INITIAL-DATA FORMULATION OF TETRAD GRAVITY UTILIZING YORKS EXTRINSIC TIME APPROACH

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