If the Einstein-Hilbert action LEH ∝ R is re-expressed in Riemann-Cartan spacetimeusing the gauge fields of translations, the vierbein field hαμ, and the gauge field of local Lorentztransformations, the spin connection Aμαβ, there exists a new gauge symmetry which permitsreshuffling the torsion, partially or totally, into the Cartan curvature term of the Einsteintensor, and back, via a new multivalued gauge transformation. Torsion can be chosen at willby an arbitrary gauge fixing functional. There exist many equivalent ways of specifying thetheory, for instance Einstein’s traditional way where LEH is expressed completely in terms ofthe metric gμν = hαμhαν, and the torsion is zero, or Einstein’s teleparallel formulation, whereLEH is expressed in terms of the torsion tensor, or an infinity of intermediate ways. As faras the gravitational field in the far-zone of a celestial object is concerned, matter composedof spinning particles can be replaced by matter with only orbital angular momentum, withoutchanging the long-distance forces, no matter which of the various new gauge representations isused.
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