  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 $\ep = v_T/c$ 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 $\ep$
independent energy estimates on weighted Sobolev spaces. These estimates are
the main tool used to analyze the behavior of solutions in the limit $\ep
\searrow 0$.
