  It has recently been demonstrated that the Shakura-Sunyaev prescription for
the kinematic viscosity in an advection-dominated accretion disk yields
physically reasonable solutions for the structure of the inflow close to the
event horizon. In particular, no violations of relativistic causality occur at
the horizon. This is somewhat surprising considering the diffusive nature of
the angular momentum transport in the Shakura-Sunyaev scenario, and it is
therefore natural to ask whether one can also obtain acceptable solutions for
the disk structure based on the various alternative models for the viscosity
that have been proposed, including the "deterministic" forms. In this paper we
perform a rigorous asymptotic analysis of the structure of an
advection-dominated accretion disk close to the event horizon of a nonrotating
black hole based on three of the alternative prescriptions for the viscosity
that have been suggested in the literature. We constrain the physical disk
model by stipulating that the stress must vanish at the horizon, which is the
fundamental inner boundary condition imposed by general relativity.
Surprisingly, we find that none of the three alternative viscosity
prescriptions yield physically acceptable disk structures close to the horizon
when the zero-torque condition is applied, whether the flow is in vertical
hydrostatic equilibrium or free-fall. Hence we conclude that the original
Shakura-Sunyaev prescription is the only one proposed so far that is physically
consistent close to the event horizon.
