Dirty black holes: Quasinormal modes for "squeezed" horizons

TL;DR

This paper analytically investigates quasinormal modes of 'squeezed' horizon black holes, including 'dirty' black holes with matter distributions, revealing that frequency spacing equals surface gravity and providing real frequency parts under certain conditions.

Contribution

It extends previous models by analyzing quasinormal modes in 'dirty' black holes with arbitrary matter, showing the frequency spacing relates to surface gravity.

Findings

Frequency spacing equals surface gravity at squeezed horizons.

Real parts of frequencies can be calculated for closely spaced horizons.

Analysis applies to static, spherically symmetric black holes with matter distributions.

Abstract

We consider the quasinormal modes for a class of black hole spacetimes that, informally speaking, contain a closely ``squeezed'' pair of horizons. (This scenario, where the relevant observer is presumed to be ``trapped'' between the horizons, is operationally distinct from near-extremal black holes with an external observer.) It is shown, by analytical means, that the spacing of the quasinormal frequencies equals the surface gravity at the squeezed horizons. Moreover, we can calculate the real part of these frequencies provided that the horizons are sufficiently close together (but not necessarily degenerate or even ``nearly degenerate''). The novelty of our analysis (which extends a model-specific treatment by Cardoso and Lemos) is that we consider ``dirty'' black holes; that is, the observable portion of the (static and spherically symmetric) spacetime is allowed to contain an arbitrary distribution of matter.