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

G. Sparano, G. Vilasi, A.M. Vinogradov
2001 Physics Letters B  
Vacuum gravitational fields invariant for a bidimensional non Abelian Lie algebra 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 for a 3-dimensional Lie algebra of Killing fields with bidimensional leaves. Global gravitational fields out of local ones are
more » ... t of local ones are also constructed.
doi:10.1016/s0370-2693(01)00722-5 fatcat:bid56llwvnhahdjcas5uqwauey