Gravitational fields with a non-Abelian, bidimensional Lie algebra of symmetries

Vacuum gravitational fields invariant for a bidimensional non-Abelian Lie a lgebra of Killing fields, are explicitly described. They are parameterized either by solutions of a transcendental equation (the tortoise equation) or by solutions of a linear second order differential equation on the plane. Gravitational fields determined via the tortoise equation, are invariant fo r a 3-dimensional Lie algebra of Killing fields with bidimensional leaves. Global gravitational fields out of local ones are also constructed. (C) 200 1 Published by Elsevier Science BN.