{"paper":{"title":"New insights on null and timelike warped symmetric spacetime splittings","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Alan Maciel, Jos\\'e P. Mimoso, Morgan Le Delliou","submitted_at":"2024-05-16T10:30:18Z","abstract_excerpt":"We explore in detail the 2+2 and 1+1+2 formalism in spherically symmetric spacetimes, spanning from deducing the dynamical equations to relating them to the well-known generalised Painlev\\'e-Gullstrand (GPG) coordinate system. The evolution equations are the Raychaudhuri equations for null rays, including those also known as cross-focusing equations whose derivation, to the best of our knowledge, we present for the first time. We physically interpret the scalars that arise in this scenario, namely the flow 2-expansion $\\Theta_{n}$, the flow acceleration $\\mathcal{A}$, and the radial extrinsic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.09968","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/2405.09968/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"}