Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes Annales Henri Poincaré 13

Abstract. We establish a Bohr–Sommerfeld type condition for quasi-normal modes of a slowly rotating Kerr–de Sitter black hole, providing their full asymptotic description in any strip of fixed width. In particular, we observe a Zeeman-like splitting of the high multipicity modes at a = 0 (Schwarzschild–de Sitter), once spherical symmetry is broken. The numerical results presented in Appendix B show that the asymptotics are in fact accurate at very low energies and agree with the numerical results established by other methods in the physics literature. We also we prove that solutions of the wave equation can be asymptotically expanded in terms of quasi-normal modes; this confirms the validity of the interpretation of their real parts as frequencies of oscillations, and imaginary parts as decay rates of gravitational waves. Quasi-normal modes (QNMs) of black holes are a topic of continued interest in theoretical physics: from the classical interpretation as ringdown of gravitational waves [C] to the recent investigations in the context of string theory [HoHu]. The ringdown1 plays a role in experimental projects aimed at the detection of gravitational waves, such as LIGO [Ab]. See [KoSch] for an overview of the vast physics literature on the topic and [BeCaSt, KoZh1