A local potential for the Weyl tensor in all dimensions
General Relativity and Quantum Cosmology
2016-08-16 v1 Mathematical Physics
Differential Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.gr-qc/0408071,
title = {A local potential for the Weyl tensor in all dimensions},
author = {S. Brian Edgar and José M. M. Senovilla},
journal= {arXiv preprint arXiv:gr-qc/0408071},
year = {2016}
}
Comments
7 pages; Latex