A local potential for the Weyl tensor in all dimensions

Details A local potential for the Weyl tensor in all dimensions A local potential for the Weyl tensor in all dimensions

2004-08-20

arxiv.org/abs/gr-qc/0408071v1

Class.Quant.Grav. 21 (2004) L133

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages; Latex

Scientific paper

10.1088/0264-9381/21/22/L01

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.

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