JournalsjemsVol. 19, No. 8pp. 2371–2444

Asymptotic completeness for superradiant Klein–Gordon equations and applications to the De Sitter–Kerr metric

  • Vladimir Georgescu

    Université Cergy-Pontoise, France

  • Christian Gérard

    Université de Paris 11, Orsay, France

  • Dietrich Häfner

    Université de Grenoble I, France
Asymptotic completeness for superradiant Klein–Gordon equations and applications to the De Sitter–Kerr metric cover
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Abstract

We show asymptotic completeness for a class of superradiant Klein–Gordon equations. Our results are applied to the Klein–Gordon equation on the De Sitter–Kerr metric with small angular momentum of the black hole. For this equation we obtain asymptotic completeness for fixed angular momentum of the field.

Cite this article

Vladimir Georgescu, Christian Gérard, Dietrich Häfner, Asymptotic completeness for superradiant Klein–Gordon equations and applications to the De Sitter–Kerr metric. J. Eur. Math. Soc. 19 (2017), no. 8, pp. 2371–2444

DOI 10.4171/JEMS/720