A FULLY (3-DIMENSIONAL REGGE CALCULUS MODEL OF THE KASNER COSMOLOGY(1))

We describe the first discrete-time four-dimensional numerical applica tion of Regge calculus. The spacetime is represented as a complex of f our-dimensional simplices, and the geometry interior to each 4-simplex is flat Minkowski spacetime. This simplicial spacetime is constructed so as to be foliated with a one-parameter family of spacelike hypersu rfaces built from tetrahedra. We implement a novel 2-surface initial-d ata prescription for Regge calculus, and provide the first fully four- dimensional application of an implicit decoupled evolution scheme (the 'Sorkin evolution scheme'). We benchmark this code on the Kasner cosm ology-a cosmology which embodies generic features of the collapse of m any cosmological models. We (i) reproduce the continuum solution with a fractional error in the 3-volume of 10(-5) after 10 000 evolution st eps; (ii) demonstrate stable evolution; (iii) preserve the standard de viation of spatial homogeneity to less than 10(-10) and (iv) explicitl y display the existence of diffeomorphism freedom in Regge calculus. W e also present the second-order convergence properties of the solution to the continuum.