PreprintCC BY 4.0arXiv
The Lanczos potential in the Plebanski paradigm of gravity
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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BibTeX
@misc{espin2026lanczos,
title = {{The Lanczos potential in the Plebanski paradigm of gravity}},
author = {Daniel Espín and Alejandro Jiménez Cano and Javier Olmedo and António Torres Manso},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.29434},
eprint = {2609.29434},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29434},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Lanczos potential in the Plebanski paradigm of gravity
AU - Daniel Espín
AU - Alejandro Jiménez Cano
AU - Javier Olmedo
AU - António Torres Manso
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2609.29434
UR - https://arxiv.org/abs/2609.29434
AB - 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.
ER -