I will describe numerical simulations of thick, magnetized accretion disks near black holes. In simulations that integrate the equation sof general relativistic MHD, the disks become turbulent due to the MRI, and accrete near the equatorial plane of the (rotating) black hole. The polar regions become strongly magnetized, in the sense that the magnetic energy density exceeds the material energy density in the rest-frame of the plasma, and can be treated using the force-free electrodynamics approximation. I will describe results from a separate set of simulations and calculations that integrate the force-free equations. The interface between the force-free regimes is astrophysically interesting both in black hole systems (where numerical evidence suggests it corresponds to the jet-launching region) and in pulsars. The force-free/MHD interface poses some significant numerical challenges for future simulators.
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