{
  "id": "1304.0407",
  "version": "v2",
  "published": "2013-04-01T18:17:08.000Z",
  "updated": "2014-10-16T14:43:57.000Z",
  "title": "Radiation field for Einstein vacuum equations with spacial dimension $n\\geq 4$",
  "authors": [
    "Fang Wang"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "In this paper, the radiation field is defined for solutions to Einstein vacuum equations which are close to Minkowski space-time with spacial dimension $n\\geq 4$. The regularity properties and asymptotic behavior of those Einstein vacuum solutions are established at the same time. In particular, the map from Cauchy intial data to the radiation field is proved to be an isomorphism when restricting to a small neighborhood of Minkowski data in suitable weighted b-Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-01T18:17:08.000Z",
      "abstract": "In this paper, I study the asymptotic behavior of solutions to Einstein Vacuum equations with spacial dimension $n\\geq 4$ and show that the M{\\o}ller wave operator defines a continuous and open map from small initial data in suitable weighted Sobolev space at $t=0$ to the Radiation field in another weighted Sobolev space at null infinity.",
      "comment": "arXiv admin note: text overlap with arXiv:math/0411109 by other authors",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-16T14:43:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "einstein vacuum equations",
      "radiation field",
      "spacial dimension",
      "wave operator defines",
      "small initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.0407W"
    }
  }
}