The universal Teukolsky equations and black hole perturbations in higher-derivative gravity

TL;DR

This paper develops a universal framework for analyzing perturbations of rotating black holes in higher-derivative gravity theories, enabling computation of quasinormal modes for highly spinning black holes relevant to gravitational wave observations.

Contribution

It introduces a universal set of Teukolsky equations for higher-derivative gravity, allowing systematic calculation of black hole perturbations and quasinormal modes beyond previous methods.

Findings

Derived decoupled radial equations for higher-derivative gravity

Computed quasinormal mode shifts for six-derivative gravity

Applicable to highly spinning, post-merger black holes

Abstract

We reduce the study of perturbations of rotating black holes in higher-derivative extensions of general relativity to a system of decoupled radial equations that stem from a set of universal Teukolsky equations. We detail a complete computational strategy to obtain these decoupled equations in general higher-derivative theories. We apply this to six-derivative gravity to compute the shifts in the quasinormal mode frequencies with respect to those of Kerr black holes in general relativity. At linear order in the angular momentum we reproduce earlier results obtained with a metric perturbation approach. In contrast with this earlier work, however, the method given here applies also to post-merger black holes with significant spin, which are of particular observational interest.