{
  "id": "2209.15610",
  "version": "v1",
  "published": "2022-09-30T17:35:20.000Z",
  "updated": "2022-09-30T17:35:20.000Z",
  "title": "Global hyperbolicity through the eyes of the null distance",
  "authors": [
    "Annegret Burtscher",
    "Leonardo García-Heveling"
  ],
  "comment": "34 pages, 4 figures",
  "categories": [
    "math.DG",
    "gr-qc",
    "math-ph",
    "math.MG",
    "math.MP"
  ],
  "abstract": "No Hopf--Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a suitable time function. Our approach is based on the observation that null distances behave particularly well for temporal functions, leading also to bi-Lipschitz equivalences and the encoding of the causal relation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-30T17:35:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C50",
      "53C23",
      "53B30",
      "83C05"
    ],
    "keywords": [
      "global hyperbolicity",
      "null distances behave",
      "lorentzian geometry",
      "hopf-rinow theorem",
      "suitable time function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}