Papers
Authors
Leo Brewin
Abstract
A geometric expression for the Gauss-Codacci equation on a simplicial (Regge)
spacetime will be presented. It will be derived by arguing that the operator
associated with the parallel transportation of a vector around a timelike
bone may also be de-composed into a product of operators associated with the
Cauchy surface and its embedding in the spacetime. It will then be shown that
this result is, for a class of weak simplicial spacetimes, term by term
equivalent with the usual continuum version of the contracted Gauss-Codacci
equation. This leads, for this class of weak simplicial spacetimes, to a
simple relationship between the \hbox{4-defect}, 3-defect and the extrinsic
curvature terms.
Reference