QUASI-NORMAL MODES OF NEARLY EXTREME REISSNER-NORDSTROM BLACK-HOLES

We present detailed calculations of the quasinormal modes of Reissner- Nordstrom black holes. While the first few, slowly damped, modes depen d on the charge of the black hole in a relatively simple way, we find that the rapidly damped modes show several peculiar features. The high er modes generally spiral into the value for the extreme black hole as the charge increases. We also discuss the possible existence of a pur ely 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-->0.