General Relativity and Gravitation

, Volume 25, Issue 10, pp 1009–1018 | Cite as

AG 2 II algebraically general twistfree vacuum spacetime

  • Duong Phan
Research Articles
  • 34 Downloads

Abstract

Several authors, e.g., Kerr and Debney (1970), Lun (1978), have obtained severalG 2 II algebraically special vacuum solutions. NoG 2 II algebraically general vacuum solutions in explicit form have been found before. In this paper, we start from a system of first order partial differential equations, obtained by using a triad formalism, which determines twistfree vacuum metrics with a spacelike Killing vector. The method of group-invariant solutions is then used and aG 2 II algebraically general twistfree vacuum solution is obtained. The solution also admits a homothetic Killing vector and is non-geodesic. It is believed to be new. The following explicit solutions are also obtained: (1) A Petrov type II with aG1-group of motions solution which belongs to Kundt's class. (2) A Petrov type III,G3 Robinson-Trautman solution. All these solutions are known.

Keywords

Differential Equation Partial Differential Equation Triad Explicit Form Differential Geometry 

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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Duong Phan
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SydneyAustralia

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