Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
Gen Yoneda, Hisaaki Shinkai
Abstract
We show how to treat the constraints and reality conditions in the SO(3)-ADM (Ashtekar) formulation of general relativity, for the case of a vacuum spacetime with a cosmological constant. We clarify the difference between the reality conditions on the metric and on the triad. Assuming the triad reality condition, we find a new variable, allowing us to solve the gauge constraint equations and the reality conditions simultaneously.
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