Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity

Details Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity

1996-02-13

arxiv.org/abs/gr-qc/9602026v1

Class.Quant.Grav. 13 (1996) 783-790

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/13/4/017

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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