Trapping of waves and null geodesics for rotating black holes

Abstract

We present dynamical properties of linear waves and null geodesics valid for Kerr and Kerr–de Sitter black holes and their stationary perturbations. The two are intimately linked by the geometric optics approximation. For the null geodesic flow the key property is the r-normal hyperbolicity of the trapped set and for linear waves it is the distribution of quasinormal modes: the exact quantization conditions do not hold for perturbations but the bounds on decay rates and the statistics of frequencies are still valid.