RELATIVISTIC REDSHIFT EFFECTS AND THE GALACTIC-CENTER STARS

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(-1) 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 similar to 0.1 km s(-1) for S2.