{
  "id": "2104.03805",
  "version": "v1",
  "published": "2021-04-08T14:31:25.000Z",
  "updated": "2021-04-08T14:31:25.000Z",
  "title": "Light-like parallel vector fields and Einstein equations of gravity",
  "authors": [
    "Isidore Mahara",
    "Célestin Kurujyibwami",
    "Venuste Nyagahakwa"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that, contrary to the situation with time-like and space-like parallel vector fields, there are real gravitational fields satisfying Einsteins equations of gravity and admitting nontrivial light-like parallel vector fields; we solve completely the field equations under this geometric constraint and obtain through Bianchi identities an interesting property for the Riemann curvature tensor corresponding with a real gravitational field admitting a nontrivial parallel vector field. The solutions we obtained turn out to be generically wave-like and then we prove by a geometric method that this class of solutions is quite different from the class of solutions corresponding with spherical waves.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-08T14:31:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "einstein equations",
      "fields satisfying einsteins equations",
      "gravitational fields satisfying einsteins",
      "real gravitational field",
      "nontrivial light-like parallel vector fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}