{
  "id": "1205.1702",
  "version": "v4",
  "published": "2012-05-08T14:05:20.000Z",
  "updated": "2012-12-25T23:20:09.000Z",
  "title": "Generalized de Sitter Space in $n$-dimensional Minkowski Space",
  "authors": [
    "David N. Pham"
  ],
  "comment": "13 pages, minor revisions",
  "categories": [
    "math.DG",
    "gr-qc"
  ],
  "abstract": "In this paper, we generalize the defining equation for de Sitter space by replacing the de Sitter radius with a function $f$ satisfying certain conditions; each resulting hypersurface is diffeomorphic to de Sitter space, and has a geometry (and causal character) which is controlled by the choice of $f$. Necessary and sufficient conditions are obtained for a hypersurface to be timelike, null, or spacelike in the generalized model; in the non-null case, the geometry is given by a warped product. Several examples of timelike, null, and spacelike hypersurfaces are presented. Lastly, we calculate the Ricci tensor and scalar curvature for a special family of 4-dimensional generalized de Sitter spaces.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-12-25T23:20:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C50"
    ],
    "keywords": [
      "sitter space",
      "dimensional minkowski space",
      "generalize",
      "hypersurface",
      "sitter radius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1113900,
      "adsabs": "2012arXiv1205.1702P"
    }
  }
}