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arXiv · 2609.29434

The Lanczos potential in the Plebanski paradigm of gravity

Daniel Espín·Alejandro Jiménez Cano·Javier Olmedo·António Torres Manso
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Abstract

We present a new Plebanski formulation of General Relativity. The key difference is that we work with a gauge vector field derived from the Lanczos potential of the Weyl tensor. We show that, on shell, the gauge vector field encodes all nontrivial gravitational degrees of freedom and, in a suitable Lorentz gauge, Bianchi identities ensure that this gauge vector field satisfies a source-free wave equation for Ricci-flat spacetimes. This description suggests new ways of interpreting the true geometrical degrees of freedom with applications in both classical and quantum gravity.

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Daniel Espín, Alejandro Jiménez Cano, Javier Olmedo, António Torres Manso. 2026-09-24. The Lanczos potential in the Plebanski paradigm of gravity. https://arxiv.org/abs/2609.29434

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