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Asymptotic Distribution of Quasi-Normal Modes for Kerr–de Sitter Black Holes

, : Asymptotic Distribution of Quasi-Normal Modes for Kerr–de Sitter Black Holes. Annales Henri Poincaré 13(5): 1101-1166

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 = (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.

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Accession: 036429325

DOI: 10.1007/s00023-012-0159-y

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