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Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole

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Abstract

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 \({\mathbb C}\) . 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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Authors and Affiliations

  1. Department of Mathematics, Evans Hall, University of California, Berkeley, CA, 94720, USA

    Semyon Dyatlov

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  1. Semyon Dyatlov
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Correspondence to Semyon Dyatlov.

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Communicated by P.T. Chruściel

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Dyatlov, S. Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole. Commun. Math. Phys. 306, 119–163 (2011). https://doi.org/10.1007/s00220-011-1286-x

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