A local potential for the Weyl tensor in all dimensions

TL;DR

This paper introduces a new local potential, a double (2,3)-form, for the Weyl curvature tensor in all dimensions, generalizing the classical four-dimensional Lanczos potential as its double dual.

Contribution

It establishes the existence of a universal local potential for the Weyl tensor in arbitrary dimensions and signatures, extending previous four-dimensional results.

Findings

Existence of a new local potential for Weyl tensors in all dimensions.

The classical Lanczos potential is a special case of the new potential.

The new potential applies to all tensors with Weyl tensor symmetries.

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.