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