Quasinormal modes of nearly extreme Reissner-Nordström black holes

We present detailed calculations of the quasinormal modes of Reissner-Nordström black holes. While the first few, slowly damped, modes depend on the charge of the black hole in a relatively simple way, we find that the rapidly damped modes show several peculiar features. The higher modes generally spiral into the value for the extreme black hole as the charge increases. We also discuss the possible existence of a purely imaginary mode for the Schwarzschild black hole: Our data suggest that there is a quadrupole quasinormal mode that limits to $\omega M=-2i$ as $Q\to 0$.