Electromagnetic effects on charged particles in NHEK

TL;DR

This paper studies how weak electromagnetic fields influence the motion of charged particles near an extreme Kerr black hole, revealing simplified equations and stable vortical motions under certain conditions with potential astrophysical relevance.

Contribution

It introduces the concept of maximally symmetric electromagnetic fields in NHEK geometry, simplifying equations of motion and analyzing stable vortical particle motions influenced by electromagnetic parameters.

Findings

Charged particle motions can be decoupled into first-order equations in MSEM fields.

Stable vortical motions exist for electromagnetic parameters above a critical value.

Charged particles in these motions radiate non-thermally, with potential astrophysical implications.

Abstract

We investigate the motions of charged particles in the near horizon region of an extreme Kerr black hole with weak electromagnetic fields. There is an enhanced symmetry in the NHEK geometry. We find that when the electromagnetic field respects this enhanced symmetry, which we refer to as the maximally symmetric electromagnetic (MSEM) field, the equations of motion of charged particles get simplified into a set of decoupled first-order differential equations. We discuss the motions of charged particles in two MSEM fields, one being the force-free field and the other being the vacuum fields. Even though the radial motions are similar to the geodesics in NHEK geometry, the angular motions could be affected by the electromagnetic field significantly. In particular, for the vacuum solution which is produced by a weakly charged black hole, there exist stable vortical motions if the electromagnetic parameter is above the critical value $\mB_c = \sqrt{3}$. These vortical motions do not cross the equatorial planes, and the charged particles in them radiate non-thermally. We discuss the corresponding astrophysical implications.