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The Gauss-Codacci equation on a Regge spacetime. II

For pt.I see ibid., vol.5, p.1205-13, 1988. 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 decomposed 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 4-defect, 3-defect and the extrinsic curvature terms.