{"paper":{"title":"Curved Space, curved Time, and curved Space-Time in Schwarzschild geodetic geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Lorenzo Resca, Nicholas A. Mecholsky, Rafael T. Eufrasio","submitted_at":"2018-12-08T03:20:14Z","abstract_excerpt":"We investigate geodesic orbits and manifolds for metrics associated with Schwarzschild geometry, considering space and time curvatures separately. For `a-temporal' space, we solve a central geodesic orbit equation in terms of elliptic integrals. The intrinsic geometry of a two-sided equatorial plane corresponds to that of a full Flamm's paraboloid. Two kinds of geodesics emerge. Both kinds may or may not encircle the hole region any number of times, crossing themselves correspondingly. Regular geodesics reach a periastron greater than the $r_S$ Schwarzschild radius, thus remaining confined to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.03259","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":""},"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"}