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Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity

Gen Yoneda·Hisaaki Shinkai
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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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Gen Yoneda, Hisaaki Shinkai. 1996-02-13. Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity. https://doi.org/10.1088/0264-9381%2F13%2F4%2F017

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