Probing Post-Newtonian Gravity near the Galactic Black Hole with Stellar   Doppler Measurements
  Stars closely approaching the massive black hole in the center of the Galaxy provide a unique opportunity to probe post-Newtonian physics in a yet unexplored regime of celestial mechanics. Recent advances in infrared stellar spectroscopy allow the precise measurement of stellar Doppler shift curves and thereby the detection of beta-squared post-Newtonian effects (gravitational redshift in the black hole's potential and the transverse Doppler shift). We formulate a detection procedure in terms of a simplified post-Newtonian parametrization. We then use simulations to show that these effects can be decisively detected with existing instruments after about a decade of observations. We find that neglecting these effects can lead to statistically significant systematic errors in the derived black hole mass and distance. 
Shay Zucker, Tal Alexander, Stefan Gillessen, Frank Eisenhauer,   Reinhard Genzel