A local potential for the Weyl tensor in all dimensions

In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential - a double (2, 3)-form, Pabcde - for the Weyl curvature tensor Cabcd, and more generally for all tensors Wabcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczo...

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Bibliographic Details
Published in:Classical and quantum gravity 2004-11, Vol.21 (22), p.L133-L137
Main Authors: Edgar, S Brian, Senovilla, José M M
Format: Article
Language:English
Subjects:
Classical general relativity
Exact sciences and technology
Fundamental problems and general formalism
General relativity and gravitation
Geometry, differential geometry, and topology
MATEMATIK
Mathematical methods in physics
MATHEMATICS
Physics
Riemannian geometries
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Summary:In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential - a double (2, 3)-form, Pabcde - for the Weyl curvature tensor Cabcd, and more generally for all tensors Wabcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor - a double (2, 1)-form, Habc - is proven to be a particular case of the new potential: its double dual.
ISSN:0264-9381
1361-6382
1361-6382
DOI:10.1088/0264-9381/21/22/L01