On the initial boundary value problem for the vacuum Einstein equations and geometric uniqueness

We formulate a well-posed initial boundary value problem (IBVP) for the vacuum Einstein equations in harmonic gauge by describing the boundary conditions of a spacetime metric in its associated gauge. This gauge is determined, equivariantly with respect to diffeomorphisms, by the spacetime metric. Further we show that vacuum spacetimes satisfying fixed initial-boundary conditions and corner conditions are geometrically unique near the initial surface. In analogy to the solution to the Cauchy problem, we also construct a unique maximal globally hyperbolic vacuum development of the initial-boundary data.
Comment: 48 pages; The Introduction has been rewritten to clarify the exposition and results, more detailed discussion of the corner geometry is added, and minor mistakes in the previous manuscript have been corrected