Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 052, 11 pages      arXiv:2306.09213      https://doi.org/10.3842/SIGMA.2024.052
Contribution to the Special Issue on Global Analysis on Manifolds in honor of Christian Bär for his 60th birthday

Stationarity and Fredholm Theory in Subextremal Kerr-de Sitter Spacetimes

Oliver Petersen a and András Vasy b
a) Department of Mathematics, Stockholm University, 10691 Stockholm, Sweden
b) Department of Mathematics, Stanford University, CA 94305-2125, USA

Received June 16, 2023, in final form June 10, 2024; Published online June 20, 2024

Abstract
In a recent paper, we proved 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 results of Vasy (2013). One central ingredient in the argument was a new definition of quasinormal modes, where a non-standard choice of stationary Killing vector field had to be used in order for the Fredholm theory to be applicable. In this paper, we show that there is in fact a variety of allowed choices of stationary Killing vector fields. In particular, the horizon Killing vector fields work for the analysis, in which case one of the corresponding ergoregions is completely removed.

Key words: subextremal Kerr-de Sitter spacetime; resonances; quasinormal modes; radial points; normally hyperbolic trapping.

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References

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