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

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

1993-03-25

arxiv.org/abs/gr-qc/9303027v1

Commun. Math. Phys. 163 (1994) 89-112

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, plain TEX

Scientific paper

10.1007/BF02101736

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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