Three Dimensional Simulations of Vertical Magnetic Flux in the Immediate Vicinity of Black Holes

This article reports on three-dimensional (3-D) MHD simulations of non-rotating and rapidly rotating black holes and the adjacent black hole accretion disk magnetospheres. A particular emphasis is placed on the vertical magnetic flux that is advected inward from large radii and threads the equatorial plane near the event horizon. In both cases of non-rotating and rotating black holes, the existence of a significant vertical magnetic field in this region is like a switch that creates powerful jets. There are many similarities in the vertical flux dynamics in these two cases in spite of the tremendous enhancement of azimuthal twisting of the field lines and enhancement of the jet power because of an "ergospheric disk" in the Kerr metric. A 3-D approach is essential because two-dimensional axisymmetric flows are incapable of revealing the nature of vertical flux near a black hole. Poloidal field lines from the ergospheric accretion region have been visualized in 3-D and much of the article is devoted to a formal classification of the different manifestations of vertical flux in the Kerr case.