Asymptotic quasinormal frequencies for black holes in nonasymptotically flat space-times

The exact computation of asymptotic quasinormal frequencies is a technical problem which involves the analytic continuation of a Schrodinger-type equation to the complex plane and then performing a method of monodromy matching at several poles in the plane. While this method was successfully used in asymptotically flat space-time, as applied to both the Schwarzschild and Reissner-Nordstrom solutions, its extension to nonasymptotically flat space-times has not been achieved yet. In this work it is shown how to extend the method to this case, with the explicit analysis of Schwarzschild-de Sitter and large Schwarzschild-anti-de Sitter black holes, both in four dimensions. We obtain, for the first time, analytic expressions for the asymptotic quasinormal frequencies of these black hole space-times, and our results match previous numerical calculations with great accuracy. We also list some results concerning the general classification of asymptotic quasinormal frequencies in d-dimensional space-times. (C) 2004 American Institute of Physics.