{"paper":{"title":"Geodesic structure of spacetime near singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"If the base point is a spacetime singularity, Synge's world function and van Vleck determinant change their scaling to capture non-trivial geodesic flows.","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Dawood Kothawala, Mayank","submitted_at":"2025-12-13T10:26:10Z","abstract_excerpt":"Geodesic flows emanating from an arbitrary point $\\mathscr{P}$ in a manifold $\\mathscr{M}$ carry important information about the geometric properties of $\\mathscr{M}$. These flows are characterized by Synge's world function and van Vleck determinant - important bi-scalars that also characterize quantum description of physical systems in $\\mathscr{M}$. If $\\mathscr{P}$ is a regular point, these bi-scalars have well known expansions around their flat space expressions, quantifying \\textit{local flatness} and equivalence principle. We show that, if $\\mathscr{P}$ is a singular point, the scaling b"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that, if P is a singular point, the scaling behavior of these bi-scalars changes drastically, capturing the non-trivial structure of geodesic flows near singularities.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That Synge's world function and van Vleck determinant remain well-defined and admit meaningful scaling expansions when the base point P is a spacetime singularity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Near spacetime singularities, Synge's world function and van Vleck determinant exhibit drastically altered scaling that reveals non-trivial geodesic flow structures.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"If the base point is a spacetime singularity, Synge's world function and van Vleck determinant change their scaling to capture non-trivial geodesic flows.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e858385a6fc6e0e1132042f9656d866fb233a3b8d84fc348c3eb27a7806cfc82"},"source":{"id":"2512.12271","kind":"arxiv","version":3},"verdict":{"id":"0928e3ee-ddad-433e-a22d-822cb5672176","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T23:01:35.056048Z","strongest_claim":"We show that, if P is a singular point, the scaling behavior of these bi-scalars changes drastically, capturing the non-trivial structure of geodesic flows near singularities.","one_line_summary":"Near spacetime singularities, Synge's world function and van Vleck determinant exhibit drastically altered scaling that reveals non-trivial geodesic flow structures.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That Synge's world function and van Vleck determinant remain well-defined and admit meaningful scaling expansions when the base point P is a spacetime singularity.","pith_extraction_headline":"If the base point is a spacetime singularity, Synge's world function and van Vleck determinant change their scaling to capture non-trivial geodesic flows."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.12271/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":23,"sample":[{"doi":"","year":null,"title":"Matter-dominated FLRW spacetime Coincidence : ∆(t, T) = 1 + ϵ2 9T 2 +O(ϵ 3) (17) Singularity : ∆(t, T) =− ℓ2t 972T 5/3t4/3 0 − ℓ2t 243T 4/3t4/3 0 + t 27T 1− ℓ2(t/t4 0)1/3 4t +...(18)","work_id":"04c509f3-74be-4ad4-8428-97dbb3a8ffed","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Radiation-dominated FLRW spacetime Coincidence : ∆(t, T) = 1 + ϵ2 8T 2 +O(ϵ 3) (19) Singularity : ∆(t, T) = ℓ2t3/2(5−2 log(t/T)) 4T 5/2t0(log(t/T)) 6 + t T 3/2 1 (log(t/T)) 3 +...(20) The different di","work_id":"3a5152f6-5256-40ac-a1d2-9eb12836aa08","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Matter-dominated FLRW spacetime Coincidence :2∆ 1/2(t, T) = 2 9T 2 (23) Singularity :2∆ 1/2(t, T)≃ 2267 2187 √ 21t2 (24)","work_id":"f0013f35-ba73-4245-8999-2ae475989184","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"∞X k=0 −1/2 k I2k(t′)α2k # dt′a(t′) (α2 +a 2(t′))3/2 = Z t T","work_id":"de47f8a0-783d-466d-bd56-9caf841e70b4","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1972,"title":"H. A.Buchdahl, Gen. Relativ. Gravit.3, 35 (1972)","work_id":"a3905415-eb6b-4bcc-bddf-f461de7e60a2","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":23,"snapshot_sha256":"81bda526329d3e9e9749f113b3048d44f2b956f70086f6f24928255c8567c04e","internal_anchors":6},"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"}