Highly Damped Quasinormal Modes of Generic Single Horizon Black Holes

TL;DR

This paper analytically computes the highly damped quasinormal modes of generic single-horizon black holes using WKB methods, clarifying previous results and highlighting the influence of near-origin behavior on mode frequencies.

Contribution

It provides a rigorous analytical foundation for the spectrum of highly damped quasinormal modes in black holes, addressing limitations of earlier analyses.

Findings

The real part of the frequency depends on the coupling near the origin.

The $ln(3)$ relation is not straightforwardly connected to quantum microstates.

The analysis clarifies the limitations of previous heuristic approaches.

Abstract

We calculate analytically the highly damped quasinormal mode spectra of generic single-horizon black holes using the rigorous WKB techniques of Andersson and Howls\cite{Andersson}. We thereby provide a firm foundation for previous analysis, and point out some of their possible limitations. The numerical coefficient in the real part of the highly damped frequency is generically determined by the behavior of coupling of the perturbation to the gravitational field near the origin, as expressed in tortoise coordinates. This fact makes it difficult to understand how the famous $ln(3)$ could be related to the quantum gravitational microstates near the horizon.