The nonlinear stability of the Schwarzschild family of black holes
The Schwarzschild family, discovered in 1915, is the most famous family of solutions of the vacuum Einstein equations of general relativity. Each member describes a static black hole. The most basic question one can ask about the family is whether the black hole exterior is nonlinearly stable as a solution of the vacuum Einstein equations. I will present a theorem on the full finite codimension asymptotic stability of the Schwarzschild family. The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos--Holzegel--Rodnianski on the linear stability of Schwarzschild. This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.
Dr Martin Taylor, Princeton University