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, formula_6 and formula_7 are just a pair of standard (real) null vectors such that formula_8. For example, we can think in terms of spherical coordinates, and take formula_9 to be the outgoing null vector, and formula_10 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