THE NEWTONIAN LIMIT FOR ASYMPTOTICALLY FLAT SOLUTIONS OF THE VLASOV-EINSTEIN SYSTEM

It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficientl y general to confirm that for this matter model as many families of th is type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweight ed Sobolev spaces for a wave equation satisfied by the second fundamen tal form of a maximal foliation.