{
  "id": "1711.10011",
  "version": "v1",
  "published": "2017-11-27T21:42:02.000Z",
  "updated": "2017-11-27T21:42:02.000Z",
  "title": "Kähler metrics via Lorentzian Geometry in dimension four",
  "authors": [
    "Amir Babak Aazami",
    "Gideon Maschler"
  ],
  "comment": "1 table",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\\\"ahler metrics $\\gK$ is constructed, defined on an open set in $M$, which coincides with $M$ in many typical examples. Under certain conditions $g$ and $\\gK$ share various properties, such as a Killing vector field or a vector field with a geodesic flow. The Ricci and scalar curvatures of $\\gK$ are computed in some cases in terms of data associated to $g$. Many examples are described, including classical spacetimes in warped products, for instance de Sitter spacetime, as well as gravitational plane waves, metrics of Petrov type~$D$ such as Kerr and NUT metrics, and metrics for which $\\gK$ is an SKR metric. For the latter an inverse ansatz is described, constructing $g$ from the SKR metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-27T21:42:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C50",
      "53C55",
      "83C60",
      "83C20"
    ],
    "keywords": [
      "kähler metrics",
      "lorentzian geometry",
      "skr metric",
      "gravitational plane waves",
      "lie bracket relations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}