Gravitational ringing of rotating black holes in higher-derivative gravity

We study gravitational perturbations of slowly-rotating black holes in a general effective-field-theory extension of general relativity that includes up to eight-derivative terms. We show that two Schr\"odinger-like equations with spin-dependent effective potentials govern the odd - and even-parity master variables. These equations are coupled for parity-violating corrections, and this coupling affects the quasinormal modes even at linear order in the higher-derivative corrections, due to their isospectrality in general relativity. We provide results for the shifts in the fundamental quasinormal mode frequencies at linear order in the spin, which we expect to be valuable for high-precision phenomenology through future gravitational wave observations.