Maxime Van de Moortel: Late-time asymptotics for the Klein-Gordon equation on a Schwarzschild black hole

Maxime Van de Moortel,
Rutgers University

Title: Late-time asymptotics for the Klein-Gordon equation on a Schwarzschild black hole

Abstract: It has long been expected that the Klein-Gordon equation on a Schwarzschild black hole behaves very differently from its analogue on flat spacetime due to the existence of stably trapped massive particles orbiting the black hole. We present our recent resolution of this question, demonstrating that despite the presence of stable trapping, solutions to the Klein-Gordon equation on Schwarzschild decay polynomially in time. Time permitting, we will explain how the proof uses, at a crucial step, results from analytic number theory related to the Riemann zeta function. This talk is based on joint work(s) with Federico Pasqualotto and Yakov Shlapentokh-Rothman.