For the vacuum Einstein equations it is not a priori clear that it is even possible to find a well-posed initial boundary value problem. Thus it is particularly interesting that Friedrich and Nagy [75] have been able to prove the well-posedness of certain initial boundary value problems for the vacuum Einstein equations. Since boundary conditions come up quite naturally when the Einstein equations are solved numerically, due to the need to use a finite grid, the results of [75] are potentially important for numerical relativity. The techniques developed there could also play a key role in the study of the initial value problem for fluid bodies (Cf. section 2.5 .)

Local and Global Existence Theorems for the Einstein
Equations
Alan D. Rendall
http://www.livingreviews.org/lrr-2000-1
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