English

Optical geometries

Differential Geometry 2025-02-19 v5 General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics math.MP

Abstract

We study the notion of optical geometry, defined to be a Lorentzian manifold equipped with a null line distribution, from the perspective of intrinsic torsion. This is an instance of a non-integrable version of holonomy reduction in Lorentzian geometry. These generate congruences of null curves, which play an important r\^{o}le in general relativity. Conformal properties of these are investigated. We also extend this concept to generalised optical geometries as introduced by Robinson and Trautman.

Keywords

Cite

@article{arxiv.2009.10012,
  title  = {Optical geometries},
  author = {Anna Fino and Thomas Leistner and Arman Taghavi-Chabert},
  journal= {arXiv preprint arXiv:2009.10012},
  year   = {2025}
}

Comments

46 pages; v2: typos fixed, some clarifications added, references added; v3: references added, minor structural and explanatory changes; v4: final version, 51 pages, accepted for publication in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze; v5: minor corrections including affiliations, as published

R2 v1 2026-06-23T18:41:46.210Z