A detailed study of quasinormal frequencies of the Kerr black hole

TL;DR

This paper computes and analyzes the quasinormal frequencies of Kerr black holes using a stable continued fraction method, revealing behaviors at the Kerr limit and confirming the algebraically special frequency's relation to quasinormal modes.

Contribution

It applies the continued fraction method to accurately compute both slowly and rapidly damped Kerr quasinormal frequencies and explores their behavior at the Kerr limit.

Findings

Successfully computed a wide range of Kerr quasinormal frequencies.

Identified peculiar behaviors of frequencies at the Kerr limit.

Confirmed the algebraically special frequency coincides with the $n=8$ mode only at Schwarzschild limit.

Abstract

We compute the quasinormal frequencies of the Kerr black hole using a continued fraction method. The continued fraction method first proposed by Leaver is still the only known method stable and accurate for the numerical determination of the Kerr quasinormal frequencies. We numerically obtain not only the slowly but also the rapidly damped quasinormal frequencies and analyze the peculiar behavior of these frequencies at the Kerr limit. We also calculate the algebraically special frequency first identified by Chandrasekhar and confirm that it coincide with the $n=8$ quasinormal frequency only at the Schwarzschild limit.