
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 
Algebraicallyspecial metrics and the
Goldberg–Sachs theorem 
3 
ShearFree NGCs in Minkowski Space 

3.1 
The
flatspace goodcut equation and goodcut functions 

3.2 
Real cuts from
the complex good cuts, I 

3.3 
Approximations 

3.4 
Asymptoticallyvanishing
Maxwell fields 
4 
The GoodCut Equation and Space 

4.1 
Asymptotically
shearfree NGCs and the goodcut equation 

4.2 
space and the goodcut
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 centerofmass world line 

6.3 
The
evolution of the complex center of mass 

6.4 
The evolution of the
Bondi energymomentum 

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
Spins Spherical Harmonics 

C.1 
Clebsch–Gordon expansions 
D 
Space
Metric 
E 
ShearFree Congruences from Complex World Lines 
F 
The
Generalized GoodCut Equation 

References 

Updates 

Tables 