Area-angle variables for general relativity

TL;DR

This paper proposes a new formulation of general relativity using area and angle variables within a triangulated 4D manifold, aiming to improve discrete and quantum gravity models.

Contribution

It introduces a modified Regge calculus with area-angle variables that satisfy local constraints, offering a novel approach to discrete and quantum gravity.

Findings

Variables satisfy local constraints within triangulation

Potential applications to classical discrete gravity

Potential applications to non-perturbative quantum gravity

Abstract

We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are local in the triangulation. We expect the formulation to have applications to classical discrete gravity and non-perturbative approaches to quantum gravity.