Asymptotic black hole quasinormal frequencies

We give a new derivation of the quasinormal frequencies of Schwarzschild black holes in d >= 4 and Reissner-Nordstrom black holes in d = 4 in the limit of in finite damping. For Schwarzschild in d >= 4 we find that the asymptotic real part is T-Hawking log(3) for scalar perturbations and for some gravitational perturbations; this confirms a result previously obtained by other means in the case d = 4. For Reissner-Nordstrom in d = 4 we find a specific generally aperiodic behavior for the quasinormal frequencies, both for scalar perturbations and for electromagnetic gravitational perturbations. The formulae are obtained by studying the monodromy of the perturbation analytically continued to the complex plane; the analysis depends essentially on the behavior of the potential in the "unphysical" region near the black hole singularity.