Cosmological post-Newtonian expansions to arbitrary order

Details Cosmological post-Newtonian expansions to arbitrary order Cosmological post-Newtonian expansions to arbitrary order

2009-08-19

arxiv.org/abs/0908.2836v1

Commun.Math.Phys.295:431-463,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1007/s00220-009-0931-0

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 $\ep=v_T/c$ $(0<\ep < \ep_0)$, 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 $M\cong [0,T)\times \Tbb^3$, and converge as $\ep \searrow 0$ to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter $\ep$ to any specified order with expansion coefficients that satisfy $\ep$-independent (nonlocal) symmetric hyperbolic equations.

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