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.
Vacuum Einstein metrics with bidimensional Killing leaves, I-Local aspects
SPARANO, Giovanni;VILASI, Gaetano;
2002-01-01
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.File in questo prodotto:
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