Singularities of the closed RW metric in Regge Calculus: a generalized evolution of the 600-cell

Abstract

An evolution scheme is developed, based on Sorkin algorithm, to evolve the most complex regular tridimensional polytope, the 600-cell. The solution of 600-cell, already studied before, is generalized by allowing a larger number of free variables. The singularities of Robertson-Walker (RW) metric are studied and a reason is given why the evolution of the 600-cell stops when its volume is still far from zero. A fit of 600-cell's evolution with a continuos metric is studied by writing a metric generalizing Friedmann's and including the 600-cell evolution too. The result is that the 600-cell meets a causality-breaking point of space-time. We also shortly discuss the way matter is introduced in Regge calculus.