The General Solution of Bianchi Type III Vacuum Cosmology
نویسنده
چکیده
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 Painlevé transcendent PV I . For particular representations of PV I 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 Painlevé transcendent. [email protected] [email protected] 1
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60 70 63 v 1 1 7 Ju l 2 00 6 The General Solution of Bianchi Type III Vacuum Cosmology
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. Imposing the space-time generalization of a ”hidden” symmetry of the generic Type III spatial slice, enables us to retrieve a two-parameter...
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