Light cones in relativity: Real, complex and virtual, with applications

TL;DR

This paper explores the geometric structures of shear-free null geodesic congruences in Minkowski and asymptotically flat space-times, revealing how complexified null infinity acts as a holographic screen linking dual descriptions of these congruences.

Contribution

It introduces a novel dual framework connecting complex null geodesic congruences with real shear-free congruences via holographic principles in asymptotically flat space-times.

Findings

Complex null geodesic congruences relate to complex world-lines.

Real congruences correspond to caustic sets in space-time.

Physical quantities like mass and angular momentum are linked to complex structures.

Abstract

We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity acts as a "holographic screen," interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex world-line; a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we show that virtually all of the interior space-time physical quantities that are identified at null infinity (center of mass, spin, angular momentum, linear momentum, force) are given kinematic meaning and dynamical descriptions in terms of the complex world-line.