Analyticity of quasinormal modes in the Kerr and Kerr-de Sitter spacetimes

Understand

We prove that quasinormal modes (or resonant states) for linear wave equations in the subextremal Kerr and Kerr-de Sitter spacetimes are real analytic.

• The main novelty of this paper is the observation that the bicharacteristic flow associated to the linear wave equations for quasinormal modes with respect to a suitable Killing vector field has a stable radial point source/sink structure rather than merely a generalized normal source/sink structure.
• The analyticity then follows by a recent result in the microlocal analysis of radial points by Galkowski and Zworski.
• The results can then be recast with respect to the standard Killing vector field.