A look at area Regge calculus

Abstract

Area Regge calculus is a candidate theory of simplicial gravity, based on the Regge action with triangle areas as the dynamical variables. It is characterized by metric discontinuities and vanishing deficit angles. Area Regge calculus arises in the large-spin limit of the Barrett-Crane spinfoam model, but not in the newer EPRL/FK model. We address the viability of area Regge calculus as a discretization of General Relativity. We argue that when all triangles are spacelike and all tetrahedra have the same signature, non-trivial solutions of the area calculus are associated with a nonzero Ricci scalar. Our argument rests on a seemingly natural regularization of the metric discontinuities. It rules out the Euclidean area calculus, as well as the Lorentzian sector with all tetrahedra spacelike - the two setups usually considered in spinfoam models. On the other hand, we argue that the area calculus has attractive properties from the point of view of finite-region observables in quantum gravity.