Initial data sets of minimal energy

The total mass of a gravitational system, the ADM mass, is considered as a functional of the initial data sets for sources and gravitation. From the condition that such a functional has a minimum under a restricted class of variations, tensorial equations for the gravitational initial data are obtained. The solutions to these equations, whose existence for a large class of source fields is asserted, represent initial data sets for gravitation satisfying the constraint equations and may be considered as having no gravitational radiation.