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A local variational theory for the Schmidt metric
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering, Physics and Mathematics.
1997 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, Vol. 38, no 8, 3347-3357 p.Article in journal (Refereed) Published
Abstract [en]

We study local variations of causal curves in a space-time with respect to b-length (or generalized affine parameter length). In a convex normal neighbourhood, causal curves of maximal metric length are geodesics. Using variational arguments, we show that causal curves of minimal b-length in sufficiently small globally hyperbolic sets are geodesics. As an application we obtain a generalization of a theorem by Schmidt, showing that the cluster curve of a partially future imprisoned, future inextendible and future b-incomplete curve must be a null geodesic. We give examples which illustrate that the cluster curve does not have to be closed or incomplete. The theory of variations developed in this work provides a starting point for a Morse theory of b-length.

Place, publisher, year, edition, pages
1997. Vol. 38, no 8, 3347-3357 p.
Keyword [en]
general relativity, variational calculus, arc length, b-boundary, Morse theory
National Category
Mathematics Natural Sciences
Identifiers
URN: urn:nbn:se:miun:diva-1594DOI: 10.1063/1.532047Local ID: 418OAI: oai:DiVA.org:miun-1594DiVA: diva2:26626
Available from: 2008-09-30 Created: 2008-09-30 Last updated: 2011-01-10Bibliographically approved

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