Living Reviews in Relativity

"Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation"
Timothy M. Adamo and Ezra T. Newman and Carlos Kozameh 

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1 Introduction
1.1 Notation and definitions
1.2 Glossary of symbols and units
2 Foundations
2.1 Asymptotic flatness and + ℑ
2.2 Bondi coordinates and null tetrad
2.3 The optical equations
2.4 The Newman–Penrose formalism
2.5 The Bondi–Metzner–Sachs group
2.6 Algebraically-special metrics and the Goldberg–Sachs theorem
3 Shear-Free NGCs in Minkowski Space
3.1 The flat-space good-cut equation and good-cut functions
3.2 Real cuts from the complex good cuts, I
3.3 Approximations
3.4 Asymptotically-vanishing Maxwell fields
4 The Good-Cut Equation and ℋ-Space
4.1 Asymptotically shear-free NGCs and the good-cut equation
4.2 ℋ-space and the good-cut equation
4.3 Real cuts from the complex good cuts, II
4.4 Summary of Real Structures
5 Simple Applications
5.1 Linearized off Schwarzschild
5.2 The Robinson–Trautman metrics
5.3 Type II twisting metrics
5.4 Asymptotically static and stationary spacetimes
6 Main Results
6.1 A brief summary – Before continuing
6.2 The complex center-of-mass world line
6.3 The evolution of the complex center of mass
6.4 The evolution of the Bondi energy-momentum
6.5 Other related results
7 Gauge (BMS) Invariance
8 Discussion/Conclusion
8.1 History/background
8.2 Other choices for physical identification
8.3 Predictions
8.4 Summary of results
8.5 Issues and open questions
8.6 New interpretations and future directions
9 Acknowledgments
A Twistor Theory
B CR Structures
C Tensorial Spin-s Spherical Harmonics
C.1 Clebsch–Gordon expansions
D ℋ-Space Metric
E Shear-Free Congruences from Complex World Lines
F The Generalized Good-Cut Equation
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