On source coupling and the teleparallel equivalent to GR

Details On source coupling and the teleparallel equivalent to GR On source coupling and the teleparallel equivalent to GR

2006-12-11

arxiv.org/abs/gr-qc/0612062v1

Proceedings of the tenth Marcel Grossman meeting on general relativity 2003, p.1498.

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages

Scientific paper

Alternatives to the usual general relativity (GR) Riemannian framework include Riemann-Cartan and teleparallel geometry. The ``teleparallel equivalent of GR" (TEGR, aka GR${}_{||}$) has certain virtues, however there have been allegations of serious source coupling limitations. Now it is quite straightforward to show that the coupled dynamical field equations of Einstein's GR with any source can be accurately represented in terms of any other connection, in particular teleparallel geometry. Using an argument similar to one used long ago to show the "effective equivalence" between GR and the Einstein-Cartan theory, we construct the teleparallel action which is equivalent to a given Riemanian one; thereby finding the ``effectively equivalent" coupling principle for all sources, including spinors. No auxiliary field is required. Can one decide which is the real "physical" geometry? Invoking the minimal coupling principle may give a unique answer.

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