conjecture is valid, this asymptotic behaviour is related to reversible black hole transformations. Other highly damped modes with $m>0$ that we computed do {\it not} show a similar behaviour. The real part of modes with $l=2$ and $m0$ is given by $2\pi T_H$ ($T_H$ being the black hole temperature). We conjecture that for all values of $l$ and $m>0$ there is an infinity of modes tending to the critical frequency for superradiance ($\omega_R=m$) in the extremal limit. Finally, we study in some detail modes branching off the so--called ``algebraically special frequency'' of Schwarzschild black holes. For the first time we find numerically that QNM {\it multiplets} emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.