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

TL;DR

This paper proves that quasinormal modes in Kerr and Kerr-de Sitter spacetimes are real analytic, revealing a new stable radial point structure in their bicharacteristic flow that enables this analyticity.

Contribution

It introduces the observation of a stable radial point source/sink structure in the bicharacteristic flow, leading to the proof of analyticity of quasinormal modes.

Findings

Quasinormal modes are proven to be real analytic in Kerr and Kerr-de Sitter spacetimes.

The stable radial point structure is key to establishing analyticity.

The results utilize recent microlocal analysis techniques by Galkowski and Zworski.

Abstract

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.