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

A. De Felice·E. Fabri
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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.

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A. De Felice, E. Fabri. 2000-09-27. The Friedmann universe of dust by Regge Calculus: study of its ending point. https://arxiv.org/abs/gr-qc/0009093

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