Observing gravitational lensing effects by Sgr A* with GRAVITY
  The massive black hole at the Galactic center Sgr A* is surrounded by a
cluster of stars orbiting around it. Light from these stars is bent by the
gravitational field of the black hole, giving rise to several phenomena:
astrometric displacement of the primary image, the creation of a secondary
image that may shift the centroid of Sgr A*, magnification effects on both
images. The near-to-come second generation VLTI instrument GRAVITY will perform
observations in the Near Infrared of the Galactic Center at unprecedented
resolution, opening the possibility of observing such effects. Here we
investigate the observability limits for GRAVITY of gravitational lensing
effects on the S-stars in the parameter space [DLS,gamma,K], where DLS is the
distance between the lens and the source, gamma is the alignment angle of the
source, and K is the source apparent magnitude in the K-band. The easiest
effect to be observed in the next years is the astrometric displacement of
primary images. In particular the shift of the star S17 from its Keplerian
orbit will be detected as soon as GRAVITY becomes operative. For exceptional
configurations it will be possible to detect effects related to the spin of the
black hole or Post-Newtonian orders in the deflection.
