Exact Solutions for Extreme Black Hole Magnetospheres
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.
Keywords
Cite
@article{arxiv.1412.4124,
title = {Exact Solutions for Extreme Black Hole Magnetospheres},
author = {Alexandru Lupsasca and Maria J. Rodriguez},
journal= {arXiv preprint arXiv:1412.4124},
year = {2015}
}
Comments
38 pages. v2: minor edits, matches published version