New Gauge Symmetry in Gravity and the Evanescent Role of Torsion

Abstract: If the Einstein-Hilbert action ${\cal L}{\rm EH}\propto R$ 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 ${\cal L}{\rm EH}$ is expressed completely in terms of the metric $g{\mu \nu}=h^ \alpha {}\mu h \alpha {}_ \nu $, and the torsion is zero, or Einstein's teleparallel formulation, where ${\cal L}_{\rm EH}$ 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.