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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.

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Author notes

  1. Stuart Boersma

    Present address: Division of Mathematics and Computer Science, Alfred University, 14802, Alfred, New York, USA

Authors and Affiliations

  1. Department of Mathematics, Oregon State University, 97331, Corvallis, Oregon, USA

    Stuart Boersma & Tevian Dray

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  1. Stuart Boersma
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  2. Tevian Dray
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Boersma, S., Dray, T. Slicing, threading and parametric manifolds. Gen Relat Gravit 27, 319–339 (1995). https://doi.org/10.1007/BF02109128

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  • DOI: https://doi.org/10.1007/BF02109128

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