The Einstein-Vlasov system in a large data regime

In this talk, our object of study is the Einstein-Vlasov system with a massless Vlasov matter field. Complementing various important works obtaining the stability of Minkowski spacetime as a solution to this system, we look at the large data regime, motivated in turn by the signature for decay rates of various Ricci, curvature and matter components, first introduced by X. An. Our work provides a semi-global existence result and a trapped surface formation result for the Einstein-Vlasov system in the absence of spherical symmetry. Our proof is based on a double null gauge. Interestingly, we give a new way of obtaining estimates for the Vlasov matter, purely by commuting with various vector fields and without the need to use Jacobi fields.