{"paper":{"title":"Growth of Perturbation in Gravitational Collapse and Accretion","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Dong Lai (Cornell), Peter Goldreich (Caltech)","submitted_at":"1999-06-25T03:07:47Z","abstract_excerpt":"When a self-gravitating spherical gas cloud collapses or accretes onto a central mass, the inner region of the cloud develops a density profile $\\rho\\propto r^{-3/2}$ and the velocity approaches free-fall. We show that in this region, nonspherical perturbations grow with decreasing radius. In the linear regime, the tangential velocity perturbation increases as $r^{-1}$, while the Lagrangian density perturbation, $\\Delta\\rho/\\rho$, grows as $r^{-1/2}$. Faster growth occurs if the central collapsed object maintains a finite multiple moment, in which case $\\Delta\\rho/\\rho$ increases as $r^{-l}$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9906400","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/astro-ph/9906400/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"}