  Recently, we introduced the "Newman-Penrose map," a novel correspondence
between a certain class of solutions of Einstein's equations and self-dual
solutions of the vacuum Maxwell equations, which we showed was closely related
to the classical double copy. Here, we give an alternative definition of this
correspondence in terms of quantities that are defined naturally on twistor
space, and a shear-free null geodesic congruence on Minkowski space whose
twistorial character is articulated by the Kerr theorem. The advantage of this
reformulation is that it is purely geometrical in nature, being manifestly
invariant under both spacetime diffeomorphisms and projective transformations
on twistor space. While the original formulation of the map may be more
convenient for most explicit calculations, the twistorial formulation we
present here may be of greater theoretical utility.
