Conditions for nonexistence of static or stationary, Einstein-Maxwell, non-inheriting black-holes

We consider asymptotically-flat, static and stationary solutions of the Einstein equations representing Einstein-Maxwell space-times in which the Maxwell field is not constant along the Killing vector defining stationarity, so that the symmetry of the space-time is not inherited by the electromagnetic field. We find that static degenerate black hole solutions are not possible and, subject to stronger assumptions, nor are static, non-degenerate or stationary black holes. We describe the possibilities if the stronger assumptions are relaxed.