{"paper":{"title":"Free motion around black holes with discs or rings: between integrability and chaos -- IV","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","nlin.CD"],"primary_cat":"astro-ph.HE","authors_text":"O. Semerak, P. Sukova, V. Witzany","submitted_at":"2015-03-31T15:10:35Z","abstract_excerpt":"The dynamical system studied in previous papers of this series, namely a bound time-like geodesic motion in the exact static and axially symmetric space-time of an (originally) Schwarzschild black hole surrounded by a thin disc or ring, is considered to test whether the often employed \"pseudo-Newtonian\" approach (resorting to Newtonian dynamics in gravitational potentials modified to mimic the black-hole field) can reproduce phase-space properties observed in the relativistic treatment. By plotting Poincar\\'e surfaces of section and using two recurrence methods for similar situations as in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09077","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"}