{
  "id": "2107.00942",
  "version": "v1",
  "published": "2021-07-02T10:04:16.000Z",
  "updated": "2021-07-02T10:04:16.000Z",
  "title": "Oscillations in wave map systems and homogenization of the Einstein equations in symmetry",
  "authors": [
    "André Guerra",
    "Rita Teixeira da Costa"
  ],
  "comment": "28 pages, 1 figure",
  "categories": [
    "math.AP",
    "gr-qc"
  ],
  "abstract": "In 1989, Burnett conjectured that, under appropriate assumptions, the limit of highly oscillatory solutions to the Einstein vacuum equations is a solution of the Einstein--massless Vlasov system. In a recent breakthrough, Huneau--Luk (arXiv:1907.10743) gave a proof of the conjecture in U(1)-symmetry and elliptic gauge. They also require control on up to fourth order derivatives of the metric components. In this paper, we give a streamlined proof of a stronger result and, in the spirit of Burnett's original conjecture, we remove the need for control on higher derivatives. Our methods also apply to general wave map equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-02T10:04:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wave map systems",
      "einstein equations",
      "oscillations",
      "general wave map equations",
      "homogenization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}