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arXiv · 2005.01623

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

Zhongshan An·Michael T. Anderson
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Abstract

We formulate an initial boundary value problem (IBVP) for the vacuum Einstein equations 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. The vacuum spacetime metric $g$ and its associated gauge $\phi_g$ are solved simultaneously in local harmonic coordinates. Further we show that vacuum spacetimes satisfying fixed initial-boundary conditions and corner conditions are geometrically unique near the initial surface. Finally, in analogy to the solution of the Cauchy problem, we also construct a unique maximal globally hyperbolic solution of the IBVP.

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Zhongshan An, Michael T. Anderson. 2020-05-04. On the initial boundary value problem for the vacuum Einstein equations and geometric uniqueness. https://arxiv.org/abs/2005.01623

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