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Algebraic Rainich theory and antisymmetrization in higher dimensions
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2002 (English)In: Classical and quantum gravity, ISSN 0264-9381, Vol. 19, no 12, 3341-3355 p.Article in journal (Refereed) Published
Abstract [en]

The classical Rainich(-Misner-Wheeler) theory gives necessary and sufficient conditions on an energy-momentum tensor T to be that of a Maxwell field (a 2-form) in four dimensions. Via Einstein's equations, these conditions can be expressed in terms of the Ricci tensor, thus providing conditions for a spacetime geometry to be an Einstein-Maxwell spacetime. One of the conditions is that T2 is proportional to the metric, and it has previously been shown in arbitrary dimension that any tensor satisfying this condition is a superenergy tensor of a simple p-form. Here we examine algebraic Rainich conditions for general p-forms in higher dimensions and their relations to identities by antisymmetrization. Using antisymmetrization techniques we find new identities for superenergy tensors of these general (non-simple) forms, and we also prove in some cases the converse: that the identities are sufficient to determine the form. As an example we obtain the complete generalization of the classical Rainich theory to five dimensions.

Place, publisher, year, edition, pages
2002. Vol. 19, no 12, 3341-3355 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-46965DOI: 10.1088/0264-9381/19/12/316OAI: diva2:267861
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2011-01-13

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Bergqvist, Göran
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The Institute of TechnologyApplied Mathematics
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