Abstract
We prove that there exists a class of non-stationary solutions to the Einstein-Euler equations which have a Newtonian limit. The proof of this result is based on a symmetric hyperbolic formulation of the Einstein-Euler equations which contains a singular parameter ∈ = v T /c, where v T is a characteristic velocity scale associated with the fluid and c is the speed of light. The symmetric hyperbolic formulation allows us to derive ε independent energy estimates on weighted Sobolev spaces. These estimates are the main tool used to analyze the behavior of solutions in the limit ∈ ↘ 0.
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