Hidden Kerr/CFT correspondence at finite frequencies

Abstract

Massless fields propagating in a generic Kerr black hole background enjoy a hidden $SL(2,\mathbb{R})\ifmmode\times\else\texttimes\fi{}SL(2,\mathbb{R})$ symmetry. We determine how the exact mode functions decompose into representations of this symmetry group. This extends earlier results on the low-frequency limit of the massless scalar case to finite frequencies and general spin. As an application, we numerically determine the parameters of the representations that appear in quasinormal modes. These results represent a first step to formulating a more precise mapping to a holographic dual conformal field theory for generic black holes.