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If the particle is endowed with mass $\\mu(\\ll M)$, it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts $\\Delta r_{\\rm isco}$ and $\\Delta\\Omega_{\\rm isco}$ in the ISCO's radius and frequency, at leading order in the mass ratio $\\mu/M$. We obtain, in the Lorenz gauge, $\\Delta r_{\\rm isco}=-3.269 (\\pm 0.003)\\mu G/c^2$ and $\\Delta\\Omega_{\\rm isco}/\\Omega_{\\rm is"},"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":"0902.0573","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2009-02-03T18:10:58Z","cross_cats_sorted":["astro-ph.HE"],"title_canon_sha256":"a950c76b5f7dc9da4b8885357da95f154f5c7256f0f2c5b7757c5675ef3415d8","abstract_canon_sha256":"913c7808cafe41f352cf49f3ddc0aeb8e8d21a282f3146ecf6559f1c90e772e8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:45:14.687747Z","signature_b64":"DYS4kv2htLyRVTegK3+hG2KRTOg6Asp2eDjI0ZtgBEtjmUNE5gFmDfId94hTLEbZctAmfx/sUeCDx5sU7hSEAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33a4fd915010929808819edcc000ab15017fd799e5a3d0a8de71246568df90f6","last_reissued_at":"2026-07-04T15:45:14.687309Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:45:14.687309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gravitational self-force correction to the innermost stable circular orbit of a Schwarzschild black hole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.HE"],"primary_cat":"gr-qc","authors_text":"Leor Barack, Norichika Sago","submitted_at":"2009-02-03T18:10:58Z","abstract_excerpt":"The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass $M$ has (areal) radius $r_{\\rm isco}= 6M G/c^2$. If the particle is endowed with mass $\\mu(\\ll M)$, it experiences a gravitational self-force whose conservative piece alters the location of the ISCO. Here we calculate the resulting shifts $\\Delta r_{\\rm isco}$ and $\\Delta\\Omega_{\\rm isco}$ in the ISCO's radius and frequency, at leading order in the mass ratio $\\mu/M$. We obtain, in the Lorenz gauge, $\\Delta r_{\\rm isco}=-3.269 (\\pm 0.003)\\mu G/c^2$ and $\\Delta\\Omega_{\\rm isco}/\\Omega_{\\rm is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0573","kind":"arxiv","version":2},"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/0902.0573/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":"0902.0573","created_at":"2026-07-04T15:45:14.687388+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.0573v2","created_at":"2026-07-04T15:45:14.687388+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.0573","created_at":"2026-07-04T15:45:14.687388+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOSP3EKQCCJJ","created_at":"2026-07-04T15:45:14.687388+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOSP3EKQCCJJQCEB","created_at":"2026-07-04T15:45:14.687388+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOSP3EKQ","created_at":"2026-07-04T15:45:14.687388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2509.09986","citing_title":"Plunge spectra as discriminators of black hole mimickers","ref_index":54,"is_internal_anchor":true},{"citing_arxiv_id":"2510.16113","citing_title":"Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary","ref_index":140,"is_internal_anchor":true},{"citing_arxiv_id":"2112.06861","citing_title":"Tests of General Relativity with GWTC-3","ref_index":119,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU","json":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU.json","graph_json":"https://pith.science/api/pith-number/GOSP3EKQCCJJQCEBT3OMAAFLCU/graph.json","events_json":"https://pith.science/api/pith-number/GOSP3EKQCCJJQCEBT3OMAAFLCU/events.json","paper":"https://pith.science/paper/GOSP3EKQ"},"agent_actions":{"view_html":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU","download_json":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU.json","view_paper":"https://pith.science/paper/GOSP3EKQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.0573&json=true","fetch_graph":"https://pith.science/api/pith-number/GOSP3EKQCCJJQCEBT3OMAAFLCU/graph.json","fetch_events":"https://pith.science/api/pith-number/GOSP3EKQCCJJQCEBT3OMAAFLCU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU/action/storage_attestation","attest_author":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU/action/author_attestation","sign_citation":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU/action/citation_signature","submit_replication":"https://pith.science/pith/GOSP3EKQCCJJQCEBT3OMAAFLCU/action/replication_record"}},"created_at":"2026-07-04T15:45:14.687388+00:00","updated_at":"2026-07-04T15:45:14.687388+00:00"}