{"paper":{"title":"Periodic orbits and their gravitational wave radiations around the Schwarzschild-MOG black hole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA"],"primary_cat":"gr-qc","authors_text":"Mubasher Jamil, Mustapha Azreg-A\\\"inou, Oreeda Shabbir","submitted_at":"2025-01-08T09:12:50Z","abstract_excerpt":"This article explores the motion of massive particles in the gravitational field of a modified gravity (MOG) black hole (BH), characterized by the parameter $\\alpha$. Using the Hamiltonian formalism, the geodesic equations and the effective potential governing particle trajectories are derived. Key features, including the innermost stable circular orbit (ISCO) and the innermost bound circular orbit (IBCO), are analyzed, revealing their dependence on the particle's energy, angular momentum, and the MOG parameter. In the extremal case, where $\\alpha=-1$, the event horizon merges with the Cauchy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.04367","kind":"arxiv","version":2},"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/2501.04367/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"}