Dirty black holes: Quasinormal modes

TL;DR

This paper analyzes the asymptotic quasinormal modes of generic static, spherically symmetric black holes surrounded by matter, revealing that the mode spacing is determined by surface gravity and independent of matter details.

Contribution

It introduces an analytical method based on the first Born approximation to determine quasinormal mode spacing for 'dirty' black holes, extending previous results to more complex geometries.

Findings

Mode spacing equals surface gravity for generic black holes.

Method agrees with known results for Schwarzschild black holes.

Extended analysis to black holes with multiple horizons.

Abstract

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.