, Volume 27, Issue 3, pp 319-339

Slicing, threading and parametric manifolds

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Abstract

We present a unified treatment of theslicing (3+1) andthreading (1+3) decompositions of spacetime in terms of foliations. It is well-known how to decompose the metric and connection in the slicing picture; this is at the heart of any initial-value problem in general relativity. We describe here the analogous problem in the threading picture, recovering the recent results of Perjés onparametric manifolds.