Regge calculus from a new angle

TL;DR

This paper introduces a novel formulation of Regge calculus using curved simplices and dihedral angles, potentially simplifying quantum gravity models with a cosmological constant.

Contribution

It presents a new approach to Regge calculus with curved simplices and a first order formulation that avoids constraints, aiding quantum gravity research.

Findings

Allows replacement of length variables with dihedral angles

Formulation with constant sectional curvature accommodates cosmological constant

First order formulation eliminates the need for constraints

Abstract

In Regge calculus space time is usually approximated by a triangulation with flat simplices. We present a formulation using simplices with constant sectional curvature adjusted to the presence of a cosmological constant. As we will show such a formulation allows to replace the length variables by 3d or 4d dihedral angles as basic variables. Moreover we will introduce a first order formulation, which in contrast to using flat simplices, does not require any constraints. These considerations could be useful for the construction of quantum gravity models with a cosmological constant.