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arXiv · gr-qc/9412015

Classical analysis of Bianchi types I and II in Ashtekar variables

Gabriela Gonzalez·Ranjeet S Tate
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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.

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Gabriela Gonzalez, Ranjeet S Tate. 1994-12-06. Classical analysis of Bianchi types I and II in Ashtekar variables. https://doi.org/10.1088/0264-9381%2F12%2F5%2F018

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