Black holes with current loops revisited

Abstract

The electromagnetic field around a Kerr black hole inside a current loop is sometimes used as the basis of a toy model for discussing the properties of particle orbits near astrophysical black holes. The motivation for the present paper is to correct the published solution to Maxwell's equations with a charged current loop. Dipole approximations and closed-form expressions in the extreme Kerr limit are also presented. Using the corrected solution, it turns out that imposing a vanishing electromotive force produces a loop with a potential which is finite everywhere outside the black hole. Ring solutions can be combined into solutions with multiple rings or current discs.

10 pages, 5 figures. v2: 3 new references, revisions in Sect. 3

Cited by in corpus (4)

• Ergoregions in Magnetised Black Hole Spacetimes
• On the various aspects of electromagnetic potentials in spacetimes with symmetries
• Effect of magnetic fields on equatorial circular orbits in Kerr spacetimes
• Charged particle dynamics in magnetosphere generated by current loop around Schwarzschild black hole