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Optical geometries (2009.10012v4)
Published 21 Sep 2020 in math.DG, gr-qc, hep-th, math-ph, and 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.