Volume elements and torsion

Details Volume elements and torsion Volume elements and torsion

2005-05-29

arxiv.org/abs/gr-qc/0505146v2

J.Math.Phys. 46 (2005) 112502

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex, 8 pages, 1 figure. v2 includes a discussion on $\lambda$-symmetry

Scientific paper

10.1063/1.2121207

We reexamine here the issue of consistency of minimal action formulation with the minimal coupling procedure (MCP) in spaces with torsion. In Riemann-Cartan spaces, it is known that a proper use of the MCP requires that the trace of the torsion tensor be a gradient, $T_\mu=\partial_\mu\theta$, and that the modified volume element $\tau_\theta = e^\theta \sqrt{g} dx^1\wedge...\wedge dx^n $ be used in the action formulation of a physical model. We rederive this result here under considerably weaker assumptions, reinforcing some recent results about the inadequacy of propagating torsion theories of gravity to explain the available observational data. The results presented here also open the door to possible applications of the modified volume element in the geometric theory of crystalline defects.

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