The nonlinear stability of the Schwarzschild metric without symmetry

I will discuss an upcoming result proving the full finite-codimension non-linear asymptotic stability of the Schwarzschild family as solutions to the Einstein vacuum equations in the exterior of the black hole region.

No symmetry is assumed. The work is based on our previous understanding of linear stability of Schwarzschild in double null gauge. Joint work with G. Holzegel, I. Rodnianski and M. Taylor.