The formalism is developed for four-dimensional spacetime, with a Lorentzian-signature metric. At each point, a tetrad (set of four vectors) is introduced. The first two vectors, l μ μ and n μ μ are just a pair of standard (real) null vectors such that l a n a = − − 1 . For example, we can think in terms of spherical coordinates, and take l a to be the outgoing null vector, and n a to be the ingoing null vector. A complex null vector is then constructed by combining a pair of real, orthogonal unit space-like vectors. In the case of spherical coordinates, the standard choice is