We carry out the first computation of gravitational quasinormal modes of black holes with arbitrary rotation in a theory with higher-derivative corrections. Our analysis focuses on a recently identified quartic curvature theory that preserves the isospectrality of quasinormal modes in the eikonal limit and that is connected to string theory. We find a master equation that governs large-momentum gravitational perturbations in this theory. By solving this equation with Wentzel-Kramers-Brillouin methods, we provide complete results for the corrections to the Kerr quasinormal mode frequencies for arbitrary spin and arbitrary $\mu =m/(\ell +1/2)$, where $\ell$ and $m$ are the harmonic numbers. Our results show that the corrections become orders of magnitude larger when the spin is close to extremality, with the modes close to the critical value of $\mu$ that separates damped and zero-damped modes being particularly sensitive. We also perform a geometric optics analysis of gravitational wave propagation around black holes and relate the equatorial “graviton sphere” orbits to quasinormal mode frequencies with $\ell =m$. We find that the usual correspondence between the Lyapunov exponent of those orbits and the imaginary part of the frequency is modified.

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• Alternative gravity theories
• Classical black holes
• Gravitation
• Gravitational waves