Cosmological post-Newtonian expansions to arbitrary order

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Abstract

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter \epsilon=v_T/c (0<\epsilon <\epsilon_0) , where c is the speed of light, and v T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M\cong [0,T)\times \mathbb T ^3 , and converge as \epsilon \searrow 0 to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter \epsilon to any specified order with expansion coefficients that satisfy \epsilon -independent (nonlocal) symmetric hyperbolic equations.
Original languageEnglish
Pages (from-to)431 - 463
Number of pages33
JournalCommunications in Mathematical Physics
Volume295
Issue number2
Publication statusPublished - 2010

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