{"paper":{"title":"Note on Legendre decomposition of the Pontryagin density in Kerr","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Leo C. Stein","submitted_at":"2014-07-02T23:43:39Z","abstract_excerpt":"In arXiv:1406.0957v1 (\"Scalar field excited around a rapidly rotating black hole in Chern-Simons modified gravity\"), Konno and Takahashi have recently developed some analytical results for the scalar field about a Kerr black hole in the decoupling limit of dynamical Chern-Simons gravity. This involved a decomposition of the source (the Pontryagin density) in terms of Legendre polynomials. Here we give a two-line expression for this decomposition which simplifies their quadruple sum. Our expressions are rational polynomials multiplying Legendre functions of the second kind, or equivalently rati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0744","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"}