An approach to computing spectral shifts for black holes beyond Kerr

TL;DR

This paper develops a method to compute spectral shifts in Kerr black holes within theories beyond general relativity, aiding future gravitational-wave tests of black hole nature and potential deviations from Einstein's theory.

Contribution

It derives a modified Teukolsky equation for black hole perturbations in extended theories of gravity, enabling calculation of spectral shifts for Kerr black holes with arbitrary spins.

Findings

Derived a modified Teukolsky equation for beyond-GR theories.

Applied eigenvalue perturbation methods to compute spectral shifts.

Provides a framework for future black hole spectroscopy in extended gravity theories.

Abstract

Recent measurements of gravitational-wave ringdown following the merger of binary black holes raise the prospect of precision black hole spectroscopy in the near future. To perform the most sensitive tests of the nature of black holes using ringdown measurements, it is critical to compute the deviations to the spectrum of black holes in particular extensions of relativity. These spectral shifts are also needed to interpret any violations of the predictions of relativity that may be detected during ringdown. Here we present a first step towards computing the shifts to the spectrum of Kerr black holes with arbitrary spins, by deriving a modified Teukolsky equation governing the perturbations of black holes in theories beyond GR. Our approach applies to a class of theories which includes dynamical Chern-Simons gravity and shift-symmetric scalar Gauss-Bonnet gravity, in the case where the deviations from relativity are small. This allows for a perturbative approach to solving the equations of motion. Further, we show how to use the modified equation to compute the leading-order spectral shifts of Kerr black holes, using eigenvalue perturbation methods. Our formalism provides a practical approach to predicting ringdown for black holes in a range of promising extensions to relativity, enabling future precision searches for their signatures in black hole ringdown.