The Einstein 3-form G alpha and its equivalent 1-form L alpha in Riemann-Cartan space

Authors
Citation
C. Heinicke, The Einstein 3-form G alpha and its equivalent 1-form L alpha in Riemann-Cartan space, GEN RELAT G, 33(6), 2001, pp. 1115-1130
Citations number
12
Categorie Soggetti
Physics
Journal title
GENERAL RELATIVITY AND GRAVITATION
ISSN journal
00017701 → ACNP
Volume
33
Issue
6
Year of publication
2001
Pages
1115 - 1130
Database
ISI
SICI code
0001-7701(200106)33:6<1115:TE3GAA>2.0.ZU;2-#
Abstract
We motivate the definition of the Einstein 3-form G(alpha) by means of the contracted 2nd Bianchi identity. This definition contains the whole curvatu re 2-form. The L-alpha 1-form, defined via G(alpha) = L-beta boolean AND *( theta (beta) boolean AND theta (alpha)) (* is the Hodge-star, theta (alpha) the coframe), is equivalent to the Einstein 3-form and contains all the in formation of the curvature 2-form relevant for the definition of the Einste in 3-form. A variational formula of Salgado on quadratic invariants of the L-alpha 1-form is discussed, generalized, and put into proper perspective.