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arXiv · 2112.01355

Wave equations in the Kerr-de Sitter spacetime: the full subextremal range

Oliver Petersen·András Vasy
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Abstract

We prove that solutions to linear wave equations in a subextremal Kerr-de Sitter spacetime have asymptotic expansions in quasinormal modes up to a decay order given by the normally hyperbolic trapping, extending the existing results. 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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Oliver Petersen, András Vasy. 2021-12-02. Wave equations in the Kerr-de Sitter spacetime: the full subextremal range. https://arxiv.org/abs/2112.01355

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