{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:XNXKDPJKQX6IYU5QHCVVL3MVSK","short_pith_number":"pith:XNXKDPJK","schema_version":"1.0","canonical_sha256":"bb6ea1bd2a85fc8c53b038ab55ed9592b88415cba9e83fd62214099044ef08e6","source":{"kind":"arxiv","id":"1209.1272","version":3},"attestation_state":"computed","paper":{"title":"Where is the PdV term in the first law of black hole thermodynamics?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Brian P. Dolan","submitted_at":"2012-09-06T12:52:21Z","abstract_excerpt":"Traditional treatments of the first law of black hole thermodynamics do not include a discussion of pressure and volume. We give an overview of recent developments proposing a definition of volume that can be used to extend the first law to include these appropriately. New results are also presenting relating to the critical point and the associated second order phase transition for a rotating black-hole in four-dimensional space-time which is asymptotically anti-de Sitter. In line with known results for a non-rotating charged black-hole, this phase transition is shown to be of Van der Waals t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.1272","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-06T12:52:21Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"ce195a6cf57c9f3f54f5973ce78a05ec01685fbfe9530b6c3110ddf3b9931986","abstract_canon_sha256":"3e31df0a27aab3e491c8ebf45304d4043c1ee3989b5c8a8f01bbafe3695a5cbd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:34.966834Z","signature_b64":"UaFC5BB4iD0L+NCE2Y48DGl426NwM/crOpxV/JIKwWzT7HgshNB9fdCQ9k3lSZX/mIIlI7rzafT/zxhE0/z5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb6ea1bd2a85fc8c53b038ab55ed9592b88415cba9e83fd62214099044ef08e6","last_reissued_at":"2026-07-05T02:05:34.966421Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:34.966421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Where is the PdV term in the first law of black hole thermodynamics?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Brian P. Dolan","submitted_at":"2012-09-06T12:52:21Z","abstract_excerpt":"Traditional treatments of the first law of black hole thermodynamics do not include a discussion of pressure and volume. We give an overview of recent developments proposing a definition of volume that can be used to extend the first law to include these appropriately. New results are also presenting relating to the critical point and the associated second order phase transition for a rotating black-hole in four-dimensional space-time which is asymptotically anti-de Sitter. In line with known results for a non-rotating charged black-hole, this phase transition is shown to be of Van der Waals t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1272","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/1209.1272/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.1272","created_at":"2026-07-05T02:05:34.966474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.1272v3","created_at":"2026-07-05T02:05:34.966474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1272","created_at":"2026-07-05T02:05:34.966474+00:00"},{"alias_kind":"pith_short_12","alias_value":"XNXKDPJKQX6I","created_at":"2026-07-05T02:05:34.966474+00:00"},{"alias_kind":"pith_short_16","alias_value":"XNXKDPJKQX6IYU5Q","created_at":"2026-07-05T02:05:34.966474+00:00"},{"alias_kind":"pith_short_8","alias_value":"XNXKDPJK","created_at":"2026-07-05T02:05:34.966474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.06704","citing_title":"Joule-Thomson Effect and Geodesic Structure of Charged AdS Black Holes in f(R,T) Coupled with Nonlinear Electrodynamics","ref_index":91,"is_internal_anchor":true},{"citing_arxiv_id":"2606.30507","citing_title":"The Role of the Volume in Black Hole Thermodynamics","ref_index":42,"is_internal_anchor":false},{"citing_arxiv_id":"2605.16536","citing_title":"Quantum-statistical constraints on Kerr-anti-de Sitter thermodynamics","ref_index":26,"is_internal_anchor":false},{"citing_arxiv_id":"1608.06147","citing_title":"Black hole chemistry: thermodynamics with Lambda","ref_index":26,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK","json":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK.json","graph_json":"https://pith.science/api/pith-number/XNXKDPJKQX6IYU5QHCVVL3MVSK/graph.json","events_json":"https://pith.science/api/pith-number/XNXKDPJKQX6IYU5QHCVVL3MVSK/events.json","paper":"https://pith.science/paper/XNXKDPJK"},"agent_actions":{"view_html":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK","download_json":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK.json","view_paper":"https://pith.science/paper/XNXKDPJK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.1272&json=true","fetch_graph":"https://pith.science/api/pith-number/XNXKDPJKQX6IYU5QHCVVL3MVSK/graph.json","fetch_events":"https://pith.science/api/pith-number/XNXKDPJKQX6IYU5QHCVVL3MVSK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK/action/storage_attestation","attest_author":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK/action/author_attestation","sign_citation":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK/action/citation_signature","submit_replication":"https://pith.science/pith/XNXKDPJKQX6IYU5QHCVVL3MVSK/action/replication_record"}},"created_at":"2026-07-05T02:05:34.966474+00:00","updated_at":"2026-07-05T02:05:34.966474+00:00"}