The Construction of Sorkin Triangulations

TL;DR

This paper analyzes the structure of Sorkin triangulations in Regge calculus, highlighting their local properties, general applicability, and implications for time evolution and initial value problems in discrete gravity.

Contribution

It reveals the local characteristics of Sorkin triangulations and demonstrates their broad applicability and validity in Regge calculus.

Findings

Identifies the local structure underlying Sorkin triangulations

Shows the general applicability of these triangulations in Regge calculus

Discusses implications for time evolution and initial value problems

Abstract

Some time ago, Sorkin (1975) reported investigations of the time evolution and initial value problems in Regge calculus, for one triangulation each of the manifolds $R*S^3$ and $R^4$. Here we display the simple, local characteristic of those triangulations which underlies the structure found by Sorkin, and emphasise its general applicability, and therefore the general validity of Sorkin's conclusions. We also make some elementary observations on the resulting structure of the time evolution and initial value problems in Regge calculus, and add some comments and speculations.