  Gauge-gravity duality is arguably our best hope for understanding quantum
gravity. Considerable progress has been made in relating scattering amplitudes
in certain gravity theories to those in gauge theories---a correspondence
dubbed the "double copy". Recently, double copies have also been realized in a
classical setting, as maps between exact solutions of gauge theories and
gravity. We present here a novel map between a certain class of real, exact
solutions of Einstein's equations and self-dual solutions of the flat-space
vacuum Maxwell equations. This map, which we call the "Newman-Penrose map", is
well-defined even for non-vacuum, non-stationary spacetimes, providing a
systematic framework for exploring gravity solutions in the context of the
double copy that have not been previously studied in this setting. To
illustrate this, we present here the Newman-Penrose map for the Schwarzschild
and Kerr black holes, and Kinnersley's photon rocket.
