Mihalis Dafermos (University of Cambridge)

The Teukolsky equation on Kerr and the black hole stability problem

The Teukolsky equation on Kerr and the black hole stability problem
I will review first the formulation of the black hole stability problem in general relativity. As part of our previous proof of linear stability of Schwarzschild, we showed both boundedness and polynomial decay estimates for solutions of the spin ±2 Teukolsky equation by exploiting a physical space transformation to solutions of the Regge-Wheeler equation. We show how this procedure can be generalised to yield similar results for the Teukolsky equation on Kerr. This equation completely describes the gauge invariant part of gravitational perturbations and provides the key to a full understanding of the stability problem. This is joint work with G. Holzegel and I. Rodnianski.