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The Lanczos potential for Weyl-candidate tensors exists only in four dimensions
Linkoping Univ, Inst Matemat, SE-58183 Linkoping, Sweden.
2000 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 32, no 12, 2307-2318 p.Article in journal (Refereed) Published
Abstract [en]

We prove that a Lanczos potential L-abc for the Weyl candidate tensor W-abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations, if the integrability conditions yield another non-trivial differential system for L-abc and W-abcd, then this system's integrability conditions should be checked, and so on. When we find a non-trivial condition involving only W-abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L-abc.

Place, publisher, year, edition, pages
2000. Vol. 32, no 12, 2307-2318 p.
Keyword [en]
Lanczos potential, existence, tensor identities
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:liu:diva-49408OAI: oai:DiVA.org:liu-49408DiVA: diva2:270304
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-12

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