{"paper":{"title":"Trilinear compensated compactness and Burnett's conjecture in general relativity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"gr-qc","authors_text":"C\\'ecile Huneau, Jonathan Luk","submitted_at":"2019-07-24T21:55:25Z","abstract_excerpt":"Consider a sequence of $C^4$ Lorentzian metrics $\\{h_n\\}_{n=1}^{+\\infty}$ on a manifold $\\mathcal M$ satisfying the Einstein vacuum equation $\\mathrm{Ric}(h_n)=0$. Suppose there exists a smooth Lorentzian metric $h_0$ on $\\mathcal M$ such that $h_n\\to h_0$ uniformly on compact sets. Assume also that on any compact set $K\\subset \\mathcal M$, there is a decreasing sequence of positive numbers $\\lambda_n \\to 0$ such that $$\\|\\partial^{\\alpha} (h_n - h_0)\\|_{L^{\\infty}(K)} \\lesssim \\lambda_n^{1-|\\alpha|},\\quad |\\alpha|\\geq 4.$$ It is well-known that $h_0$, which represents a \"high-frequency limit\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.10743","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1907.10743/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"}