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In relation to the BSSN formulation of the Einstein equations, we write downthe boundary conditions that result from the vanishing of the projection of theEinstein tensor normally to a timelike hypersurface. Furthermore, by setting upa well-posed system of propagation equations for the constraints, we showexplicitly that there are three constraints that are incoming at the boundarysurface and that the boundary equations are linearly related to them. Thisindicates that such boundary conditions play a role in enforcing thepropagation of the constraints in the region interior to the boundary.Additionally, we examine the related problem for a strongly hyperbolicfirst-order reduction of the BSSN equations and determine the characteristicfields that are prescribed by the three boundary conditions, as well as thosethat are left arbitrary.Comment: 11 page

Einstein boundary conditions for the Einstein equations in the conformal-traceless decomposition