Initial-data formulation of tetrad gravity utilizing York's extrinsic time approach

An ability to analyze the geometrodynamic degrees of freedom and initial-data formulation is central to the canonical quantization of gravity. In the metric theory of gravity York provided the most powerful technique to analyze the dynamic degrees of freedom and to solve the initial-data problem. In this paper we extend York's analysis to tetrad gravity. Such an extension is necessary for the quantization of gravity when coupled to a half-integer-spin field. We present a comparative analysis of the geometric information carried by (1) a 3-metric of an initial hypersurface and (2) the spacelike triad of a time-gauged tetrad. We apply the tetrad initial-data formulation to Ashtekar's connection variables, and provide a comparison with other alternative choices of canonical tetrad variables.