Papers
Authors
Leo Brewin
Abstract
The detailed construction of six Regge spacetimes, each being an
approximation to a time symmetric Friedmann dust filled universe,
will be presented. These spacetimes are a generalization of those
originally constructed by Collins and Williams\R(1). This paper
will present new methods for the subdivision of each Cauchy
surface into a set of tetrahedra, for the construction of the
general 4-dimensional block and for the implementation of the
constraints of homogeneity and isotropy. A new action sum for
pure dust in a Regge spacetime will also be presented. The
evolution of the Regge spaces will be seen to terminate prior to
the full collapse of the universe. This will be shown to occur
when the particle horizon for an observer at the centre of one
tetrahedron has contracted so as to just touch the vertices of
that tetrahedron. It is argued that this is a generic feature and
will occur in any Regge spacetime whenever the local curvature
becomes too large.
Reference