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.
https://indico.math.cnrs.fr/event/7152/