Asymptotic distribution of quasi-normal modes for Kerr-de Sitter black holes

Understand

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 multiplicity 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 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.