{"paper":{"title":"Local uniqueness of the Black String with small circle size","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Daniel Platt, Emma Albertini","submitted_at":"2025-05-07T17:10:02Z","abstract_excerpt":"In this article we study uniqueness of the Black String, i.e. the product of 4-dimensional Schwarzschild space with a circle of length L.\n  In arXiv:2410.20967, this was reduced to a non-linear elliptic PDE, and we use this setup to show that for small L the Black String is infinitesimally rigid as a Ricci-flat metric.\n  Using a fixed point theorem, we prove that this implies local uniqueness, i.e. there exist no other Ricci-flat metrics near the Black String, and we give bounds for the size of the neighborhood in which the Black String is unique.\n  We compare this with the toy problem of a sc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.04573","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/2505.04573/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"}