Force-free Currents and the Newman-Penrose Tetrad of a Kerr Black Hole: Exact Local Solutions

Abstract

In a previous article we derived a class of solutions to the force-free magnetosphere in a Kerr background. Here, the streaming surface, defined by constant values of the toriodal component of the electromagnetic vector potential $A$, were generated by constant values of $\theta$. The electromagnetic current vector flowed along the in-falling principle null geodesic vector of the geometry. Subsequently, we generalized this to obtain an out-going principle null geodesic vector as well. In this article, we derive solutions that are complimentary to the above mentioned criteria. Namely, here the solution has a streaming surface generated by spheres of constant radial coordinate $r$, and the current vector is generated by linear combinations of $m$ and $m^{\star }$, the remaining bases vectors in the Newman-Penrose null tetrad.

6 pages

References in corpus (4)

• Spacetime approach to force-free magnetospheres
• Electromotive Force in the Blandford-Znajek Process
• Force-Free Electrodynamics around Extreme Kerr Black Holes
• Towards an understanding of the force-free magnetosphere of rapidly spinning black holes

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• Black Hole Polarimetry I: A Signature of Electromagnetic Energy Extraction
• Blandford--Znajek monopole expansion revisited: novel non-analytic contributions to the power emission
• Force-Free Foliations
• Analytic properties of force-free jets in the Kerr spacetime -- III: uniform field solution
• Moving away from the Near-Horizon Attractor of the Extreme Kerr Force-Free Magnetosphere
• Force-free Electrodynamics and Foliations in an arbitrary Spacetime
• The Null and Force-Free Electromagnetic Field
• The Non-Null and Force-Free Electromagnetic Field
• Particle acceleration driven by null electromagnetic fields near a Kerr black hole