  Analytical solutions to force-free electrodynamics around black holes are
fundamental for building simple models of accretion disk and jet dynamics. We
present a (nonexhaustive) classification of complex highest-weight solutions to
the force-free equations in the near-horizon region of the extremal Kerr black
hole. Several classes of real magnetically dominated or null solutions, either
axisymmetric or nonaxisymmetric, are described which admit finite energy and
angular momentum with respect to the asymptotically flat observer. Subtleties
related to the velocity of light surface in the near-horizon region are
discussed.
