Global existence for the spherically symmetric Einstein-Vlasov system   with outgoing matter
  We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete. 
Hakan Andreasson, Markus Kunze, Gerhard Rein