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

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.

39 pages

References in corpus (16)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• The holographic principle
• The Holographic Principle
• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• Maxwell Fields and Shear-Free Null Geodesic Congruences
• Tensorial Spin-s Harmonics
• On Extracting Physical Content from Asymptotically Flat Space-Time Metrics
• CR Structures and Asymptotically Flat Space-Times
• The Generalized Good Cut Equation
• The Universal Cut Function and Type II Metrics
• The Real Meaning of Complex Minkowski-Space World-Lines
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• Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences
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• Electromagnetic Induced Gravitational Perturbations

Cited by in corpus (8)

• Transformations of asymptotic gravitational-wave data
• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• The Kerr-Newman metric: A Review
• Kerr-Newman electron as spinning soliton
• Stringlike structures in Kerr-Schild geometry: N=2 string, twistors and Calabi-Yau twofold
• Quasi-Local Energy of a Charged Rotating Object Described by the Kerr-Newman Metric
• Stringlike structures in the real and complex Kerr-Schild geometry
• Newton's 2nd Law, Radiation Reaction & Type II Einstein-Maxwell Fields