Geometrically Thin Disk Accreting Into a Black Hole

A numerical model of a steady state, thin and isothermal accretion disk 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. It is likely that this conclusion is correct also for non-isothermal and non-steady disks, as long as the total thickness at the inner edge, $ H_{in} $, is much smaller than the radius there, $ r_{in} \approx r_{ms} $. The very existence of thin disks is not proven or disproven in this work, but such disks are believed to exists for moderate accretion rates.