Class.Q.Grav. Vol.5(1988) pp.1193-1204 25-May-1987 THE RIEMANN AND EXTRINSIC CURVATURE TENSORS IN THE REGGE CALCULUS
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چکیده
A detailed analysis of the Riemann tensor in the neighbourhood of one bone and of the extrinsic curvature in the neighbourhood 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 formulae will be presented for both the Riemann and extrinsic curvature tensors. These results are applied, using the formalism developed in an earlier paper [1] , in deriving an exact formula for the integral extrinsic curvature. It is argued that for integrals of R2, R3 · · · contributions must be expected from the legs, vertices,... rather than just from the bones. This work provides the background material for the following paper in which the Gauss-Codacci equation is applied to a Regge spacetime.
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تاریخ انتشار 2011