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The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System

Alan D. Rendall
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Abstract

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 sufficiently general to confirm that for this matter model as many families of this type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweighted Sobolev spaces for a wave equation satisfied by the second fundamental form of a maximal foliation.

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Alan D. Rendall. 1993-03-25. The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System. https://doi.org/10.1007/bf02101736

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