Lupsasca, AlexandruRodriguez, MariaStrominger, Andrew2015-08-262014Lupsasca, Alexandru, Maria J. Rodriguez, and Andrew Strominger. 2014. “Force-Free Electrodynamics Around Extreme Kerr Black Holes.” J. High Energ. Phys. 2014 (12) (December). doi:10.1007/jhep12(2014)185.1029-8479http://nrs.harvard.edu/urn-3:HUL.InstRepos:20423190Plasma-filled magnetospheres can extract energy from a spinning black hole and provide the power source for a variety of observed astrophysical phenomena. These magnetospheres are described by the highly nonlinear equations of force-free electrodynamics, or FFE. Typically these equations can only be solved numerically. In this paper we consider the FFE equations very near the horizon of a maximally spinning black hole, where the energy extraction takes place. Thanks to an enhanced conformal symmetry which appears in this near-horizon region, we are able to analytically obtain several infinite families of exact solutions of the full nonlinear equations.en-USJournal Article2015-08-13Lupsasca, Alexandru, Rodriguez, Maria, Strominger, Andrew2015-08-2610.1007/jhep12(2014)185