Gravitational fields with a non Abelian bidimensional Lie algebra of symmetries

Details Gravitational fields with a non Abelian bidimensional Lie algebra of symmetries Gravitational fields with a non Abelian bidimensional Lie algebra of symmetries

2001-02-28

arxiv.org/abs/gr-qc/0102112v1

Phys.Lett. B513 (2001) 142-146

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

8 pagese, latex, no figures

Scientific paper

10.1016/S0370-2693(01)00722-5

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 also constructed.

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