  We show that when the gravitational force is correctly calculated in dealing
with the vertical hydrostatic equilibrium of black hole accretion disks, the
relationship that is valid for geometrically thin disks, i.e., $c_s/\Omega_K H
=$ constant, where $c_s$ is the sound speed, $\Omega_K$ is the Keplerian
angular velocity, and $H$ is the half-thickness of the disk, does not hold for
slim disks. More importantly, by adopting the correct vertical gravitational
force in studies of thermal equilibrium solutions, we find that there exists a
maximally possible accretion rate for each radius in the outer region of
optically thick accretion flows, so that only the inner region of these flows
can possibly take the form of slim disks, and strong outflows from the outer
region are required to reduce the accretion rate in order for slim disks to be
realized.
