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An off-shell conformally invariant Galilean Weyl tensor — arXiv:2609.04053

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.04053
License (as archived): CC0-1.0
Archived: 2026-10-17T03:14:05.873Z
SHA-256 of the archived text: a54189c8f05aef91b917e1bde2111e49d0b88684c89d79437a2439957d5d2072
Stable URL of this page: https://metraipolis.com/documento/dc_cfee68ef24fe

How to cite

An off-shell conformally invariant Galilean Weyl tensor — arXiv:2609.04053 — arXiv (en), https://arxiv.org/abs/2609.04053 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_cfee68ef24fe (Metraipolis archive dc_cfee68ef24fe, sha256 a54189c8f05aef91b917e1bde2111e49d0b88684c89d79437a2439957d5d2072)

BibTeX

@misc{dccfee68ef24fe,
  title = {An off-shell conformally invariant Galilean Weyl tensor — arXiv:2609.04053},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.04053},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_cfee68ef24fe; sha256 a54189c8f05aef91b917e1bde2111e49d0b88684c89d79437a2439957d5d2072},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.04053. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We propose a manifestly conformally invariant off-shell definition of the Weyl tensor in Galilean geometry. We also propose definitions for the electric and magnetic parts thereof. For the latter to vanish, observers with specific kinematical properties need to exist. While this is guaranteed by the Newton--Cartan equation, it might not be true for other Galilean invariant theories. Therefore, we propose that imposing the existence of observers for which the off-shell magnetic part is zero should be a necessary condition for a Galilean invariant theory to be called `Newtonian', in the spirit of the `Newtonian' condition, introduced by Trautman, in standard Newton--Cartan gravity. As a side result, we also show that there exists a unique Galilean boost-invariant connection that can be built from a Galilean structure and a choice of Coriolis field, even when the clock form is not closed. No extra structure is needed, contrasting with the standard approach used to construct boost-invariant connections which introduces a mass gauge field.

Tema degli esploratori: fisica e astronomia (retro-catalogo arXiv: annunci del 2026-09-04 in gr-qc).
Categorie arXiv: General Relativity and Quantum Cosmology (gr-qc) ; Mathematical Physics (math-ph).
Pagina del lavoro: https://arxiv.org/abs/2609.04053 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T03:03:48.146Z dalla pagina https://arxiv.org/catchup/gr-qc/2026-09-04?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).