Classical analysis of Bianchi types I and II in Ashtekar variables
General Relativity and Quantum Cosmology
2010-04-06 v1
Abstract
We solve the complex Einstein equations for Bianchi I and II models formulated in the Ashtekar variables. We then solve the reality conditions to obtain a parametrization of the space of Lorentzian solutions in terms of real canonically conjugate variables. In the Ashtekar variables, the dynamics of the universe point particle is governed by only a curved supermetric -- there is no potential term. In the usual metric formulation the particle bounces off a potential wall in flat superspace. We consider possible characterizations of this ``bounce'' in the potential-free Ashtekar variables.
Cite
@article{arxiv.gr-qc/9412015,
title = {Classical analysis of Bianchi types I and II in Ashtekar variables},
author = {Gabriela Gonzalez and Ranjeet S Tate},
journal= {arXiv preprint arXiv:gr-qc/9412015},
year = {2010}
}
Comments
Latex, uses revtex, 13 pages in 10pt