Geometrically Thin Disk Accreting Into a Black Hole
  A numerical model of a steady state, thin accretion disk with a constant effective speed of sound is presented. We demonstrate that `zero torque' inner boundary condition is a reasonable approximation provided that the disk thickness, including the thickness of the torquing magnetic fields, is small everywhere. It is likely that this conclusion is correct also for non-steady disks, as long as the total thickness at the sonic point, H_c, is much smaller than the radius there, r_c ~ r_{ms}. The very existence of thin disks is not proved or disproved in this work, but such disks are believed to exist for moderate accretion rates.   Within our model there is a small torque at r_{ms}, which may increase disk luminosity by several percent. An important result of our analysis is that the physically acceptable steady state solutions in our toy model exist only for \alpha < 0.14 (100 v_s/c)^{1/3}.   A significant torque may be applied to a thin disk if there is a large scale magnetic field, like in a modified Blandford-Znajek mechanism. 
Niayesh Afshordi, Bohdan Paczynski (Princeton University Observatory)