  The high pericenter velocities (up to a few percent of light) of the S stars
around the Galactic-center black hole suggest that general relativistic effects
may be detectable through the time variation of the redshift during pericenter
passage. Previous work has computed post-Newtonian perturbations to the stellar
orbits. We study the additional redshift effects due to perturbations of the
light path (what one may call "post-Minkowskian'' effects), a calculation that
can be elegantly formulated as a boundary-value problem. The post-Newtonian and
post-Minkowskian redshift effects are comparable: both are O(beta^3) and amount
to a few km/s at pericenter for the star S2. On the other hand, the
post-Minkowskian redshift contribution of spin is O(beta^5) and much smaller
than the O(beta^4) post-Newtonian effect, which would be approximately 0.1km/s
for S2.
