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

TL;DR

This paper demonstrates that a broad class of asymptotically flat solutions to the Einstein-Vlasov system have a Newtonian limit, confirming the physical intuition that such solutions approximate classical gravity in the appropriate regime.

Contribution

It establishes the existence of families of solutions with a Newtonian limit for the Einstein-Vlasov system, using energy estimates in Sobolev spaces.

Findings

Existence of asymptotically flat solutions with Newtonian limit

Use of energy estimates in Sobolev spaces for wave equations

Confirmation of physical intuition about matter models

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.