Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole

Details Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole

2010-03-31

arxiv.org/abs/1003.6128v5

Commun.Math.Phys.306:119-163,2011

Mathematics

Analysis of PDEs

48+eps pages, 5 figures; changes in presentation made and references added

Scientific paper

10.1007/s00220-011-1286-x

We provide a rigorous definition of quasi-normal modes for a rotating black hole. They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature. If the black hole rotates slowly enough, we show that these poles form a discrete subset of the complex plane. As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.

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