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 non-spinning black hole. The disk has a thickness $h/r\sim0.05-0.1$ over the radial range $(2-20)GM/c^2$. 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 & Thorne (1973). Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only $\sim2%$ 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. 
Rebecca Shafee (1), Jonathan C. McKinney (2), Ramesh Narayan (3),   Alexander Tchekhovskoy (3), Charles F. Gammie (4), Jeffr...