Sharp decay estimates for the Klein-Gordon equation on Kerr-AdS Seminar

Joint Work with Gustav Holzegel. I will present recent results concerning the behaviour of solutions to the Klein-Gordon equation on the Kerr-AdS black hole spacetimes. In particular, I will describe a stable trapping phenomenon, linked with the classical geodesic flow associated with the problem. Due to the stability of the trapping, the best decay rate achievable is then only logarithmic in time. If time permits, I will describe some connexions with nonlinear problems arising from the study of the Einstein equations. The talk is based on the two articles arXiv:1303.5944 and arXiv:1110.6794.