{"paper":{"title":"Quasilinear wave equations on Kerr black holes in the full subextremal range $|a|<M$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.AP","math.DG","math.MP"],"primary_cat":"gr-qc","authors_text":"Gustav Holzegel, Igor Rodnianski, Martin Taylor, Mihalis Dafermos","submitted_at":"2024-10-04T17:44:21Z","abstract_excerpt":"We prove global existence, boundedness and decay for small data solutions $\\psi$ to a general class of quasilinear wave equations on Kerr black hole backgrounds in the full sub-extremal range $|a|<M$. The method extends our previous [DHRT22], which considered such equations on a wide class of background spacetimes, including Kerr, but restricted in that case to the very slowly rotating regime $|a|\\ll M$ (which may be treated simply as a perturbation of Schwarzschild $a=0$). To handle the general $|a|<M$ case, our present proof is based on two ingredients: (i) the linear inhomogeneous estimates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.03639","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/2410.03639/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"}