Abstract
Several authors, e.g., Kerr and Debney (1970), Lun (1978), have obtained severalG2II algebraically special vacuum solutions. NoG2II 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 aG2II 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.
Published Version
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