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 -