TY - JOUR

T1 - The Gauss-Codacci equation on a Regge spacetime. II

AU - Brewin, L.

PY - 1993/12/1

Y1 - 1993/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=36149037503&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/10/5/012

DO - 10.1088/0264-9381/10/5/012

M3 - Article

AN - SCOPUS:36149037503

SN - 0264-9381

VL - 10

SP - 947

EP - 960

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 5

M1 - 012

ER -