{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:7U3CES7BOZNCPSTR3GPWATLLNF","short_pith_number":"pith:7U3CES7B","schema_version":"1.0","canonical_sha256":"fd36224be1765a27ca71d99f604d6b697e4c3b02b7575f031d7733e4e72fee01","source":{"kind":"arxiv","id":"2412.14831","version":2},"attestation_state":"computed","paper":{"title":"Tidal Love numbers and quasi-normal modes of the Schwarzschild-Hernquist black hole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA"],"primary_cat":"gr-qc","authors_text":"Geoffrey Comp\\`ere, Ludovico Machet, Sumanta Chakraborty","submitted_at":"2024-12-19T13:20:01Z","abstract_excerpt":"We derive the model of the Schwarzschild black hole immersed into a dark matter halo with a relativistic Hernquist profile, the Schwarzschild-Hernquist black hole, and obtain its tidal Love numbers and quasi-normal modes. We thoroughly compare our odd and even parity perturbation equations with the literature and point out that two distinct choices of matter perturbations lead to distinct spectra. We establish that the quasi-normal modes admit qualitatively distinct scaling laws in terms of dark matter densities for non-relativistic and relativistic halos. We develop a stable numerical scheme "},"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":"2412.14831","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-12-19T13:20:01Z","cross_cats_sorted":["astro-ph.GA"],"title_canon_sha256":"26c57fe9a6a229ad0b1590c7ed7f5d897ac375679da328e800f2aa29fffc962a","abstract_canon_sha256":"188bf1306f629fd52affb853b6aea97e20be837e2be0e1d64e8cfadb15c8a278"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:40:59.707613Z","signature_b64":"02gJmJkVI5jPTGF38HP1begPDDYaEvV9xXh206G7c9g30XLmWJOhSaHPqUT6s+LkPzb+N3vT0OmRIeMKCpM5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd36224be1765a27ca71d99f604d6b697e4c3b02b7575f031d7733e4e72fee01","last_reissued_at":"2026-07-05T10:40:59.707029Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:40:59.707029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tidal Love numbers and quasi-normal modes of the Schwarzschild-Hernquist black hole","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.GA"],"primary_cat":"gr-qc","authors_text":"Geoffrey Comp\\`ere, Ludovico Machet, Sumanta Chakraborty","submitted_at":"2024-12-19T13:20:01Z","abstract_excerpt":"We derive the model of the Schwarzschild black hole immersed into a dark matter halo with a relativistic Hernquist profile, the Schwarzschild-Hernquist black hole, and obtain its tidal Love numbers and quasi-normal modes. We thoroughly compare our odd and even parity perturbation equations with the literature and point out that two distinct choices of matter perturbations lead to distinct spectra. We establish that the quasi-normal modes admit qualitatively distinct scaling laws in terms of dark matter densities for non-relativistic and relativistic halos. We develop a stable numerical scheme "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.14831","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/2412.14831/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":"2412.14831","created_at":"2026-07-05T10:40:59.707107+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.14831v2","created_at":"2026-07-05T10:40:59.707107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.14831","created_at":"2026-07-05T10:40:59.707107+00:00"},{"alias_kind":"pith_short_12","alias_value":"7U3CES7BOZNC","created_at":"2026-07-05T10:40:59.707107+00:00"},{"alias_kind":"pith_short_16","alias_value":"7U3CES7BOZNCPSTR","created_at":"2026-07-05T10:40:59.707107+00:00"},{"alias_kind":"pith_short_8","alias_value":"7U3CES7B","created_at":"2026-07-05T10:40:59.707107+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":6,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.11380","citing_title":"Quasinormal modes and tidal responses of black holes in generic anisotropic matter environments","ref_index":21,"is_internal_anchor":false},{"citing_arxiv_id":"2512.05767","citing_title":"Tidal Love numbers for regular black holes","ref_index":46,"is_internal_anchor":false},{"citing_arxiv_id":"2605.11364","citing_title":"Bardeen spacetime as quantum corrected black hole: Grey-body factors and quasinormal modes of gravitational perturbations","ref_index":64,"is_internal_anchor":false},{"citing_arxiv_id":"2605.03025","citing_title":"Can wormholes have vanishing Love numbers?","ref_index":53,"is_internal_anchor":false},{"citing_arxiv_id":"2605.00693","citing_title":"Dynamical tidal Love numbers of black holes under generic perturbations: Connecting black hole perturbation theory with effective field theory","ref_index":66,"is_internal_anchor":false},{"citing_arxiv_id":"2605.02633","citing_title":"Axial tidal Love numbers of black holes in matter environments","ref_index":64,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF","json":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF.json","graph_json":"https://pith.science/api/pith-number/7U3CES7BOZNCPSTR3GPWATLLNF/graph.json","events_json":"https://pith.science/api/pith-number/7U3CES7BOZNCPSTR3GPWATLLNF/events.json","paper":"https://pith.science/paper/7U3CES7B"},"agent_actions":{"view_html":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF","download_json":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF.json","view_paper":"https://pith.science/paper/7U3CES7B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.14831&json=true","fetch_graph":"https://pith.science/api/pith-number/7U3CES7BOZNCPSTR3GPWATLLNF/graph.json","fetch_events":"https://pith.science/api/pith-number/7U3CES7BOZNCPSTR3GPWATLLNF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF/action/storage_attestation","attest_author":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF/action/author_attestation","sign_citation":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF/action/citation_signature","submit_replication":"https://pith.science/pith/7U3CES7BOZNCPSTR3GPWATLLNF/action/replication_record"}},"created_at":"2026-07-05T10:40:59.707107+00:00","updated_at":"2026-07-05T10:40:59.707107+00:00"}