Abstract
We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations for which the fluid density and spatial threevelocity converge to a solution of the Poisson-Euler equations of Newtonian gravity. The results presented here generalize those of [10] to allow for a larger class of initial data. As in [10], the proof is based on a nonlocal symmetric hyperbolic formulation of the Einstein-Euler equations which contain a singular parameter ǫ = vT /c with vT a characteristic speed associated to the fluid and c the speed of light. Energy and dispersive estimates on weighted Sobolev spaces are the main technical tools used to analyze the solutions in the singular limit ǫ ց 0.
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