Post-Newtonian expansions for perfect fluids

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Abstract

We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations that have a first post-Newtonian expansion. The results here are based on the elliptic-hyperbolic formulation of the Einstein-Euler equations used in [15], which contains a singular parameter \epsilon = v_T/c , where v T is a characteristic velocity associated with the fluid and c is the speed of light. As in [15], energy estimates on weighted Sobolev spaces are used to analyze the behavior of solutions to the Einstein-Euler equations in the limit \epsilon\searrow 0 , and to demonstrate the validity of the first post-Newtonian expansion as an approximation.
Original languageEnglish
Pages (from-to)847 - 886
Number of pages40
JournalCommunications in Mathematical Physics
Volume288
Issue number3
Publication statusPublished - 2009

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