An analytic model of stationary, axisymmetric black-hole magnetospheres built by solving the vacuum Maxwell equations on a Kerr background, with the poloidal magnetic field generated by a toroidal current in a thin equatorial disk whose current direction reverses at a chosen radius. The reversal splits the magnetosphere into an inner region (field lines linking hole and disk, or encircling the disk's inner edge) and an outer region (disk to infinity). The model gives the spin dependence: away from the hole the spin-induced electric field scales with spin but keeps its direction, while near the horizon the field depends strongly on spin, and in the maximal-spin (extremal) case magnetic field lines are expelled from the horizon (a Meissner-like effect) with the horizon becoming an electric equipotential surface.
This paper constructs an analytic model of stationary, axisymmetric vacuum magnetospheres around Kerr (rotating) black holes by solving the vacuum Maxwell equations on the Kerr background. The poloid…