Type: Article

A discretization of Holst's action for general relativity

Beltrán, Carlos E.; Zapata, José A.;

Abstract:

A discrete model for gravity inspired by spin foam models is presented with spacetime replaced by a simplicial structure equipped with a discretized Lorenz-like connection and tetrad field. Besides the connection, a Lie algebra valued discretized 2-form is used, called a B field. With each simplex of the structure (called spacetime atom) a copy of Minkowski space is associated so that the B field (when it is non-degenerate) provides a communication system between relative reference frames in those copies. The curvature degrees of freedom are described on the level of spacetime atoms and the actions for matter couplings split as a sum over them. In the continuous space, there are several actions leading to Einstein equations; however, they lead to different field equations in the discretized space. The continuous limit of the presented model results in Holst's action for general relativity.