A local potential for the Weyl tensor in all dimensions

Abstract

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.

7 pages; Latex

References in corpus (1)

• The non-existence of a Lanczos potential for the Weyl curvature tensor in dimensions n>=7

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