The Real Meaning of Complex Minkowski-Space World-Lines

Details The Real Meaning of Complex Minkowski-Space World-Lines The Real Meaning of Complex Minkowski-Space World-Lines

2009-11-21

arxiv.org/abs/0911.4205v1

Class.Quant.Grav.27:075009, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages

Scientific paper

10.1088/0264-9381/27/7/075009

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.

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