{"paper":{"title":"Gaussian curvature and Lyapunov exponent as probes of black hole phase transitions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Jing-Fei Zhang, Shi-Hao Zhang, Xin Zhang, Zi-Qiang Zhao, Zi-Yuan Li","submitted_at":"2025-09-05T13:39:55Z","abstract_excerpt":"First-order phase transitions of black holes have been extensively studied within thermodynamic frameworks, yet the corresponding evolution of spacetime geometric properties remains unclear. This paper establishes a purely differential geometric framework to probe such phase transitions by analyzing the curvature of unstable null orbits. Using the geodesic curvature of the null circular orbit in the optical metric to locate the light ring, we demonstrate that the corresponding Gaussian curvature $K$ serves as a direct geometric signature of the phase transition. During a first-order phase tran"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05103","kind":"arxiv","version":3},"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/2509.05103/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"}