Ringing of rapidly rotating black holes in effective field theory

TL;DR

This paper computes quasinormal mode frequency corrections for rapidly rotating black holes within effective field theory, using numerical solutions and spectral methods to analyze deviations from general relativity.

Contribution

It introduces a numerical approach to evaluate leading-order cubic-curvature corrections to black hole quasinormal modes in the high-spin regime.

Findings

Frequency corrections are computed for modes with l≤5 and all m for spins up to 0.99M.

Corrections grow significantly as the black hole spin approaches extremality.

The method achieves relative errors below 10^{-4} across a broad parameter range.

Abstract

Within the effective field theory approach to gravity, deviations from general relativity can be systematically described by higher-curvature operators. However, computing the resulting corrections to black hole quasinormal mode spectra remains challenging in the rapidly rotating regime, where perturbative expansions in the spin break down. We use recently constructed numerical rotating black hole solutions to compute quasinormal mode frequency corrections at leading order in the effective field theory. Focusing on scalar perturbations, we evaluate cubic-curvature corrections, which constitute the leading modifications. We employ a pseudo-spectral collocation method to solve the resulting perturbation equations on these backgrounds, enabling accurate computation across a broad parameter range. We obtain frequency corrections for fundamental modes with $l\le5$ for all $m$, and the first overtone of $2 \le l \le 5$ modes for all $m$ for spins up to $a=0.99M$, with relative errors below $10^{-4}$. We observe that corrections to certain modes grow significantly as the spin approaches the near-extremal regime.