Higher-derivative corrections to the Kerr quasinormal mode spectrum

TL;DR

This paper analyzes how higher-derivative modifications to Einstein's theory affect the quasinormal modes of rotating black holes, providing detailed corrections for various modes and spins, and discussing the validity of linear approximations.

Contribution

It presents the most comprehensive calculation of higher-derivative corrections to Kerr black hole quasinormal modes, including overtones and a wide range of spins, with results expressed as polynomial fits.

Findings

Leading-order corrections for all modes with l=2,3,4 and n=0,1,2 are provided.

Overtones are more sensitive to higher-derivative corrections than fundamental modes.

Results are accurate up to spins between approximately 0.7 and 0.95.

Abstract

We provide the most complete analysis so far of quasinormal modes of rotating black holes in a general higher-derivative extension of Einstein's theory. By finding the corrections to the Teukolsky equation and expressing them in a simple form, we are able to apply a generalized continued fraction method that allows us to find the quasinormal mode frequencies including overtones. We obtain the leading-order corrections to the Kerr quasinormal mode frequencies of all the $(l,m,n)$ modes with $l=2,3,4$, $-l\le m\le l$ and $n=0,1,2$, and express them as a function of the black hole spin $\chi$ using polynomial fits. We estimate that our results remain accurate up to spins between $\chi\sim 0.7$ and $\chi\sim 0.95$, depending on the mode. We report that overtones are overall more sensitive to corrections, which is expected from recent literature on this topic. We also discuss the limit of validity of the linear corrections to the quasinormal mode frequencies by estimating the size of nonlinear effects in the higher-derivative couplings. All our results are publicly available in an online repository.