Optical geometries

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 rôle in general relativity. Conformal properties of these are investigated. We also extend this concept to generalised optical geometries as introduced by Robinson and Trautman.

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