{"paper":{"title":"The existence and upper bound for stable photon spheres in static spherically symmetric black holes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Jiaqi Fu, Yiting Cen, Yong Song","submitted_at":"2025-08-27T12:14:20Z","abstract_excerpt":"In this work, we establish the existence conditions and a universal upper bound on the radius of stable photon spheres (SPS) outside the event horizons of static, spherically symmetric, asymptotically flat black holes surrounded by matter fields. We prove that stable photon spheres exist if the external matter satisfies specific conditions. Furthermore, under the additional assumption of a monotonically decreasing mass-radius ratio $m(r)/r^3$ outside the horizon, we derive a strict upper bound on the radius $r_{\\mathrm{sps}}$ of any stable photon sphere: $r_{\\mathrm{sps}}<6M$, where $M$ is the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.19823","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/2508.19823/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"}