"Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation"
by
Timothy M. Adamo and Ezra T. Newman and Carlos Kozameh
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Abstract
1
Introduction
1.1
Notation and definitions
1.2
Glossary of symbols and units
2
Foundations
2.1
Asymptotic flatness and
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
-Space
4.1
Asymptotically shear-free NGCs and the good-cut equation
4.2
-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
-Space Metric
E
Shear-Free Congruences from Complex World Lines
F
The Generalized Good-Cut Equation
References
Updates
Tables