Riemann-Cartan Connection and its Decomposition. One More Assessment of "ECE Theory"
General Physics
2011-09-27 v1 General Relativity and Quantum Cosmology
Abstract
In this short pedagogical note we clarify some subtleties concerning the symmetries of the coefficients of a Riemann-Cartan connection and the symmetries of the coefficients of the contorsion tensor that has been a source of some confusion in the literature, in particular in a so called 'ECE theory'. We show in details that the coefficients of the contorsion tensor of a Riemann-Cartan connection has a symmetric part and an antisymmetric part, the symmetric part defining the strain tensor of the connection. Moreover, the contorsion tensor has also a bastard anti-symmetry when written with all its indices in the `covariant' positions.
Keywords
Cite
@article{arxiv.1109.5403,
title = {Riemann-Cartan Connection and its Decomposition. One More Assessment of "ECE Theory"},
author = {J. Fernando T. Giglio and Waldyr A. Rodrigues},
journal= {arXiv preprint arXiv:1109.5403},
year = {2011}
}