2003/01/07 by G. Sparano, G. Vilasi, A. Vinogradov
Physics and Astronomy · #gr-qc
published as Differ.Geom.Appl. 16 (2002) 95-120 · LateX file, 33 pages, 2 figures
arxiv created 2003/01/07 · arxiv updated 2009/11/30
The solutions of vacuum Einstein's field equations, for the class of Riemannian metrics admitting a non Abelian bidimensional Lie algebra of Killing fields, are explicitly described. They are parametrized either by solutions of a transcendental equation (the tortoise equation), or by solutions of a linear second order differential equation in two independent variables. Metrics, corresponding to solutions of the tortoise equation, are characterized as those that admit a 3-dimensional Lie algebra of Killing fields with bidimensional leaves.