Generalized Harmonic Equations in 3+1 Form
General Relativity and Quantum Cosmology
2013-05-29 v2
Abstract
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature, lapse function and shift vector, plus fields that represent the time derivatives of the lapse and shift. This allows for a direct comparison between the generalized harmonic and the Arnowitt-Deser-Misner formulations. The 3+1 generalized harmonic equations are also written in terms of conformal variables and compared to the Baumgarte-Shapiro-Shibata-Nakamura equations with moving puncture gauge conditions.
Cite
@article{arxiv.1109.1707,
title = {Generalized Harmonic Equations in 3+1 Form},
author = {J. David Brown},
journal= {arXiv preprint arXiv:1109.1707},
year = {2013}
}
Comments
This version (accepted for publication) contains some minor corrections and additional references