Description:

Title: Polynomial decay in time for the Klein-Gordon equation on a Schwarzschild black hole

Abstract: It is expected that the Klein-Gordon equation on a Schwarzschild black hole behaves very differently from the wave equation at late-time, due to the presence of stable (timelike) trapping. We present our recent work demonstrating that despite the presence of stable timelike trapping on the Schwarzschild black hole, solutions to the Klein-Gordon equation with strongly localized initial data nevertheless decay polynomially in time. We will also explain how the proof uses, at a crucial step, results from analytic number theory related to the Riemann zeta function. Joint work(s) with Federico Pasqualotto and Yakov Shlapentokh-Rothman.