Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-07-17
Class.Quant.Grav. 24 (2007) 875-887
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex2e, 18 pages, accepted in CQG
Scientific paper
10.1088/0264-9381/24/4/008
The second order Ordinary Differential Equation which describes the unknown part of the solution space of some vacuum Bianchi Cosmologies is completely integrated for Type III, thus obtaining the general solution to Einstein's Field Equations for this case, with the aid of the sixth Painlev\'{e} transcendent $P_{VI}$. For particular representations of $P_{VI}$ we obtain the known Kinnersley two-parameter space-time and a solution of Euclidean signature. The imposition of the space-time generalization of a "hidden" symmetry of the generic Type III spatial slice, enables us to retrieve the two-parameter subfamily without considering the Painlev\'{e} transcendent.
Christodoulakis Th.
Terzis Petros A.
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