On decay of waves on curved backgrounds
Talk by Prof. Dr. Wilhelm Schlag
Date: 26.11.10 Time: 11.00 - 12.00 Room: ETH HIT F 31.2
I will present an overview of some recent work on decay of waves on a Schwarzschild background. The underlying approach is to perform an angular momentum (spherical harmonic) decomposition which then leads to both the question of the decay law for fixed angular momentum (Price law) as well as the question on how to sum the bounds over all momenta. The latter leads one to analyze a semiclassical Schroedinger operator on the line with an inverse square potential at positive infinity (and exponential decay at negative infinity) with a nondegenerate maximum (which occurs at the photon sphere). In contrast to the common approach in semiclassical theory one needs a representation of the spectral measure in the doubly asymptotic regime in which both the energy and the semiclassical parameter are small. We deal with the potential maximum by means of Mourre theory, and the Hunizker-Sigal-Soffer propagation estimates. This is joint work with R. Donninger (Chicago and EPFL Lausanne) and A. Soffer (Rutgers).