Quasinormal modes: the approach to extremality

Abstract: It is now an observational fact that perturbed black holes produce radiation at fixed (complex) frequencies which are characteristic of the spacetime rather than the perturbation. The work of Vasy `13 shows how to identify these frequencies as part of the spectrum of some natural non-self-adjoint operator when the spacetime is bounded by sub-extremal horizons. Key to this approach is the imposition of (Sobolev) regularity of the eigenmodes across the horizons. When an extremal horizon is present this approach breaks down. I will discuss work with Gajic establishing continuity results for the extremal limit, which necessitates going beyond Sobolev regularity.