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arXiv:2005.01623 [math.AP]AbstractReferencesReviewsResources

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

Zhongshan An, Michael T. Anderson

Published 2020-05-04Version 1

Westudytheinitialboundaryvalueproblem(IBVP)forthevacuumEinsteinequations in harmonic gauge by adding a new field corresponding to the choice of harmonic gauge. Two classes of boundary data for the metric, together with Dirichlet boundary data for the harmonic gauge field, are 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 these initial boundary data.

Comments: 37 pages
Categories: math.AP, gr-qc, math.DG
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