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

Vladimir Georgescu (1) , Christian Gérard (2) , Dietrich Häfner (3)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay
3 IF - Institut Fourier

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.

Keywords: superradiance; Asymptotic completeness; Klein-Gordon equation; De Sitter Kerr metric

Domains: Analysis of PDEs [math.AP]; Mathematical Physics [math-ph]; General Relativity and Quantum Cosmology [gr-qc]

Vladimir Georgescu, Christian Gérard, Dietrich Häfner. Asymptotic completeness for superradiant Klein-Gordon equations and applications to the De Sitter Kerr metric. Journal of the European Mathematical Society, 2017, 19 (8), pp.2371-2444. ⟨hal-00994029⟩