The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space
General Relativity and Quantum Cosmology
2015-06-25 v1
Abstract
The definition of the Einstein 3-form G_a is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior product. The L_a is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the L_a 1-form is discussed, generalized, and put into proper perspective.
Cite
@article{arxiv.gr-qc/0012037,
title = {The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space},
author = {Christian Heinicke},
journal= {arXiv preprint arXiv:gr-qc/0012037},
year = {2015}
}
Comments
LaTeX, 13 Pages. To appear in Gen. Rel. Grav