Letter to the Editor

doi:10.1088/0264-9381/21/22/L01

LETTER TO THE EDITOR

A local potential for the Weyl tensor in all dimensions

S Brian Edgar et al 2004 Class. Quantum Grav. 21 L133-L137 doi: 10.1088/0264-9381/21/22/L01

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S Brian Edgar¹ and José M M Senovilla²
¹ Matematiska Institutionen, Linköpings Universitet, Linköping, S-581 83, Sweden
² Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
E-mail: bredg@mai.liu.se and wtpmasej@lg.ehu.es

Abstract. In all dimensions n ≥ 4 and arbitrary signature, we demonstrate the existence of a new local potential—a double (2, 3)-form, P^ab_cde—for the Weyl curvature tensor C_abcd, and more generally for all tensors W_abcd with the symmetry properties of the Weyl tensor. The classical four-dimensional Lanczos potential for a Weyl tensor—a double (2, 1)-form, H^ab_c—is proven to be a particular case of the new potential: its double dual.

PACS numbers: 02.40.Ky, 04.20.Cv

Print publication: Issue 22 (21 November 2004)
Received 29 August 2004, in final form 31 August 2004
Published 29 October 2004

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A local potential for the Weyl tensor in all dimensions

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