A near-axis expansion of the force-free stream equation shows that no regular, monopole-like Kerr magnetosphere can be continuously deformed to the Schwarzschild split-monopole in the zero-spin limit.
Exact Solutions for Extreme Black Hole Magnetospheres
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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 classification of the subset that form highest-weight representations of the spacetime's SL(2,R) x 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 dependence, 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 currents and allows us to resum the highest-weight primaries and their SL(2,R)-descendants.
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gr-qc 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Force-free electrodynamics near rotation axis of a Kerr black hole
A near-axis expansion of the force-free stream equation shows that no regular, monopole-like Kerr magnetosphere can be continuously deformed to the Schwarzschild split-monopole in the zero-spin limit.