We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations that have a first post-Newtonian expansion. The results here are based on the elliptic-hyperbolic formulation of the Einstein-Euler equations used in , which contains a singular parameter \epsilon = v_T/c , where v T is a characteristic velocity associated with the fluid and c is the speed of light. As in , energy estimates on weighted Sobolev spaces are used to analyze the behavior of solutions to the Einstein-Euler equations in the limit \epsilon\searrow 0 , and to demonstrate the validity of the first post-Newtonian expansion as an approximation.
|Pages (from-to)||847 - 886|
|Number of pages||40|
|Journal||Communications in Mathematical Physics|
|Publication status||Published - 2009|