{"paper":{"title":"General Relativistic Shock Wave Solutions with Black Hole Formation: The Singular Isothermal Sphere Case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO","astro-ph.GA","gr-qc"],"primary_cat":"astro-ph.HE","authors_text":"(2) Google, (3) CfA/SAO), Chien-Ting J. Chen (1), Fabio Pacucci (3) ((1) USRA/NASA MSFC, Michael J. Cai (2)","submitted_at":"2026-06-28T21:18:59Z","abstract_excerpt":"The rapid emergence at $z\\gtrsim 6$ of ubiquitous populations of supermassive black holes (SMBHs) revealed by JWST and of quasars with estimated masses $M_\\bullet > 10^{10} M_\\odot$ demands efficient pathways for early growth. The smooth collapse of a singular isothermal sphere (SIS) has been solved analytically in full general relativity, but the shock waves that inevitably accompany such collapse have not. Here, we derive general-relativistic self-similar shock-wave solutions for the collapse of an SIS to a black hole, extending the framework of Cai \\& Shu (2005) to discontinuous flows. We o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29607","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29607/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"}