Quasinormal modes of Kerr-de Sitter black holes via the Heun function

TL;DR

This paper computes quasinormal mode frequencies of Kerr-de Sitter black holes using the newly implemented Heun functions in Mathematica 12.1, enabling rapid and precise numerical evaluations.

Contribution

It introduces a novel method leveraging Heun functions to efficiently calculate quasinormal modes of Kerr-de Sitter black holes.

Findings

Rapid computation of quasinormal modes with arbitrary precision

Application to asymptotically flat rotating black holes

Utilization of Mathematica's new Heun functions

Abstract

This note addresses quasinormal mode frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky's equations for Kerr-de Sitter black holes are mapped to Heun's equations, we are able to compute their quasinormal mode frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating black holes.