On the compatibility of Lorentz-metrics with linear connections on 4-dimensional manifolds
General Relativity and Quantum Cosmology
2009-11-11 v1
Abstract
This paper considers 4-dimensional manifolds upon which there is a Lorentz metric, h, and a symmetric connection and which are originally assumed unrelated. It then derives sufficient conditions on the metric and connection (expressed through the curvature tensor) for the connection to be the Levi-Civita connection of some (local) Lorentz metric, g, and calculates the relationship between g and h. Some examples are provided which help to assess the strength of the sufficient conditions derived.
Keywords
Cite
@article{arxiv.gr-qc/0509067,
title = {On the compatibility of Lorentz-metrics with linear connections on 4-dimensional manifolds},
author = {G. S. Hall and D. P. Lonie},
journal= {arXiv preprint arXiv:gr-qc/0509067},
year = {2009}
}
Comments
LaTex2e, 19 pages, uses iop style files