We show how the use of the normal projection of the Einstein tensor as a setof boundary conditions relates to the propagation of the constraints, for tworepresentations of the Einstein equations with vanishing shift vector: the ADMformulation, which is ill posed, and the Einstein-Christoffel formulation,which is symmetric hyperbolic. Essentially, the components of the normalprojection of the Einstein tensor that act as non-trivial boundary conditionsare linear combinations of the evolution equations with the constraints thatare not preserved at the boundary, in both cases. In the process, therelationship of the normal projection of the Einstein tensor to the recentlyintroduced ``constraint-preserving'' boundary conditions becomes apparent.
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