Optical geometries

TL;DR

This paper explores optical geometries in Lorentzian manifolds, focusing on intrinsic torsion and conformal properties, and extends the concept to generalized optical geometries relevant in general relativity.

Contribution

It introduces a novel perspective on optical geometries via intrinsic torsion and extends the framework to generalized geometries, enriching the understanding of null congruences in Lorentzian manifolds.

Findings

Analysis of conformal properties of optical geometries

Extension to generalized optical geometries by Robinson and Trautman

Insights into null congruences in Lorentzian manifolds

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.