  We model the variability profiles of millisecond period X-ray pulsars. We
performed three-dimensional magnetohydrodynamic simulations of disk accretion
to millisecond period neutron stars with a misaligned magnetic dipole moment,
using the pseudo-Newtonian Paczynski-Wiita potential to model general
relativistic effects. We found that the shapes of the resulting funnel streams
of accreting matter and the hot spots on the surface of the star are quite
similar to those for more slowly rotating stars obtained from earlier
simulations using the Newtonian potential. The funnel streams and hot spots
rotate approximately with the same angular velocity as the star. The spots are
bow-shaped (bar-shaped) for small (large) misalignment angles. We found that
the matter falling on the star has a higher Mach number when we use the
Paczynski-Wiita potential than in the Newtonian case.
  Having obtained the surface distribution of the emitted flux, we calculated
the variability curves of the star, taking into account general relativistic,
Doppler and light-travel-time effects. We found that general relativistic
effects decrease the pulse fraction (flatten the light curve), while Doppler
and light-travel-time effects increase it and distort the light curve. We also
found that the light curves from our hot spots are reproduced reasonably well
by spots with a gaussian flux distribution centered at the magnetic poles. We
also calculated the observed image of the star in a few cases, and saw that for
certain orientations, both the antipodal hot spots are simultaneously visible,
as noted by earlier authors.
