Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity

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.

LaTeX file, 12 pages, no figures; to appear in Classical and Quantum Gravity

References in corpus (3)

• The reality conditions for the new canonical variables of General Relativity
• Solving the Constraints of General Relativity
• A Connection Approach to Numerical Relativity

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