Torsion Degrees of Freedom in the Regge Calculus as Dislocations on the Simplicial Lattice

Abstract

Using the notion of a general conical defect, the Regge Calculus is generalized by allowing for dislocations on the simplicial lattice in addition to the usual disclinations. Since disclinations and dislocations correspond to curvature and torsion singularities, respectively, the method we propose provides a natural way of discretizing gravitational theories with torsion degrees of freedom like the Einstein-Cartan theory. A discrete version of the Einstein-Cartan action is given and field equations are derived, demanding stationarity of the action with respect to the discrete variables of the theory.