{"paper":{"title":"Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"Gustav Holzegel","submitted_at":"2010-10-15T16:45:12Z","abstract_excerpt":"In this paper, we introduce a class of spacetimes $\\left(\\mathcal{M},g\\right)$ which satisfy the vacuum Einstein equations and dynamically approach a Schwarzschild solution of mass $M$, a class we shall call \\emph{ultimately Schwarzschildean spacetimes}. The approach is captured in terms of boundedness and decay assumptions on appropriate spacetime-norms of the Ricci-coefficients and spacetime curvature. Given such assumptions at the level of $k$ derivatives of the Ricci-coefficients (and hence $k-1$ derivatives of curvature), we prove boundedness and decay estimates for $k$ derivatives of \\em"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3216","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}