  We discuss the initial-boundary value problem for the
Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field
equations which has been used extensively in numerical simulations of binary
black holes and neutron stars. We specify nine boundary conditions for this
system with the following properties: (i) they impose the momentum constraint
at the boundary, which is shown to preserve all the constraints throughout
evolution, (ii) they approximately control the incoming gravitational degrees
of freedom by specifying the Weyl scalar Psi_0 at the boundary, (iii) they
control the gauge freedom by requiring a Neumann boundary condition for the
lapse, by setting the normal component of the shift to zero, and by imposing a
Sommerfeld-like condition on the tangential components of the shift, (iv) they
are shown to yield a well-posed problem in the limit of weak gravity. Possible
numerical applications of our results are also discussed briefly.
