2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34451The 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.LateX file, 33 pages, 2 figuresGeneral Relativity and Quantum Cosmologytext