Old and new results for superenergy tensors from dimensionally dependent tensor identities
2003 (English)Article in journal (Refereed) Published
It is known that some results for spinors, and in particular for superenergy spinors, are much less transparent and require a lot more effort to establish, when considered from the tensor viewpoint. In this paper we demonstrate how the use of dimensionally dependent tensor identities enables us to derive a number of 4-dimensional identities by straightforward tensor methods in a signature independent manner. In particular, we consider the quadratic identity for the Bel-Robinson tensor TabcxTabcy = dxy TabcdTabcd/4 and also the new conservation law for the Chevreton tensor, both of which have been obtained by spinor means, both of these results are rederived by tensor means for 4-dimensional spaces of any signature, using dimensionally dependent identities, and, moreover, we are able to conclude that there are no direct higher dimensional analogs. In addition we demonstrate a simple way to show the nonexistense of such identities via counter examples, in particular we show that there is no nontrivial Bel tensor analog of this simple Bel-Robinson tensor quadratic identity. On the other hand, as a sample of the power of generalizing dimensionally dependent tensor identities from four to higher dimensions, we show that the symmetry structure, trace-free and divergence-free nature of the 4-dimensional Bel-Robinson tensor does have an analog for a class of tensors in higher dimensions.
Place, publisher, year, edition, pages
2003. Vol. 44, no 12, 6140-6159 p.
IdentifiersURN: urn:nbn:se:liu:diva-23073DOI: 10.1063/1.1624094Local ID: 2463OAI: oai:DiVA.org:liu-23073DiVA: diva2:243386