  A strongly well-posed initial boundary value problem based upon
constraint-preserving boundary conditions of the Sommerfeld type has been
established for the harmonic formulation of the vacuum Einstein's equations.
These Sommerfeld conditions have been previously presented in a 4-dimensional
geometric form. Here we recast the associated boundary data as 3-dimensional
tensor fields intrinsic to the boundary. This provides a geometric presentation
of the boundary data analogous to the 3-dimensional presentation of Cauchy data
in terms of 3-metric and extrinsic curvature. In particular, diffeomorphisms of
the boundary data lead to vacuum spacetimes with isometric geometries. The
proof of well-posedness is valid for the harmonic formulation and its
generalizations. The Sommerfeld conditions can be directly applied to existing
harmonic codes which have been used in simulating binary black holes, thus
ensuring boundary stability of the underlying analytic system. The geometric
form of the boundary conditions also allows them to be formally applied to any
metric formulation of Einstein's equations, although well-posedness of the
boundary problem is no longer ensured. We discuss to what extent such a formal
application might be implemented in a constraint preserving manner to 3+1
formulations, such as the Baumgarte-Shapiro-Shibata-Nakamura system which has
been highly successful in binary black hole simulation.
