Area Regge calculus and continuum limit

TL;DR

This paper explores the relationship between discrete and continuum formulations of area-based general relativity, introducing a tensor-connection approach and proving its continuum limit correspondence.

Contribution

It introduces a generalized Regge calculus with area tensor-connection variables and proves its continuum limit aligns with continuum area tensor-connection gravity.

Findings

Continuum limit of area tensor-connection Regge calculus reproduces general relativity.

Generalized Regge calculus can be formulated with area tensor-connection variables.

Establishes a rigorous link between discrete and continuum area-based gravity models.

Abstract

Encountered in the literature generalisations of general relativity to independent area variables are considered, the discrete (generalised Regge calculus) and continuum ones. The generalised Regge calculus can be either with purely area variables or, as we suggest, with area tensor-connection variables. Just for the latter, in particular, we prove that in analogy with corresponding statement in ordinary Regge calculus (by Feinberg, Friedberg, Lee and Ren), passing to the (appropriately defined) continuum limit yields the generalised continuum area tensor-connection general relativity.