Quasi-normal mode frequencies and gravitational perturbations of black holes with any subextremal spin in modified gravity through METRICS: the scalar-Gauss-Bonnet gravity case

TL;DR

This paper extends the METRICS approach to compute quasinormal mode frequencies of rotating black holes in scalar-Gauss-Bonnet gravity, providing the first accurate results for rapid rotation in this modified gravity theory.

Contribution

It develops a novel method to calculate black hole perturbations and quasinormal modes in modified gravity without simplifying the field equations, specifically applied to scalar-Gauss-Bonnet gravity.

Findings

Computed leading-order corrections to quasinormal frequencies for rotating black holes in scalar-Gauss-Bonnet gravity.

Achieved high numerical accuracy for frequencies up to spin parameter 0.85.

First accurate computation of quasinormal modes for rapidly rotating black holes in this theory.

Abstract

The gravitational waves emitted in the ringdown phase of binary black-hole coalescence are a unique probe of strong gravity. Understanding how deviations from general relativity affect the ringdown phase of black holes, however, is extremely challenging, as it requires solving highly-coupled and sometimes higher-order partial differential equations. We here extend a novel approach, \textit{Metric pErTuRbations wIth speCtral methodS} (METRICS), to study the metric perturbations and the quasinormal mode frequencies of ringing black holes in modified gravity. We first derive the asymptotic behavior of metric perturbations at the event horizon and spatial infinity for rotating black holes beyond general relativity. We then extend the eigenvalue-perturbation theory approach of METRICS to allow us to compute the leading-order modified gravity corrections to the quasinormal-mode frequencies and metric perturbations. We apply METRICS to rotating black holes in scalar-Gauss-Bonnet gravity. Without decoupling or simplifying the linearized field equations in this theory, we compute the leading-order corrections to the quasinormal frequencies of the axial and polar perturbations of the $nlm = 022$, 021 and 033 modes of black holes of $a \leq 0.85$. The numerical accuracy of the METRICS frequencies is $\leq 10^{-5}$ for $a \leq 0.6$, $\lesssim 10^{-4}$ for $0.6 < a \leq 0.7 $, and $\lesssim 10^{-2}$ for $0.7 < a \leq 0.85 $ for all modes studied. We fit the frequencies as a polynomial in spin, whose coefficients (up to second order in spin) are consistent with those obtained in previous slow-rotating approximations. These results are the first accurate computations of the gravitational quasinormal-mode frequencies of rapidly rotating black holes (of $a \sim 0.85$) in scalar-Gauss-Bonnet gravity.