Physical laboratory at the center of the Galaxy

We review the physical processes that occur at the center of the Galaxy and that are related to the supermassive black hole Sgr A* residing there. The discovery of high-velocity S0 stars orbiting Sgr A* for the first time allowed measuring the mass of this supermassive black hole, the closest one to us, with a 10\% accuracy, with the result $M_h=(4.1\pm0.4)\times 10^6M_\odot$. Further monitoring can potentially discover the Newtonian precession of the S0 star orbits in the gravitational field of the black hole due to invisible distributed matter. This will yield the "weight" of the elusive dark matter concentrated there and provide new information for the identification of dark matter particles. The weak accretion activity of the "dormant quasar" at the Galactic center occasionally shows up as quasiperiodic X-ray and near-IR oscillations with mean periods of $11$ and $19$ min. These oscillations can possibly be interpreted as related to the rotation frequency of the Sgr A* event horizon and to the latitude oscillations of hot plasma spots in the accretion disk. Both these frequencies depend only on the black hole gravitational field and not on the accretion model. Using this interpretation yields quite the accurate values for both the mass $M_h$ and the spin $a$ (Kerr rotation parameter) of Sgr A*: $M_h=(4.2\pm0.2)\times 10^6M_\odot$ and $a=0.65\pm0.05$.