Kerr Black Hole Ringdown in Effective Field Theory

We develop a systematic effective field theory calculation of the quasinormal modes of Kerr black holes valid for arbitrary spin, providing model-independent corrections to their ringdown spectrum directly relevant for gravitational-wave observations. Close to extremality, the effective field theory corrections in the grand-canonical ensemble exhibit an oscillatory dependence on $\log \tau_{H}$, with $\tau_H \equiv T_H/\Omega_H$ a dimensionless measure of the black hole temperature. This behaviour signals an underlying discrete-scale-invariant structure.