Variation of Area Variables in Regge Calculus

TL;DR

This paper explores using areas of two-simplexes as dynamical variables in Regge calculus, demonstrating that Einstein-Regge equations can be recovered through appropriate constraints when varying the action with respect to these areas.

Contribution

It introduces a novel approach of employing areas of two-simplexes instead of edge lengths as variables in Regge calculus, with a method to recover Einstein-Regge equations.

Findings

Einstein-Regge equations are recoverable using area variables.

Appropriate constraints enable the variation of the action with respect to areas.

The approach offers a new perspective on discretizing gravity.

Abstract

We consider the possibility to use the areas of two-simplexes, instead of lengths of edges, as the dynamical variables of Regge calculus. We show that if the action of Regge calculus is varied with respect to the areas of two-simplexes, and appropriate constraints are imposed between the variations, the Einstein-Regge equations are recovered.