2001/02/28 by G. Sparano, G. Vilasi, A. M. Vinogradov +1 · 19 citations
Mathematics · Physics and Astronomy · #Abelian group #Adjoint representation #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Black Holes and Theoretical Physics #Differential equation #Gravitation #Gravitational field #Homogeneous space #Invariant (physics) #Lie algebra #Lie bracket of vector fields #gr-qc #hep-th
paper · pdf · doi:10.1016/s0370-2693(01)00722-5
published in Physics Letters B 513(1-2), 142-146 (Elsevier BV) · 8 pagese, latex, no figures
arxiv created 2001/02/28 · openalex publication_date 2001/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.