Form Connections
General Relativity and Quantum Cosmology
2007-05-23 v1 High Energy Physics - Theory
Abstract
Riemannian geometry in four dimensions naturally leads to an SL(3) connection that annihilates a basis for self-dual two-forms. Einstein's equations may be written in terms of an SO(3) connection, with SO(3) chosen as an appropriate subgroup of SL(3). We show how a set of "neighbours" of Einstein's equations arises because the subgroup may be chosen in different ways. An explicit example of a non-Einstein metric obtained in this way is given. Some remarks on three dimensional space-times are made.
Cite
@article{arxiv.gr-qc/9305004,
title = {Form Connections},
author = {Ingemar Bengtsson},
journal= {arXiv preprint arXiv:gr-qc/9305004},
year = {2007}
}
Comments
9 pages, G\"oteborg, ITP 93-9