Can the Energy of a Weak Gravitational Field Become Negative?

Abstract
The energy-momentum linkages for asymptotically flat solutions of Einstein's equations are considered as functionals of the metric field variables. When the metric components are varied, it is found that the extrema of the rest mass occur only when its value is zero. By considering the weak-field limit, flat space-time is shown to be a local minimum. The implications of this result for the sign of the weak-field energy are discussed, and the effects of nongravitational sources are investigated.
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