{"paper":{"title":"The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Chen-Kai Qiao","submitted_at":"2024-07-19T05:19:04Z","abstract_excerpt":"Photon sphere has attracted significant attention since the capture of black hole shadow images by Event Horizon Telescope. Recently, a number of studies have highlighted that the number of photon spheres and their distributions near black holes are strongly constrained by black hole properties. Specifically, for black holes with event horizons and proper asymptotic behaviors, the number of stable and unstable photon spheres satisfies the relation $n_{\\text{stable}} - n_{\\text{unstable}} = -1$. In this study, we provide a new proof on this relation using a geometric analysis, which is carried "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.14035","kind":"arxiv","version":5},"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/2407.14035/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"}