Purely imaginary quasinormal modes of the Kerr geometry

TL;DR

This paper introduces a novel, general method based on Heun polynomials to accurately determine purely imaginary quasinormal modes of Kerr black holes, correcting previous inaccuracies and revealing limitations of existing asymptotic expansion techniques.

Contribution

It presents a new, broadly applicable method for computing Kerr quasinormal modes and demonstrates its effectiveness while highlighting the failure of traditional asymptotic approaches.

Findings

Prior results on purely imaginary quasinormal modes are incorrect

The Heun polynomial-based method is versatile and accurate

Matched asymptotic expansions can fail in certain cases

Abstract

We present a method for determining the purely imaginary quasinormal modes of the Kerr geometry. Such modes have previously been explored, but we show that prior results are incorrect. The method we present, based on the theory of Heun polynomials, is very general and can be applied to a broad class of problems, making it potentially useful to all branches of physics. Furthermore, our application provides an example where the method of matched asymptotic expansions seems to have failed. A deeper understanding of why it fails in this case may provide useful insights for other situations.