Coping with different languages in the null tetrad formulation of general relativity

Abstract

We describe how, in spite of differing conventions regarding spacetime signature, sign of the Riemann tensor, and definition of the Ricci tensor, we were able to construct a precise dictionary relating various notations which are being employed in the null tetrad formulation of general relativity. In addition, we give in appendices the forms assumed by the Newman–Penrose equations and the corresponding abstract structural equations when nontraditional assumptions are made with respect to the three sign conventions.