Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2010-07-09
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTeX source file, 37 pages, no figures
Scientific paper
Lie group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein's field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three- dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi Type, as well as the scaling and the time reparametrization symmetry. The method is applied to Bianchi Types I; II; IV and V. The result is the acquisition, in each case, of the entire solution space of either Lorenzian of Euclidean signature. This includes all the known solutions for each Type and the general solution of Type IV (in terms of sixth Painlev\'e transcendent PVI).
Christodoulakis Th.
Terzis Petros A.
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