New Minimal Distortion Shift Gauge
Abstract
Based on the recent understanding of the role of the densitized lapse function in Einstein's equations and of the proper way to pose the thin sandwich problem, a slight readjustment of the minimal distortion shift gauge in the 3+1 approach to the dynamics of general relativity allows this shift vector to serve as the vector potential for the longitudinal part of the extrinsic curvature tensor in the new approach to the initial value problem, thus extending the initial value decomposition of gravitational variables to play a role in the evolution as well. The new shift vector globally minimizes the changes in the conformal 3-metric with respect to the spacetime measure rather than the spatial measure on the time coordinate hypersurfaces, as the old shift vector did.
Keywords
Cite
@article{arxiv.gr-qc/0603069,
title = {New Minimal Distortion Shift Gauge},
author = {Robert T. Jantzen and James W. York,},
journal= {arXiv preprint arXiv:gr-qc/0603069},
year = {2012}
}
Comments
5 page ReVTeX4 twocolumn latex file, no figures; slight revision: last sentence of section 2 deleted and replaced, citations reordered, additonal paragraph added to introduction with short explanation of the initial value problem and its thin sandwich variation, Yvonne Choquet-Bruhat reference added and acknowledgment expanded to include her