William L. Boyce, Jorge E. Santos

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 $\log τ_{H}$, with $τ_H \equiv T_H/Ω_H$ a dimensionless measure of the black hole temperature. This behaviour signals an underlying discrete-scale-invariant structure.