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

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

2011-01-06

arxiv.org/abs/1101.1260v2

Mathematics

Analysis of PDEs

66 pages, 6 figures; journal version (to appear in Annales Henri Poincar\'e)

Scientific paper

10.1007/s00023-012-0159-y

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.

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