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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.