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

TL;DR

This paper presents new exact local solutions for force-free magnetospheres around Kerr black holes, focusing on radial streaming surfaces and currents expressed through Newman-Penrose tetrad vectors, expanding previous models.

Contribution

It introduces solutions with streaming surfaces at constant radius and currents formed from Newman-Penrose tetrad vectors, complementing earlier solutions based on constant theta surfaces.

Findings

Derived solutions with radial streaming surfaces.

Expressed currents as linear combinations of Newman-Penrose vectors.

Extended the class of known force-free Kerr magnetosphere 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.