Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911735237050368 |
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| author | An, Zhongshan Anderson, Michael T. |
| author_facet | An, Zhongshan Anderson, Michael T. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07128 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data An, Zhongshan Anderson, Michael T. Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry 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. |
| title | Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2505.07128 |