Motion of charged particles around a rotating black hole in a magnetic field

TL;DR

This paper investigates how an external magnetic field influences the stability and motion of charged particles around rotating black holes, revealing enlarged stable regions and potential for relativistic orbits.

Contribution

It introduces a Hamilton-Jacobi formalism to analyze marginally stable circular orbits in magnetic fields around rotating black holes, including analytical solutions for strong fields.

Findings

Magnetic fields enlarge the stability region near the black hole horizon.

Strong magnetic fields enable relativistic innermost stable circular orbits.

Analytical solutions are derived for maximally rotating black holes with strong magnetic fields.

Abstract

We study the effects of an external magnetic field, which is assumed to be uniform at infinity, on the marginally stable circular motion of charged particles in the equatorial plane of a rotating black hole. We show that the magnetic field has its greatest effect in enlarging the region of stability towards the event horizon of the black hole. Using the Hamilton-Jacobi formalism we obtain the basic equations governing the marginal stability of the circular orbits and their associated energies and angular momenta. As instructive examples, we review the case of the marginal stability of the circular orbits in the Kerr metric, as well as around a Schwarzschild black hole in a magnetic field. For large enough values of the magnetic field around a maximally rotating black hole we find the limiting analytical solutions to the equations governing the radii of marginal stability. We also show that the presence of a strong magnetic field provides the possibility of relativistic motions in both direct and retrograde innermost stable circular orbits around a Kerr black hole.