The Riemann and extrinsic curvature tensors in the Regge calculus

Details The Riemann and extrinsic curvature tensors in the Regge calculus The Riemann and extrinsic curvature tensors in the Regge calculus

Sep 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988cqgra...5.1193b&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 5, Sept. 1, 1988, p. 1193-1203.

Physics

10

Curvature, Regge Poles, Riemann Manifold, Tensor Analysis, Coordinates, Gravitation Theory, Space-Time Functions

Scientific paper

A detailed analysis of the Riemann tensor in the neighborhood of one bone and of the extrinsic curvature in the neighborhood of one triangular face in a simplicial geometry is presented. Unlike most previous analyses, this analysis makes no reference to any particular choice of smoothing scheme. Explicit formulas are presented for both the Riemann and extrinsic curvature tensors. These results are applied, using the formalism developed by Brewin (1988), in deriving an exact formula for the integral extrinsic curvature. It is argued that for integrals of R2, R3, etc., contributions must be expected from the legs, vertices, etc., rather than just from the bones.

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