  An outstanding issue in the treatment of boundaries in general relativity is
the lack of a local geometric interpretation of the necessary boundary data.
For the Cauchy problem, the initial data is supplied by the 3-metric and
extrinsic curvature of the initial Cauchy hypersurface.. This Cauchy data
determines a solution to Einstein's equations which is unique up to a
diffeomorphism. Here, we show how three pieces of boundary data, which are
associated locally with the geometry of the boundary, likewise determine a
solution of the initial-boundary value problem which is unique up to a
diffeomorphism. One piece of this data, constructed from the extrinsic
curvature of the boundary, determines the dynamical evolution of the boundary.
The other two pieces constitute a conformal class of rank-2, positive definite
metrics, which represent the two gravitational degrees of freedom.
