Abstract
This paper investigates a new series of solutions to the initial-value constraints of general relativity which is obtained by perturbing the trace of the extrinsic curvature. This analysis is important for two reasons. Firstly, it completes the proof that flat space is a local energy minimum. Secondly, it casts light on the extent to which this variable can be identified with the gauge degree of freedom in the initial-value problem.
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