The black hole at the Galactic Center: observations and models
  One of the most interesting astronomical objects is the Galactic Center. We
concentrate our discussion on a theoretical analysis of observational data of
bright stars in the IR-band obtained with large telescopes. We also discuss the
importance of VLBI observations of bright structures which could characterize
the shadow at the Galactic Center. There are attempts to describe the Galactic
Center with alternative theories of gravity and in this case one can constrain
parameters of such theories with observational data for the Galactic Center. In
particular, theories of massive gravity are intensively developing and
theorists have overcome pathologies presented in initial versions of these
theories. In theories of massive gravity, a graviton is massive in contrast
with GR where a graviton is massless. Now these theories are considered as an
alternative to GR. For example, the LIGO-Virgo collaboration obtained the
graviton mass constraint of about $1.2 \times 10^{-22}$ eV in their first
publication about the discovery of the first gravitational wave detection event
that resulted of the merger of two massive black holes. Surprisingly, one could
obtain a consistent and comparable constraint of graviton mass at a level
around $m_{g} < 2.9 \times 10^{-21}$ eV from analysis of observational data on
the trajectory of the star S2 near the Galactic Center. Therefore, observations
of bright stars with existing and forthcoming telescopes such as the European
Extremely Large Telescope (E-ELT) and the Thirty Meter Telescope (TMT) are
extremely useful for investigating the structure of the Galactic Center in the
framework of GR, but these observations also give a tool to confirm, rule out
or constrain alternative theories of gravity.
