Existence of CMC and Constant Areal Time Foliations in T 2 Symmetric Spacetimes with Vlasov Matter

Abstract

The global structure of solutions of the Einstein equations coupled to the Vlasov equation is investigated in the presence of a two-dimensional symmetry group. It is shown that there exist global CMC and areal time foliations. The proof is based on long-time existence theorems for the partial differential equations resulting from the Einstein–Vlasov system when conformal or areal coordinates are introduced.