Simulations of Magnetized Disks Around Black Holes: Effects of Black
  Hole Spin, Disk Thickness, and Magnetic Field Geometry
  The standard general relativistic model of a razor-thin accretion disk around
a black hole, developed by Novikov & Thorne (NT) in 1973, assumes the shear
stress vanishes at the radius of the innermost stable circular orbit (ISCO) and
that, outside the ISCO, the shear stress is produced by an effective turbulent
viscosity. However, astrophysical accretion disks are not razor-thin, it is
uncertain whether the shear stress necessarily vanishes at the ISCO, and the
magnetic field, which is thought to drive turbulence in disks, may contain
large-scale structures that do not behave like a simple local scalar viscosity.
We describe three-dimensional general relativistic magnetohydrodynamic
simulations of accretion disks around black holes with a range of spin
parameters, and we use the simulations to assess the validity of the NT model.
Our fiducial initial magnetic field consists of multiple (alternating polarity)
poloidal field loops whose shape is roughly isotropic in the disk in order to
match the isotropic turbulence expected in the poloidal plane. For a thin disk
with an aspect ratio |h/r| ~ 0.07 around a non-spinning black hole, we find a
decrease in the accreted specific angular momentum of 2.9% relative to the NT
model and an excess luminosity from inside the ISCO of 3.5%. The deviations in
the case of spinning black holes are of the same order. In addition, the
deviations decrease with decreasing |h/r|. We therefore conclude that
magnetized thin accretion disks in x-ray binaries in the thermal/high-soft
spectral state ought to be well-described by the NT model, especially at
luminosities below 30% of Eddington where we expect a very small disk thickness
|h/r| <~ 0.05. We also discuss how the stress and the luminosity inside the
ISCO depend on the assumed initial magnetic field geometry. (abridged)
