  In relation to the BSSN formulation of the Einstein equations, we write down
the boundary conditions that result from the vanishing of the projection of the
Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up
a well-posed system of propagation equations for the constraints, we show
explicitly that there are three constraints that are incoming at the boundary
surface and that the boundary equations are linearly related to them. This
indicates that such boundary conditions play a role in enforcing the
propagation of the constraints in the region interior to the boundary.
Additionally, we examine the related problem for a strongly hyperbolic
first-order reduction of the BSSN equations and determine the characteristic
fields that are prescribed by the three boundary conditions, as well as those
that are left arbitrary.
