  The origin of the rapid quasi-periodic variabilities observed in a number of
accreting black hole X-ray binaries is not understood. It has been suggested
that these variabilities are associated with diskoseismic oscillation modes of
the black hole accretion disk. In particular, in a disk with no magnetic field,
the so-called g-modes (inertial oscillations) can be self-trapped at the inner
region of the disk due to general relativistic effects. Real accretion disks,
however, are expected to be turbulent and contain appreciable magnetic fields.
We show in this paper that even a weak magnetic field (with the magnetic energy
much less than the thermal energy) can modify or "destroy" the self-trapping
zone of disk g-modes, rendering their existence questionable in realistic black
hole accretion disks. The so-called corrugation modes (c-modes) are also
strongly affected when the poloidal field approaches equal-partition. On the
other hand, acoustic oscillations (p-modes), which do not have vertical
structure, are not affected qualitatively by the magnetic field, and therefore
may survive in a turbulent, magnetic disk.
