{"paper":{"title":"Type II Critical Collapse of a Self-Gravitating Nonlinear $\\sigma$-Model","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Christiane Lechner, Jonathan Thornburg, Michael P\\\"urrer, Peter C. Aichelburg, Sascha Husa","submitted_at":"2000-02-18T22:34:33Z","abstract_excerpt":"We report on the existence and phenomenology of type II critical collapse within the one-parameter family of SU(2) $\\sigma$-models coupled to gravity. Numerical investigations in spherical symmetry show discretely self-similar (DSS) behavior at the threshold of black hole formation for values of the dimensionless coupling constant $\\ccbeta$ ranging from 0.2 to 100; at 0.18 we see small deviations from DSS. While the echoing period $\\Delta$ of the critical solution rises sharply towards the lower limit of this range, the characteristic mass scaling has a critical exponent $\\gamma$ which is almo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0002067","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}