{"paper":{"title":"Connecting 2-Forms, Conformal Transformations, Curvature Invariants and Topological Classes in Einstein Spacetimes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Fedor V. Kusmartsev, Jack C. M. Hughes","submitted_at":"2024-03-18T07:29:28Z","abstract_excerpt":"The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can be used for two ends. First, it allows for a simple generalization of the Birkhoff theorem to Schwarzschild (A)de-Sitter spacetime. Second, it provides the means to construct an Abelian endomorphism group on the space of 2-forms. It is observed that taking the trace over this group element-wise induces a further Abelian group which may be identified with a te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.11527","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.11527/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"}