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 stars 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.
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