{"paper":{"title":"Well-posed geometric boundary data in General Relativity, I: Dirichlet boundary data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc","math.DG"],"primary_cat":"math.AP","authors_text":"Michael T. Anderson, Zhongshan An","submitted_at":"2025-05-11T21:43:22Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07128","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.07128/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}