{"paper":{"title":"A note on field equations in generalized theories of gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Jun-Jin Peng","submitted_at":"2023-06-20T14:28:00Z","abstract_excerpt":"In the work (arXiv:1109.3846 [gr-qc]), to obtain a simple and economic formulation of field equations for generalised theories of gravity described by the Lagrangian $\\sqrt{-g}L\\big(g^{\\alpha\\beta},R_{\\mu\\nu\\rho\\sigma}\\big)$, the key equality $\\big(\\partial L/\\partial g^{\\mu\\nu}\\big)_{R_{\\alpha\\beta\\kappa\\omega}} =2P_{\\mu}^{~\\lambda\\rho\\sigma}R_{\\nu\\lambda\\rho\\sigma}$ was derived. In this note, it is demonstrated that such an equality can be directly derived from an off-shell Noether current associated with an arbitrary vector field. As byproducts, a generalized Bianchi identity related to the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.11561","kind":"arxiv","version":9},"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/2306.11561/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"}