ON THE COMMUTATOR EQUATIONS IN THE EXTENDED GHP FORMALISM

Ludwig has recently developed an extension of the GHP formalism (EGHP formalism) which contains fewer variables and fewer equations than the original GHP formalism; on the other hand, the EGHP commutator equati ons are more complicated than their GHP counterparts, having explicit conformally-weighted parts as well as explicit spin- and boost-weighte d parts which also occur in the GHP commutator equations. To extract a ll the information from the EGHP commutator equations, one would expec t to have to apply them to at least seven real, appropriately weighted quantities. However it is shown-because of the redundancy inherent in tetrad formalisms-that, alongside the EGHP Bianchi and Ricci equation s, it is always sufficient to apply all the EGHP commutator equations to only six real (three complex) quantities, four of which should be z ero-weighted, functionally independent scalars while the other two sho uld have non-zero spin and boost weight but any conformal weight. Furt hermore, it is shown that, alongside the EGHP Bianchi and Ricci equati ons, it is almost always sufficient to apply all the EGHP commutator e quations to only four real (two complex), zero-weighted, functionally independent scalars.