{"paper":{"title":"Primordial Black Hole Formation in $f(R)=R+\\alpha R^2$ Gravity: Perturbative and Non-Perturbative Analysis","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["astro-ph.CO","hep-th"],"primary_cat":"gr-qc","authors_text":"A. Eid, G.G.L. Nashed","submitted_at":"2026-01-03T09:47:38Z","abstract_excerpt":"We present a complete analytic and semi-analytic study of gravitational collapse and primordial black hole (PBH) formation in the quadratic $f(R)$ model $f(R)=R+\\alpha R^2$. We first derive the perturbative expansion around General Relativity (GR), working to first order in the small parameter $\\alpha$. For a collapsing flat FLRW dust interior we compute the explicit first-order corrections to the scale factor, the stellar radius, and the horizon formation time. { We then use these results to infer the expected trend in the PBH formation threshold $\\delta_c$, rather than a direct quantitative "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.02416","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/2601.02416/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"}