Stars lensed by the supermassive black hole in the center of the Milky
  Way: predictions for ELT, TMT, GMT, and JWST
  Gravitational lensing is an important prediction of general relativity,
providing both its test and a tool to detect faint but amplified sources and to
measure masses of lenses. For some applications (e.g. testing the theory), a
point source lensed by a point-like lens would be more advantageous. However,
until now only one gravitationally lensed star has been resolved. The future
telescopes will resolve very small lensing signatures for stars orbiting the
supermassive black hole (SMBH) in the center of the Milky Way. The lensing
signatures should however be easier to detect for background stars. We predict
that ELT, TMT, and GMT will resolve the lensed images of around 100 (60) stars
in the disk and 30 (20) stars in the bulge in the background of the SMBH, down
to 28 (27) mag (Vega) limits at K-band, requiring 5 (1) hr of integration. In
order to detect several such stars one needs the limit of at least 24 mag. With
a decade-long monitoring one can also detect the rotation of the lensed images.
The detection of elongated images will not be possible, because this would
require a nearly perfect source-lens alignment. JWST will likely be limited by
the confusion caused by stars near the Galactic center. The detection of such
lensed images will provide a very clean test of general relativity, when
combined with the SMBH mass measurement from orbital motions of stars, and
accurate measurements of the SMBH properties, because both the source and the
lens can be considered point-like.
