We explore the presence of torques at the inner edges of geometrically thin
black hole accretion disks using three-dimensional MHD simulations in a ps
eudo-Newtonian potential. By varying the saturation level of the magnetorot
ational instability that leads to angular momentum transport, we show that
the dynamics of gas inside the radius of marginal stability varies dependin
g upon the magnetic field strength just outside that radius. Weak fields ar
e unable to causally connect material within the plunging region to the res
t of the disk, and zero torque is an approximately correct boundary conditi
on at the radius of marginal stability. Stronger fields, which we obtain ar
tificially but which may occur physically within more complete disk models,
are able to couple at least some parts of the plunging region to the rest
of the disk. In this case, angular momentum (and implicitly energy) is extr
acted from the material in the plunging region. Furthermore, the magnetic c
oupling to the plunging region can be highly time dependent with large fluc
tuations in the torque at the radius of marginal stability. This implies va
rying accretion efficiencies, both across systems and within a given system
at different times. The results suggest a possible link between changes in
X-ray and outflow activity, with both being driven by transitions between
weak and strong field states.