VACUUM EINSTEIN METRICS WITH BIDIMENSIONAL KILLING LEAVES: I - LOCAL ASPECTS
Authors: G. Sparano, G. Vilasi, A. M. Vinogradov
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.
26 pages, LaTeX-2e (AmS-LaTeX), 2 figures (EPS format).
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