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2010•Journal of Hyperbolic Differential EquationsOpen access

A RIGOROUS FORMULATION OF THE COSMOLOGICAL NEWTONIAN LIMIT WITHOUT AVERAGING

Todd A. Oliynyk

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Abstract

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein–Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged.

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We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein–Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged.

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Available abstract

We prove the existence of a large class of one-parameter families of cosmological solutions to the Einstein–Euler equations that have a Newtonian limit. This class includes solutions that represent a finite, but otherwise arbitrary, number of compact fluid bodies. These solutions provide exact cosmological models that admit Newtonian limits but, are not, either implicitly or explicitly, averaged.

Key concepts: Limit (mathematics), Newtonian limit, Newtonian fluid, Class (philosophy), Physics, Euler equations, Einstein, Euler's formula

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