The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space

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.

LaTeX, 13 Pages. To appear in Gen. Rel. Grav

References in corpus (1)

• Computer algebra in gravity: Programs for (non-)Riemannian spacetimes. I

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