Perturbations of spinning black holes beyond General Relativity: Modified Teukolsky equation

TL;DR

This paper derives a modified Teukolsky equation to describe perturbations of non-Kerr black holes in modified gravity, enabling tests of gravity theories beyond General Relativity through gravitational wave analysis.

Contribution

It introduces the first derivation of a modified Teukolsky equation for non-Kerr black holes in modified gravity, extending the analysis to Petrov type I backgrounds.

Findings

Derived the modified Teukolsky equation for non-Ricci-flat, Petrov type D black holes.

Extended the derivation to Petrov type I black holes as perturbations of type D.

Established a foundation for analyzing gravitational waves in modified gravity scenarios.

Abstract

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed for tests of relativistic gravity in the strong, dynamical and nonlinear regime. Outside Einstein's relativity, spinning black holes may be different from their general relativistic counterparts, and their merger may then lead to a modified ringdown. We study the latter and, for the first time, derive a modified Teukolsky equation, i.e., a set of linear, decoupled differential equations that describe dynamical perturbations of non-Kerr black holes for the radiative Newman-Penrose scalars $\Psi_0$ and $\Psi_4$. We first focus on non-Ricci-flat, Petrov type D black hole backgrounds in modified gravity, and derive the modified Teukolsky equation through direct decoupling and through a new approach, proposed by Chandrasekhar, that uses certain gauge conditions. We then extend this analysis to non-Ricci-flat, Petrov type I black hole backgrounds in modified gravity, assuming they can be treated as a linear perturbation of Petrov type D, black hole backgrounds in GR by generalizing Chandrasekhar's approach, and derive the decoupled modified Teukolsky equation. Our work lays the foundation to study the gravitational waves emitted in the ringdown phase of black hole coalescence in modified gravity for black holes of any spin. Our work can also be extended to compute gravitational waves emitted by extreme mass-ratio binary inspirals in modified gravity.