{"paper":{"title":"Small-amplitude nonlinear waves on a black hole background","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Igor Rodnianski, Mihalis Dafermos","submitted_at":"2005-03-01T20:51:02Z","abstract_excerpt":"Let G(x) be a C^0 function such that |G(x)|\\le K|x|^{p} for |x|\\le c, for constants K,c>0. We consider spherically symmetric solutions of \\Box_g\\phi=G(\\phi) where g is a Schwarzschild or more generally a Reissner-Nordstrom metric, and such that \\phi and \\nabla \\phi are compactly supported on a complete Cauchy surface. It is proven that for p> 4, such solutions do not blow up in the domain of outer communications, provided the initial data are small. Moreover, |\\phi|\\le C(\\max\\{v,1\\})^{-1}, where v denotes an Eddington-Finkelstein advanced time coordinate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503024","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":""},"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"}