Dirty black holes: Quasinormal modes

In this paper, we investigate the asymptotic nature of the quasinormal modes for "dirty" black holes -- generic static and spherically symmetric spacetimes for which a central black hole is surrounded by arbitrary "matter" fields. We demonstrate that, to the leading asymptotic order, the [imaginary] spacing between modes is precisely equal to the surface gravity, independent of the specifics of the black hole system. Our analytical method is based on locating the complex poles in the first Born approximation for the scattering amplitude. We first verify that our formalism agrees, asymptotically, with previous studies on the Schwarzschild black hole. The analysis is then generalized to more exotic black hole geometries. We also extend considerations to spacetimes with two horizons and briefly discuss the degenerate-horizon scenario.Comment: 15 pages; uses iopart.cls setstack.sty; V2: one additional reference added, no physics changes; V3: two extra references, minor changes in response to referee comment

The asymptotic quasinormal mode spectrum of non-rotating black holes

A conjectured connection to quantum gravity has led to a renewed interest in highly damped black-hole quasinormal modes (QNMs). In this paper we present simple derivations (based on the WKB approximation) of conditions that determine the asymptotic QNMs for both Schwarzschild and Reissner–Nordström black holes. This confirms recent results obtained by Motl and Neitzke, but our analysis fills several gaps left by their discussion. We study the Reissner–Nordström results in some detail, and show that, in contrast to the asymptotic QNMs of a Schwarzschild black hole, the Reissner–Nordström QNMs are typically not periodic in the imaginary part of the frequency. This leads to the charged black hole having peculiar properties which complicate an interpretation of the results in the context of quantum gravity