Study on Rescaling Extrinsic Curvature in Gravitational Initial Data
Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological solutions to the Einstein equations so we assume that the 3-space is compact, without boundary. In this article we investigate, using both analytic and numerical techniques, what happens when the extrinsic curvature is increased while the background geometry is held fixed. This is equivalent to trying to magnify the local gravitational wave kinetic energy on an unchanged background. We find that the physical intrinsic curvature does not blow up. Rather the local volume of space expands to accommodate this attempt to increase the kinetic energy.
KeywordsScalar Curvature Einstein Equation Compact Manifold Conformal Transformation Extrinsic Curvature
SBai and NÓM were supported by Grant 07/RFP/PHYF148 from Science Foundation Ireland