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Nicolas Besset: Low frequency resonances of the charged Klein-Gordon equation in the De Sitter-Reissner-Nordström spacetime.

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mercredi 30 mars 2022 mercredi 30 mars 2022
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Abstract: Resonances are complex frequencies which describe the oscillation and damping of solutions to wave-type equations at large time scales.

In black hole type spacetimes such as the De Sitter-Reissner-Nordström (DSRN) solution of Einstein-Maxwell equations, we can define resonances for characteristic wave-type operators thanks to the analytic Fredholm theory.

We construct in this talk boundary parametrices for the spectral family associated to the charged Klein-Gordon equation in the DSRN spacetime and deduce the index 0 Fredholm property used to define resonances. We then discuss the localization of low frequency resonances depending on the product of the charges of the black hole and the Klein-Gordon field, its mass or its angular momentum.


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