Quasinormal modes of Kerr black holes using a spectral decomposition of the metric perturbations

TL;DR

This paper introduces a spectral decomposition method to accurately compute quasinormal modes of rotating Kerr black holes, covering a broad spectrum and achieving high precision for various spin parameters.

Contribution

The paper presents a novel spectral decomposition approach for calculating Kerr black hole quasinormal modes, enabling high-accuracy results across a wide parameter range.

Findings

Achieves accuracy of 10^{-6} for a/M<0.8

Reproduces fundamental modes with <0.1% error for a/M<0.98

Calculates a large spectrum of quasinormal modes

Abstract

We report a new method to calculate the quasinormal modes of rotating black holes, using a spectral decomposition to solve the partial differential equations that result from introducing linear metric perturbations to a rotating background. Our approach allows us to calculate a large sector of the quasinormal mode spectrum. In particular, we study the accuracy of the method for the $(l=2)$-led and $(l=3)$-led modes for different values of the $M_z$ azimuthal number, considering the fundamental modes as well as the first two excitations. We show that our method reproduces the Kerr fundamental modes with an accuracy of $10^{-6}$ or better for $a/M<0.8$, while it stays below $0.1\%$ for $a/M<0.98$.