TheFriedmannuniverse of dust by ReggeCalculus: study of its endingpoint

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. PACS number(s): 04.20.-q, 04.25.Dm Submitted to Class. Quantum Grav. Date: 7 February 2008 † e-mail: [email protected] § e-mail: [email protected] 1 2 A De Felice and E Fabri