Towards a more robust algorithm for computing the Kerr quasinormal mode frequencies

TL;DR

This paper enhances the spectral Leaver's method for calculating Kerr black hole quasinormal mode frequencies by analytically computing derivatives, improving accuracy and integrating these into a Python package.

Contribution

It introduces an analytical derivative computation approach for spectral Leaver's method and incorporates it into the qnm Python package, improving robustness.

Findings

Analytical derivatives improve frequency computation accuracy.

Implementation in qnm package facilitates easier use.

Method enhances robustness of Kerr QNM calculations.

Abstract

Leaver's method has been the standard for computing the quasinormal mode (QNM) frequencies for a Kerr black hole (BH) for a few decades. We start with a spectral variant of Leaver's method introduced by Cook and Zalutskiy (arXiv: 1410.7698) and propose improvements in the form of computing the necessary derivatives analytically, rather than by numerical finite differencing. We also incorporate this derivative information into qnm, a Python package which finds the QNM frequencies via the spectral variant of Leaver's method. We confine ourselves to first derivatives only.