Abstract
We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classifica-tion of the subset that form highest-weight representations of the spacetime’s SL(2, ℝ)×U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2, ℝ) highest-weight conditions lead to stationary solutions with non-trivial angular de-pendence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2, ℂ) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2, ℂ) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear cur-rents. This allows us to resum the highest-weight primaries and their SL(2, ℝ)-descendants.
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Lupsasca, A., Rodriguez, M.J. Exact solutions for extreme black hole magnetospheres. J. High Energ. Phys. 2015, 90 (2015). https://doi.org/10.1007/JHEP07(2015)090
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DOI: https://doi.org/10.1007/JHEP07(2015)090