{"paper":{"title":"Asymptotic Behavior of Massless Dirac Waves in Schwarzschild geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Chunjing Xie, Joel Smoller","submitted_at":"2011-04-14T14:15:01Z","abstract_excerpt":"In this paper, we show that massless Dirac waves in the Schwarzschild geometry decay to zero at a rate $t^{-2\\lambda}$, where $\\lambda=1, 2,...$ is the angular momentum. Our technique is to use Chandrasekhar's separation of variables whereby the Dirac equations split into two sets of wave equations. For the first set, we show that the wave decays as $t^{-2\\lambda}$. For the second set, in general, the solutions tend to some explicit profile at the rate $t^{-2\\lambda}$. The decay rate of solutions of Dirac equations is achieved by showing that the coefficient of the explicit profile is exactly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2772","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"}