  The local axisymmetric stability of hydrodynamical and magnetized,
nearly-Keplerian gaseous accretion disks around non-rotating black holes is
examined in the vicinity of the classical marginally-stable orbit (at radii ~
R_ms). An approximate Paczynski-Wiita pseudo-Newtonian potential is used.
Hydrodynamical disks are linearly unstable inside a radius which differs
slightly from the classical R_ms value because of finite pressure and radial
stratification effects. Linear stresses associated with unstable hydrodynamical
modes vanish exactly at the radius of marginal stability and are generally
positive inside of that radius. When a magnetic field is introduced, however,
the concept of radius of marginal stability becomes largely irrelevant because
there are linearly unstable magneto-rotational modes everywhere. Associated
linear stresses are positive and continuous across the region of hydrodynamical
marginal stability, even for large-scale "hydro-like" modes subject only to
weak magnetic tension. This conclusion is valid for arbitrarily thin disks (in
ideal MHD) and it does not require a large-scale "radially-connecting" magnetic
field. Results on hydrodynamical diskoseismic modes trapped in deep
relativistic potential wells should be revised to account for the
short-wavelength Alfven-like behavior of inertio-gravity waves in magnetized
disks.
