  The discovery of high-amplitude brightness oscillations during type I X-ray
bursts from six low-mass X-ray binaries has provided a powerful new tool to
study the properties of matter at supranuclear densities, the effects of strong
gravity, and the propagation of thermonuclear burning. There is substantial
evidence that these brightness oscillations are produced by spin modulation of
one or two localized hot spots confined to the stellar surface. It is therefore
important to calculate the expected light curves produced by such hot spots
under various physical assumptions, so that comparison with the observed light
curves may most sensitively yield information about the underlying physical
quantities. In this paper we make general relativistic calculations of the
light curves and oscillation amplitudes produced by a rotating neutron star
with one or two hot spots as a function of spot size, stellar compactness,
rotational velocity at the stellar surface, spot location, orientation of the
line of sight of the observer, and the angular dependence of the surface
specific intensity. We find that stellar rotation and beaming of the emission
tend to increase the observed oscillation amplitudes whereas greater
compactness and larger spot size tend to decrease them. By applying these
results to 4U 1636--536, we show that this source must have two emitting spots
and place strong constraints on the neutron star's magnetic field geometry. We
also show that the data on the phase lags between photons of different energies
in the persistent pulsations in SAX J1808--58 can be fit well with a model in
which the observed hard leads are due to Doppler beaming.
