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The Cauchy problem and the initial boundary value problem in numerical relativity

Some simple ideas on numerical tractability are introduced, and are used to determine under what conditions unconstrained evolution of Einstein's field equations for the Cauchy problem is possible. The initial boundary value problem for Einstein's equations is discussed and a precise description of what boundary data are needed is given. Unconstrained evolution is numerically tractable if and only if the boundary conditions respect the momentum constraints.