Classification of image distortions in terms of Petrov types

TL;DR

This paper derives formulas to classify and visualize how spacetime curvature causes elliptical distortion patterns in light from small sources, based on Petrov types and observer velocity.

Contribution

It introduces a method to compute and graphically represent distortion patterns for all Petrov types using Newman-Penrose formalism, considering observer motion.

Findings

Distortion patterns depend on Petrov type and observer velocity.

Formulas relate Weyl tensor to observable distortion patterns.

Graphical representations illustrate differences among Petrov types.

Abstract

An observer surrounded by sufficiently small spherical light sources at a fixed distance will see a pattern of elliptical images distributed over the sky, owing to the distortion effect (shearing effect) of the spacetime geometry upon light bundles. In lowest non-trivial order with respect to the distance, this pattern is completely determined by the conformal curvature tensor (Weyl tensor) at the observation event. In this paper we derive formulas that allow to calculate these distortion patterns in terms of the Newman-Penrose formalism. Then we represent the distortion patterns graphically for all Petrov types, and we discuss their dependence on the velocity of the observer.