| We study decay properties of linear waves on Kerr and Kerr-de Sitter black hole backgrounds. We are particularly interested in quasi-normal modes (QNMs), which are the complex frequencies of exponentially decaying and oscillating solutions to the wave equation. For slowly rotating Kerr-de Sitter black holes, we show that QNMs obey a quantization condition; that is, they lie asymptotically on a lattice. We also obtain a resonance expansion of linear waves in terms of QNMs. For the general Kerr-de Sitter case and its small stationary perturbations, we use r-normal hyperbolicity of the set of trapped lightlike rays to obtain a band of QNMs with a Weyl law. |
