The Generalized Thin-Sandwich Problem and its Local Solvability

We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field configuration for the total system and its derivative with respect to coordinate-time determines a solution to the field equations (generalized thin-sandwich problem). Sufficient conditions for local solvability (in the space of fields) are established.