Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric

Nicolas Besset (1) , Dietrich Häfner (1)

1 IF - Institut Fourier

We show the existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the De Sitter–Kerr–Newman metric for small charge and mass of the field and small angular momentum of the black hole. The mechanism behind is that the zero resonance that exists for zero charge, mass and angular momentum moves into the upper half plane.

Mots clés: Charged Klein–Gordon equation; De Sitter–Kerr–Newman metric; growing modes

Domaines: Physique mathématique [math-ph]

Nicolas Besset, Dietrich Häfner. Existence of exponentially growing finite energy solutions for the charged Klein–Gordon equation on the de Sitter–Kerr–Newman metric. J.Hyperbol.Diff.Equat., 2021, 18 (02), pp.293-310. ⟨10.1142/S0219891621500090⟩. ⟨hal-02550047⟩