Analysis and PDE Seminar: Resonances on asymptotically flat black holes

Seminar | April 29 | 4:10-5 p.m. | 740 Evans Hall

 Dejan Gajic, University of Cambridge

 Department of Mathematics

A fundamental problem in the context of Einstein’s equations of general relativity is to understand the dynamical evolution of small perturbations of stationary black hole solutions. It is expected that there is a discrete set of characteristic frequencies that play a dominant role at late times and carry information about the nature of the black hole, much like how the normal frequencies of a vibrating guitar string play an important role in the resulting sound wave. These frequencies are called quasinormal frequencies or resonant frequencies and they are closely related to scattering resonances in the study of Schrödinger-type equations. I will consider the linear wave equation on black hole backgrounds as a toy model for Einstein’s equations and give an introduction to resonances in this setting. Then I will discuss a new method of defining and studying resonances on asymptotically flat spacetimes, developed from joint work with Claude Warnick, which puts resonances on the same footing as normal modes by showing that they are eigenfunctions of a natural operator acting on a Hilbert space.