Constraints on force-free magnetospheres for Kerr(-AdS) black holes with non-null currents

Force-free magnetospheres are of particular interest due to their role in energy extraction from Kerr black holes via the Blandford-Znajek process. Recently, a class of exact analytic solutions has been found with null currents [1,2]. In this paper, we elaborate some constraints on various force-free magnetosphere solutions with non-null currents, utilizing the Newman-Penrose electromagnetic scalars to categorize a range of different cases. We perform a thorough search for stationary and axisymmetric (SAS) solutions, and find that putative SAS solutions within the categories considered generically exhibit singularities on the horizon. We also present some non-SAS solutions found via spacetime-dependent electric-magnetic duality rotations. Additional special solutions in flat, pure AdS and near-horizon-extreme-Kerr (NHEK) spacetimes are also presented.