{"paper":{"title":"The Role of the Volume in Black Hole Thermodynamics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"William Ballik","submitted_at":"2026-06-29T16:13:54Z","abstract_excerpt":"Gibbons et al. [arXiv:hep-th/0408217] found the energy $E$ of Kerr--anti-de Sitter black holes by integrating the first law of black hole thermodynamics. They found that $E$ corresponds to the Ashtekar--Magnon--Das (AMD) energy associated with an asymptotically nonrotating frame, whereas the AMD ``energy'' which I will call $F$ associated with an asymptotically rotating frame does not satisfy the first law. In Cveti\\v{c} et al. [arXiv:1012.2888], the first law was extended by interpreting $E$ as an enthalpy and $\\Lambda$ as being proportional to a pressure. The term conjugate to the pressure w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30507","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.30507/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"}