We consider Einstein gravity coupled to matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate under what conditions a free specification of a spatial field configuration and its time derivative allows us to solve the constraints for lapse, shift, and other gauge parameters and hence determine a solution to the field equations (thin-sandwich problem). We establish sufficient conditions under which the thin-sandwich problem can be solved locally in field space.
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© 1999 American Institute of Physics.
1999
American Institute of Physics
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