{"paper":{"title":"Field equations and Noether potentials for higher-order theories of gravity with Lagrangians involving $\\Box^i R$, $\\Box^i R_{\\mu\\nu}$ and $\\Box^i R_{\\mu\\nu\\rho\\sigma}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Hua Li, Jun-Jin Peng","submitted_at":"2024-02-27T11:42:18Z","abstract_excerpt":"In this paper, we aim to perform a systematical investigation on the field equations and Noether potentials for the higher-order gravity theories endowed with Lagrangians depending on the metric and the Riemann curvature tensor, together with $i$th ($i=1,2,\\cdot\\cdot\\cdot$) powers of the Beltrami-d'Alembertian operator $\\Box$ acting on the latter. We start with a detailed derivation of the field equations and the Noether potential corresponding to the Lagrangian $\\sqrt{-g}L_R(R,\\Box R,\\cdot\\cdot\\cdot,\\Box^m R)$ through the direct variation of the Lagrangian and a method based upon the conserve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.17429","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/2402.17429/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"}