Torsion degrees of freedom in the Regge calculus as dislocations on the simplicial lattice (Q5959867)

Only few attempts have been made until now to include concepts of Riemann-Cartan geometry into the Regge Calculus, and, when they were made, then torsion was not treated on the same simplicial footing as curvature. In view of the great interest of gravitational physics in non-Riemannian geometry, it is an obvious problem to look for a calculus that incorporates torsion in the same natural way as curvature. Motivated by the application of non-Riemannian geometry to the theory of defects in solids showing the close connection between torsion and dislocations, the authors generalize the Regge Calculus by allowing for dislocations on the simplicial lattice by addition to the usual disclinations related to curvature. By introducing this way the notion of a general conical defect they are able to discretize gravitational theories with torsion degrees of freedom like Einstein-Cartan theory. A discrete version of the Einstein-Cartan action is given and field equations are derived by its variation with respect to the discrete variables, namely link lengths and Burgers vectors.