New Gauge Symmetry in Gravity and the Evanescent Role of Torsion

Abstract

If the Einstein-Hilbert action LEH ∝ R is re-expressed in Riemann-Cartan spacetime using the gauge fields of translations, the vierbein field h α μ, and the gauge field of local Lorentz transformations, the spin connection Aμα β , 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 new multivalued gauge transformation. Torsion can be chosen at will by an arbitrary gauge fixing functional. There exist many equivalent ways of specifying the theory, for instance Einstein's traditional way where LEH is expressed completely in terms of the metric gμν = h α μhαν, and the torsion is zero, or Einstein's teleparallel formulation, where LEH 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. c