Polynomial Decay for the KleinGordon Equation on the Schwarzschild Black Hole
Polynomial Decay for the KleinGordon Equation on the Schwarzschild Black Hole

Yakov ShlapentokhRothman, University of Toronto
Fine Hall 314
We will start with a quick review of previous instability results concerning solutions to the KleinGordon equation on rotating Kerr black holes and the corresponding conjectural consequences for the dynamics of the EinsteinKleinGordon system. Then we will discuss recent work where we show that, despite the presence of stably trapped timelike geodesics on Schwarzschild, solutions to the corresponding KleinGordon equation arising from strongly localized initial data nevertheless decay polynomially. Time permitting we will explain how the proof uses, at a crucial step, results from analytic number theory for bounding exponential sums. The talk is based on joint work(s) with Federico Pasqualotto and Maxime Van de Moortel.