{"paper":{"title":"A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Avy Soffer, Roland Donninger, Wilhelm Schlag","submitted_at":"2009-08-28T21:14:31Z","abstract_excerpt":"Price's Law states that linear perturbations of a Schwarzschild black hole fall off as $t^{-2\\ell-3}$ for $t \\to \\infty$ provided the initial data decay sufficiently fast at spatial infinity. Moreover, if the perturbations are initially static (i.e., their time derivative is zero), then the decay is predicted to be $t^{-2\\ell-4}$. We give a proof of $t^{-2\\ell-2}$ decay for general data in the form of weighted $L^1$ to $L^\\infty$ bounds for solutions of the Regge--Wheeler equation. For initially static perturbations we obtain $t^{-2\\ell-3}$. The proof is based on an integral representation of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4292","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":""},"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"}