The Real Meaning of Complex Minkowski-Space World-Lines

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.

16 pages

References in corpus (3)

• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• On Extracting Physical Content from Asymptotically Flat Space-Time Metrics
• The Universal Cut Function and Type II Metrics

Cited by in corpus (4)

• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• Light cones in relativity: Real, complex and virtual, with applications
• Maxwell, Yang-Mills, Weyl and eikonal fields defined by any null shear-free congruence
• Gaussian beams and caustic avoidance in gravitational optics