Playlist - On the mathematical theory of black holes

On the reality of black holes. I will give a quick introduction to the initial-value problem in GR and overview of the problems of Rigidity, Stability and Collapse and how they fit with regard to the Final State Conjecture.

I will discuss in some detail the main difficulties of the problem of non-linear stability of black holes and the recent advances on the related issue of linear stability.

I will discuss a recent result in collaboration with J. Szeftel concerning the non-linear stability of the Schwarzschild spacetime under axially symmetric, polarized perturbations.