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arXiv · 2505.07128

Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data

Zhongshan An·Michael T. Anderson
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Abstract

In this first work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations with Dirichlet boundary data on a finite timelike boundary, provided the Brown- York stress tensor of the boundary is a Lorentz metric of the same signature (up to an overall sign) as the induced Lorentz metric on the boundary. This is a convexity-type assumption which is an exact analog of a similar result in the Riemannian setting. This assumption on the (extrinsic) Brown-York tensor cannot be dropped in general.

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Zhongshan An, Michael T. Anderson. 2025-05-11. Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data. https://arxiv.org/abs/2505.07128

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