{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:P5FRXF5PXPHE6KZNK2X732TZUW","short_pith_number":"pith:P5FRXF5P","schema_version":"1.0","canonical_sha256":"7f4b1b97afbbce4f2b2d56affdea79a5b9f65c8a38931c198f3cc97abc4af7ae","source":{"kind":"arxiv","id":"1806.06596","version":1},"attestation_state":"computed","paper":{"title":"Black Hole Topology in $f(R)$ Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Akash K Mishra, Mostafizur Rahman, Sudipta Sarkar","submitted_at":"2018-06-18T10:56:43Z","abstract_excerpt":"Hawking's topology theorem in general relativity restricts the cross-section of the event horizon of a black hole in $3+1$ dimension to be either spherical or toroidal. The toroidal case is ruled out by the topology censorship theorems. In this article, we discuss the generalization of this result to black holes in $f(R)$ gravity in $3+1$ and higher dimensions. We obtain a sufficient differential condition on the function $f'(R)$, which restricts the topology of the horizon cross-section of a black hole in $f(R)$ gravity in $3+1$ dimension to be either $S^2$ or $S^1 \\times S^1$. We also extend"},"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":"1806.06596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-06-18T10:56:43Z","cross_cats_sorted":[],"title_canon_sha256":"137f139f829ab4c6a36adccf55948fd1b778d525969873fb7be43680677b7271","abstract_canon_sha256":"289cf6ac7677a53a0d470edbaf147ac94a355898d291e7dd248505095795e499"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:04.467110Z","signature_b64":"csAd8pcqk0yVxvLgK9oxXnlWUiQLmwvFj74ztOxuVrXuz658MLTL2HeXUYzH61arl0a5CZn4KVRdXAvuo6UOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f4b1b97afbbce4f2b2d56affdea79a5b9f65c8a38931c198f3cc97abc4af7ae","last_reissued_at":"2026-05-18T00:11:04.466338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:04.466338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Black Hole Topology in $f(R)$ Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Akash K Mishra, Mostafizur Rahman, Sudipta Sarkar","submitted_at":"2018-06-18T10:56:43Z","abstract_excerpt":"Hawking's topology theorem in general relativity restricts the cross-section of the event horizon of a black hole in $3+1$ dimension to be either spherical or toroidal. The toroidal case is ruled out by the topology censorship theorems. In this article, we discuss the generalization of this result to black holes in $f(R)$ gravity in $3+1$ and higher dimensions. We obtain a sufficient differential condition on the function $f'(R)$, which restricts the topology of the horizon cross-section of a black hole in $f(R)$ gravity in $3+1$ dimension to be either $S^2$ or $S^1 \\times S^1$. We also extend"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06596","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":"1806.06596","created_at":"2026-05-18T00:11:04.466478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.06596v1","created_at":"2026-05-18T00:11:04.466478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.06596","created_at":"2026-05-18T00:11:04.466478+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5FRXF5PXPHE","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5FRXF5PXPHE6KZN","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5FRXF5P","created_at":"2026-05-18T12:32:43.782077+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/P5FRXF5PXPHE6KZNK2X732TZUW","json":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW.json","graph_json":"https://pith.science/api/pith-number/P5FRXF5PXPHE6KZNK2X732TZUW/graph.json","events_json":"https://pith.science/api/pith-number/P5FRXF5PXPHE6KZNK2X732TZUW/events.json","paper":"https://pith.science/paper/P5FRXF5P"},"agent_actions":{"view_html":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW","download_json":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW.json","view_paper":"https://pith.science/paper/P5FRXF5P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.06596&json=true","fetch_graph":"https://pith.science/api/pith-number/P5FRXF5PXPHE6KZNK2X732TZUW/graph.json","fetch_events":"https://pith.science/api/pith-number/P5FRXF5PXPHE6KZNK2X732TZUW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW/action/storage_attestation","attest_author":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW/action/author_attestation","sign_citation":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW/action/citation_signature","submit_replication":"https://pith.science/pith/P5FRXF5PXPHE6KZNK2X732TZUW/action/replication_record"}},"created_at":"2026-05-18T00:11:04.466478+00:00","updated_at":"2026-05-18T00:11:04.466478+00:00"}