The Friedmann universe of dust by Regge Calculus: study of its ending point

TL;DR

This paper investigates why the evolution of a 600-cell in a Friedmann universe model halts prematurely, revealing it encounters a causality-breaking singularity, and analyzes this phenomenon through embedding in a higher-dimensional spacetime.

Contribution

It introduces a novel explanation for the stopping point in 600-cell evolution, linking it to a causality-breaking singularity and modeling it via Einstein equations in higher dimensions.

Findings

The 600-cell evolution stops before volume reaches zero.

The stopping point corresponds to a causality-breaking singularity.

Embedding in five-dimensional spacetime helps analyze the singularity.

Abstract

We develop an evolution scheme, based on Sorkin algorithm, to evolve the most complex regular tridimensional polytope, the 600-cell. This application has been already studied before and all authors found a stop point for the evolution of the spatial section. In our opinion a clear and satisfactory meaning to this behaviour has not been given. In this paper we propose a reason why the evolution of the 600-cell stops when its volume is still far from 0. We find that the 600-cell meets a causality-breaking singularity of space-time. We study the nature of this singularity by embedding the 600-cell into a five-dimensional Lorentzian manifold. We fit 600-cell's evolution with a continuos metric and study it as a solution of Einstein equations.