Highly damped quasinormal modes of Kerr black holes

Abstract

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 not show a similar behaviour. The real part of modes with l=2 and m<0 seems to asymptotically approach a constant value \omega_R\simeq -m\varpi, \varpi\simeq 0.12 being (almost) independent of a. For any perturbing field, trajectories in the complex plane of QNM's with m=0 show a spiralling behaviour, similar to the one observed for Reissner-Nordstrom (RN) black holes. Finally, for any perturbing field, the asymptotic separation in the imaginary part of consecutive modes with m>0 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 multiplets emerge from the algebraically special Schwarzschild modes, confirming a recent speculation.