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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