Classification of image distortions in terms of Petrov types

Abstract

An observer surrounded by sufficiently small sphericallight sources at a fixed distance will see a pattern ofelliptical images distributed over the sky, owing to thedistortion effect (shearing effect) of the spacetimegeometry upon light bundles. In lowest non-trivial orderwith respect to the distance, this pattern is completelydetermined by the conformal curvature tensor (Weyltensor) at the observation event. In this paper we deriveformulae that allow one to calculate these distortionpatterns in terms of the Newman-Penrose formalism. Thenwe represent the distortion patterns graphically for allPetrov types, and we discuss their dependence on thevelocity of the observer.