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

We study the initial boundary value problem (IBVP) for the vacuum Einstein equations in harmonic gauge by adding a new field corresponding to the choice of harmonic gauge. For the gauge-type field, both free initial and Dirichlet boundary data as well as initial and boundary data coupled to the metric are analysed and shown to lead to well-posed formulations of the IBVP. In addition, these formulations lead to a solution of the problem of geometric uniqueness, as emphasized by H. Friedrich. In analogy to the solution to the Cauchy problem, we also prove the existence of a unique maximal globally hyperbolic vacuum development of the initial boundary data.

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