Geometric Finiteness and Non-quasinormal Modes of the BTZ Black Hole

TL;DR

This paper explores the geometric finiteness of the BTZ black hole and demonstrates how invariance of wave solution monodromies relates to non-quasinormal mode frequencies, linking hyperbolic geometry with black hole perturbations.

Contribution

It establishes a connection between the geometric structure of the BTZ black hole and the invariance of wave monodromies, explaining non-quasinormal modes through hyperbolic geometry.

Findings

BTZ black hole is geometrically finite.

Invariance of monodromies leads to non-quasinormal mode frequencies.

Connection between hyperbolic structure and wave solutions established.

Abstract

The BTZ black hole is geometrically finite. This means that its three dimensional hyperbolic structure as encoded in its metric is in 1-1 correspondence with the Teichmuller space of its boundary, which is a two torus. The equivalence of different Teichmuller parameters related by the action of the modular group therefore requires the invariance of the monodromies of the solutions of the wave equation around the inner and outer horizons in the BTZ background. We show that this invariance condition leads to the non-quasinormal mode frequencies discussed by Birmingham and Carlip.