# Gustav Holzegel

## Imperial College London

### The non-linear stability of the Schwarzschild family of black holes

I will discuss recent work with M. Dafermos, I. Rodnianski and M. Taylor proving the full finite codimension asymptotic stability of the Schwarzschild family of black holes in the exterior of the black hole region. The proof is expressed entirely in physical space and based on our previous understanding of linear stability of the Schwarzschild family in a double null gauge.