Observational tests of general relativity and alternative theories of gravity with Galactic Center observations using current and future large observational facilities

It is established that there are supermassive black holes in centers of galaxies. A supermassive black hole with mass around 4 × 10⁶ M_⊙ is located at the Galactic Center. Such an approach for the Galactic Center looks rather natural, in spite of that consequences of model must be checked with observations. We discuss opportunities to check this with forthcoming observations of shadows in mm band for the Galactic Center as it was done recently for M87★. Observations of bright stars moving near the Galactic Center gives another opportunity to evaluate gravitational potential. We discuss opportunities to use these observations to constrain alternative theories of gravity.