A space--time calculus based on pairs of null directions

A formalism is presented for the treatment of space-times, which is intermediate between a fully covariant approach and the spin-coefficient method of Newman and Penrose. With the present formalism, a pair of null directions only, rather than an entire null tetrad, is singled out at each point. The concept of a spin- and boost-weighted quantity is defined, the formalism operating entirely with such quantities. This entails the introduction of modified differentiation operators, one of which represents a natural extension of the definition of the operator ð which had been introduced earlier by Newman and Penrose. For suitable problems, the present formalism should lead to considerable simplifications over that achieved by the standard spin-coefficient method.