{"paper":{"title":"Gravitational Enstrophy: Local Geometric Origin and Inverse-Cascade Constraints","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["astro-ph.HE","hep-th"],"primary_cat":"gr-qc","authors_text":"Luis Lehner","submitted_at":"2026-08-04T14:01:20Z","abstract_excerpt":"Two-dimensional fluids conserve energy and enstrophy, driving inverse energy cascades via Fj\\o rtoft's argument. We show General Relativity admits an analogous structure: for linear radiative perturbations of Petrov type D backgrounds (Kerr, Kerr--AdS), the gravitational-wave energy $W = \\sum_k W_k$ and magnetic Weyl enstrophy $\\mathcal{Z} = \\int B_{ab} B^{ab} \\sqrt{\\gamma} \\, d^3x \\approx \\sum_k \\omega_k^2 W_k$ are approximately conserved in the zero-angular momentum frame, where vorticity coupling vanishes identically and curl exchange cancels mode-by-mode. This yields a gravitational Fj\\o r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03697","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03697/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}