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Vacuum Einstein metrics with bidimensional Killing leaves. I-Local aspects

G. Sparano·G. Vilasi·A. Vinogradov
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Abstract

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.

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G. Sparano, G. Vilasi, A. Vinogradov. 2003-01-07. Vacuum Einstein metrics with bidimensional Killing leaves. I-Local aspects. https://arxiv.org/abs/gr-qc/0301020

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