Three-dimensional simulations of magnetized thin accretion disks around black holes: Stress in the plunging region

We describe three-dimensional general relativistic magnetohydrodynamic simulations of a geometrically thin accretion disk around a nonspinning black hole. The disk has a thickness h/r ∼ 0.05-0.1 over the radial range (2-20)GM/c². In steady state, the specific angular momentum profile of the inflowing magnetized gas deviates by less than 2% from that of the standard thin disk model of Novikov and Thorne. Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only ∼2% of the inward flux of angular momentum at this radius. Both results indicate that magnetic coupling across the ISCO is relatively unimportant for geometrically thin disks.