Objective

From Thorne (1980)
Each major school of relativity theory has invented its own notation and formalism
Regge-Wheeler harmonics
Sachs-Pirani symmetric trace-free harmonics
Mathews-Zerilli Clebsch-Gordon-coupled harmonics
Newman-Penrose spin-weighted spherical harmonics

Since 1966 people have stopped inventing new formalisms, but there has been no attempt at consolidation