{"paper":{"title":"Hidden symmetry group for particle orbits (timelike geodesics) in Schwarzschild spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Timelike geodesics in Schwarzschild spacetime admit a complete Noether symmetry group consisting of Killing symmetries plus three hidden transformations.","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Mahdieh Gol Bashmani Moghadam, Stephen C. Anco","submitted_at":"2026-04-17T19:02:26Z","abstract_excerpt":"For the timelike geodesic equations in Schwarzschild spacetime, three hidden conserved quantities were found recently, which are analogues of dynamical quantities related to the well-known Laplace-Runge-Lenz (LRL) vector in Newtonian gravity. In particular, the geodesic equations possess an LRL angle, an LRL Killing-vector time and an LRL proper-time, each of which is a conserved quantity for all timelike geodesics. The present work provides a natural symmetry interpretation for these three quantities by applying Noether's theorem in reverse to the geodesic Lagrangian. This yields three hidden"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Together with the Killing symmetries, these transformations comprise the complete Noether symmetry group of the timelike equatorial geodesic equations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the three recently identified conserved quantities (LRL angle, LRL Killing-vector time, LRL proper-time) arise directly from valid hidden symmetry transformations obtained by reversing Noether's theorem on the geodesic Lagrangian, without additional constraints or coordinate restrictions beyond equatorial motion.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Hidden symmetries complete the Noether symmetry group for equatorial timelike geodesics in Schwarzschild spacetime.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Timelike geodesics in Schwarzschild spacetime admit a complete Noether symmetry group consisting of Killing symmetries plus three hidden transformations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8f45e35f750aacd8f61f2352aa1d4285dbe0ac2c9ad95488fcd54ed8280b5c5d"},"source":{"id":"2604.16644","kind":"arxiv","version":2},"verdict":{"id":"a7d08974-9022-4e3b-980f-69c72ed94948","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T07:26:33.969596Z","strongest_claim":"Together with the Killing symmetries, these transformations comprise the complete Noether symmetry group of the timelike equatorial geodesic equations.","one_line_summary":"Hidden symmetries complete the Noether symmetry group for equatorial timelike geodesics in Schwarzschild spacetime.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the three recently identified conserved quantities (LRL angle, LRL Killing-vector time, LRL proper-time) arise directly from valid hidden symmetry transformations obtained by reversing Noether's theorem on the geodesic Lagrangian, without additional constraints or coordinate restrictions beyond equatorial motion.","pith_extraction_headline":"Timelike geodesics in Schwarzschild spacetime admit a complete Noether symmetry group consisting of Killing symmetries plus three hidden transformations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.16644/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"}