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Vacuum solutions to the Einstein equations can be viewed as the interplaybetween the geometry and the gravitational wave energy content. The constraintson initial data reflect this interaction. We assume we are looking atcosmological solutions to the Einstein equations so we assume that the 3-spaceis compact, without boundary. In this article we investigate, using bothanalytic and numerical techniques, what happens when the extrinsic curvature isincreased while the background geometry is held fixed. This is equivalent totrying to magnify the local gravitational wave kinetic energy on an unchangedbackground. We find that the physical intrinsic curvature does not blow up.Rather the local volume of space expands to accommodate this attempt toincrease the kinetic energy.

Scaling up the extrinsic curvature in gravitational initial data