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We prove that solutions to linear wave equations in a subextremal Kerr–de Sitter space- time have asymptotic expansions in quasinormal modes up to a decay order given by the normally hyperbolic trapping, extending the result of the second named author (2013). The main novelties are a different way of obtaining a Fredholm setup that defines the quasinormal modes and a new analysis of the trapping of lightlike geodesics in the Kerr–de Sitter spacetime, both of which apply in the full subextremal range. In particular, this reduces the question of decay for solutions to wave equations to the question of mode stability.
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Analyticity of Quasinormal Modes in the Kerr and Kerr–de Sitter Spacetimes
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.
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- PAR ID:
- 10502933
- Publisher / Repository:
- arXiv:2104.04500
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 402
- Issue:
- 3
- ISSN:
- 0010-3616
- Page Range / eLocation ID:
- 2547 to 2575
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00220-023-04776-9
