The Lanczos potential for Weyl-candidate tensors exists only in four dimensions
2000 (English)In: General Relativity and Gravitation, ISSN 0001-7701, Vol. 32, no 12, 2307-2318 p.Article in journal (Refereed) Published
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.
Lanczos potential, existence, tensor identities
IdentifiersURN: urn:nbn:se:liu:diva-49408OAI: oai:DiVA.org:liu-49408DiVA: diva2:270304