The Real Meaning of Complex Minkowski-Space World-Lines

TL;DR

This paper explores how complex world-lines in Minkowski space induce shear-free null geodesic congruences in real Minkowski space, revealing geometric connections between complex and real structures.

Contribution

It establishes a direct geometric link showing how complex world-lines project into real Minkowski space as shear-free null geodesic congruences.

Findings

Complex world-lines induce shear-free null geodesic congruences in real Minkowski space.

The paper clarifies the geometric relationship between complex curves and real null structures.

It provides a framework for understanding complex Minkowski space effects in real spacetime.

Abstract

In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.