{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:F2RAN525QHGGKF5YELECMVFKZF","short_pith_number":"pith:F2RAN525","schema_version":"1.0","canonical_sha256":"2ea206f75d81cc6517b822c82654aac949efbc5e840cc62da55058b1740b8a3f","source":{"kind":"arxiv","id":"0903.4723","version":1},"attestation_state":"computed","paper":{"title":"On Hawking's Local Rigidity Theorems for Charged Black Holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Pin Yu","submitted_at":"2009-03-27T01:35:58Z","abstract_excerpt":"We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, R\\'{a}cz and Wald, which was limited to the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field $T$ which tangent to the horizon and not vanishing on the bifurcate sphere, then space-time must be locally axially symmetric without the analyticity assumption. This axial symm"},"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":"0903.4723","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-03-27T01:35:58Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"ed6b4416cb11b9e69110c3abe6164e65a8787f63d6d0ad313d2dd4019c4723b1","abstract_canon_sha256":"55ef9bcea8616ee3f6258b3c671c5dfd4361c78b26a88d20fa9847bdb1384159"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:00.120556Z","signature_b64":"1KKajFu1zDpawywT68V+rYDydWPsGmsCM9cdJdbDixgF78fg0DMMKrnmeHI55+ZiM3+Ue0ZkJIyyA3lT0lUsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea206f75d81cc6517b822c82654aac949efbc5e840cc62da55058b1740b8a3f","last_reissued_at":"2026-05-18T02:35:00.119985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:00.119985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Hawking's Local Rigidity Theorems for Charged Black Holes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"gr-qc","authors_text":"Pin Yu","submitted_at":"2009-03-27T01:35:58Z","abstract_excerpt":"We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, R\\'{a}cz and Wald, which was limited to the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field $T$ which tangent to the horizon and not vanishing on the bifurcate sphere, then space-time must be locally axially symmetric without the analyticity assumption. This axial symm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4723","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":""},"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":"0903.4723","created_at":"2026-05-18T02:35:00.120069+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.4723v1","created_at":"2026-05-18T02:35:00.120069+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.4723","created_at":"2026-05-18T02:35:00.120069+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2RAN525QHGG","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2RAN525QHGGKF5Y","created_at":"2026-05-18T12:25:59.703012+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2RAN525","created_at":"2026-05-18T12:25:59.703012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF","json":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF.json","graph_json":"https://pith.science/api/pith-number/F2RAN525QHGGKF5YELECMVFKZF/graph.json","events_json":"https://pith.science/api/pith-number/F2RAN525QHGGKF5YELECMVFKZF/events.json","paper":"https://pith.science/paper/F2RAN525"},"agent_actions":{"view_html":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF","download_json":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF.json","view_paper":"https://pith.science/paper/F2RAN525","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.4723&json=true","fetch_graph":"https://pith.science/api/pith-number/F2RAN525QHGGKF5YELECMVFKZF/graph.json","fetch_events":"https://pith.science/api/pith-number/F2RAN525QHGGKF5YELECMVFKZF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF/action/storage_attestation","attest_author":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF/action/author_attestation","sign_citation":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF/action/citation_signature","submit_replication":"https://pith.science/pith/F2RAN525QHGGKF5YELECMVFKZF/action/replication_record"}},"created_at":"2026-05-18T02:35:00.120069+00:00","updated_at":"2026-05-18T02:35:00.120069+00:00"}