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Exact Solutions for Extreme Black Hole Magnetospheres
- Source :
- JHEP 1507 (2015) 090
- Publication Year :
- 2014
-
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.<br />Comment: 38 pages. v2: minor edits, matches published version
Details
- Database :
- arXiv
- Journal :
- JHEP 1507 (2015) 090
- Publication Type :
- Report
- Accession number :
- edsarx.1412.4124
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP07(2015)090