New Gauge Symmetry in Gravity and the Evanescent Role of Torsion

If the Einstein-Hilbert action ${\mathcal{L}}_{\mathrm{E}\mathrm{H}}\propto R$ is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field $h^{\alpha }{}_{\mu }$, and the gauge field of local Lorentz transformations, the spin connection $A_{\mu \alpha }{}^{\beta }$, there exists a new gauge symmetry which permits reshuffling the torsion, partially or totally, into the Cartan curvature term of the Einstein tensor, and back, via a {\em new multivalued gauge transformation/}. Torsion can be chosen at will by an arbitrary gauge fixing functional. There exist many equivalent ways of specifing the theory, for instance Einstein’s traditional way where ${\cal L}{\rm EH}$isexpressedcompletelyintermsofthemetric$g{\mu \nu}=h^ \alpha {}\mu h \alpha {}_ \nu $, and the torsion is zero, or Einstein’s teleparallel formulation, where ${\mathcal{L}}_{\mathrm{E}\mathrm{H}}$ is expressed in terms of the torsion tensor, or an infinity of intermediate ways. As far as the gravitational field in the far-zone of a celestial object is concerned, matter composed of spinning particles can be replaced by matter with only orbital angular momentum, without changing the long-distance forces, no matter which of the various new gauge representations is used.