ON NON-RIEMANNIAN PARALLEL TRANSPORT IN REGGE CALCULUS

TL;DR

This paper explores the integration of non-Riemannian parallel transport into Regge calculus, demonstrating that Regge lattices can support arbitrary affine connections, extending the geometric framework of discrete spacetime models.

Contribution

It introduces the concept of non-Riemannian parallel transport in Regge calculus and shows how to define arbitrary affine connections on Regge lattices.

Findings

Regge lattices are locally equivalent to constant curvature spaces

Allows defining arbitrary linear affine connections on Regge lattices

Extends geometric tools available for discrete spacetime models

Abstract

We discuss the possibility of incorporating non-Riemannian parallel transport into Regge calculus. It is shown that every Regge lattice is locally equivalent to a space of constant curvature. Therefore well known-concepts of differential geometry imply the definition of an arbitrary linear affine connection on a Regge lattice.