2+2-DECOMPOSITION OF ASHTEKAR VARIABLES

We derive a 2 + 2 formulation of Ashtekar variables, focusing on the i mportant special case of a double null foliation of spacetime. The sig nificance of the 2 + 2 formalism in general is that it isolates the tr ue gravitational degrees of freedom. The derivation mirrors that of a recent paper by Goldberg et al in which Ashtekar's 3 + 1 canonical for mulation of Einstein's theory of gravitation is reformulated in terms of a time parameter whose level sets are null hypersurfaces. In this p aper we restrict attention to the Lagrangian formulation.