Conditions for non-existence 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.