Symbol/Acronym 
Definition 
, 
Future null infinity, Complex future null infinity 
, , 
Future, Past timelike infinity, Spacelike infinity 
, 
Minkowski space, Complex Minkowski space 
, 
Bondi time coordinate, Retarded Bondi time () 
Derivation with respect to 

Derivation with respect to 

Affine parameter along null geodesics 

; stereographic coordinates on 

Tensorial spin spherical harmonics 

, 
; spinweighted operator on the twosphere 
Metric function on ; often 

Application of operator to while the variable is held constant 

Null tetrad system; 

NGC 
Null Geodesic Congruence 
NP/SC 
Newman–Penrose/SpinCoefficient Formalism 
Metric coefficients in the Newman–Penrose formalism 

Weyl tensor components in the Newman–Penrose formalism 

Maxwell tensor components in the Newman–Penrose formalism 

Complex divergence of a null geodesic congruence 

Twist of a null geodesic congruence 

, 
Complex shear, Asymptotic complex shear of a NGC 
; Gravitational constant 

Complex auxiliary (CR) potential function 

Derivation with respect to 

GoodCut Equation, describing asymptotically shearfree NGCs 

GoodCut Function (GCF) on 

Stereographic angle field for an asymptotically shearfree NGC at 

CR equation, describing the embedding of into 

space 
Complex fourdimensional solution space to the GoodCut Equation 
Complex electromagnetic dipole 

Complex centerofcharge world line, lives in space 

Complex electromagnetic quadrupole 

Complex center of mass world line, lives in space 



Complex gravitational dipole 

Complex gravitational quadrupole 

Universal Cut Function (UCF) corresponding to the complex center of mass world line 

Identification between coefficient of the UCF and gravitational quadrupole 

Bondi Mass Aspect 

Bondi mass 

Bondi linear threemomentum 

Vacuum linear theory identification of angular momentum 

In much of what follows, we use simplified units where . However, in Section 6 we will revert to a notation which makes dependence upon numerical constants explicit for the sake of comparing our results with wellknown quantities in classical mechanics and electromagnetism. We therefore include the following reference table for the units of several prominent objects in our calculations to ease in verifying that correct powers of dimensional constants (e.g., , ) appear in our final results. Here stands for the units of a given quantity, and

http://www.livingreviews.org/lrr20121 
Living Rev. Relativity 15, (2012), 1
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