{"paper":{"title":"On the massive wave equation on slowly rotating Kerr-AdS spacetimes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG"],"primary_cat":"gr-qc","authors_text":"Gustav Holzegel","submitted_at":"2009-02-05T20:47:21Z","abstract_excerpt":"The massive wave equation $\\Box_g \\psi - \\alpha\\frac{\\Lambda}{3} \\psi = 0$ is studied on a fixed Kerr-anti de Sitter background $(\\mathcal{M},g_{M,a,\\Lambda})$. We first prove that in the Schwarzschild case (a=0), $\\psi$ remains uniformly bounded on the black hole exterior provided that $\\alpha < {9/4}$, i.e. the Breitenlohner-Freedman bound holds. Our proof is based on vectorfield multipliers and commutators: The usual energy current arising from the timelike Killing vector field $T$ (which fails to be non-negative pointwise) is shown to be non-negative with the help of a Hardy inequality aft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.0973","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"}