Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-12-05
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTeX 2e source file, 17 pages, no figures
Scientific paper
A diagonal Bianchi Type III space-time is treated, both at the classical and quantum level, in the context of Horava - Lifshitz gravity. The system of the classical equations of motion is reduced to one independent Abel's equation of the ?rst kind. Closed form solution are presented for various values of the coupling constants appearing in the action. Due to the method used, solutions of Euclidean, Lorentzian and neutral signature are attained. The solutions corresponding to \lamda <> 1 are seen to develop curvature singularities as the other constants approach their Einsteinian values, in contrast to those with \lamda = 1 which tend to the known Einstein gravity solutions. At the quantum level, the resulting Wheeler-DeWitt equation is explicitly solved for \lamda = 1, \sigma = 0 and \lamda = 1/3 . The ensuing wave-functions diverge in the Einsteinian limit.
Christodoulakis Th.
Dimakis N.
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