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Communications in Mathematical Physics

, Volume 163, Issue 1, pp 89–112 | Cite as

The Newtonian limit for asymptotically flat solutions of the Vlasov-Einstein system

  • Alan D. Rendall
Article

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.

Keywords

Neural Network Statistical Physic Complex System Wave Equation Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Alan D. Rendall
    • 1
  1. 1.Max-Planck-Institut für AstrophysikGarching bei MünchenGermany

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