ИСТИНА

In October 2019, the Nobel prize in physics was awarded for clarifying ©the founda-tions of our modern understanding of the history of the Universe from the Great Explosion to the present dayª, in particular, half of the prize was given to J. Peebles for his work on physical cosmology, and half of the prize was divided between M. Mayor and D. Queloz for the discovery of the ˇrst exoplanet near a solar-type star. In fact, this also means recognition of the importance of investigations in gravity, astrophysics and cosmology. The application of astronomical observations of the Galactic Center to obtain restrictions on the gravitational ˇeld near a supermassive black hole was discussed in this paper. Since Newton's times, it has been known that the gravitational potential can be estimated from the analysis of test body motions in this ˇeld. There are currently two main methods of observation to study the gravitational potential in the Galactic Center to prove a presence of a supermassive black hole there, namely, (a) monitoring orbits of bright stars near the Galactic Center using the largest telescopes with adaptive optics; (b) measuring the size and shape of shadows around the black hole that provides an alternative way to evaluate the parameters of a black hole with the Event Horizon Telescope. In April 2019, the Event Horizon Telescope collaboration reported the reconstruction of bright structures in the vicinity of the supermassive black hole in the center of M87 galaxy. Earlier, we discussed the opportunities to test theories of gravity with observations of bright stars at the Galactic Center of the Galaxy. Recently, the LIGOÄVirgo collaboration not only did it detect gravitational waves and binary black holes, but it also found the upper limit on graviton mass mg < 1.2 • 10−22 eV [1]. We showed that the analysis of the trajectories of bright stars could constrain graviton mass with a comparable accuracy. We discussed opportunities to improve the current estimates of the graviton mass with subsequent observations by Keck, VLT, GRAVITY, E-ELT and TMT, and thus opportunities to reach a graviton mass constraint such low as mg < 5 • 10−23 eV [2]. We also discussed the recent results of the GRAVITY and Keck collaboration on the estimation of gravitational redshifts for S2 star near its pericenter passage. These results conˇrmed predictions of General Relativity for the Galactic Center. Therefore, the analysis makes ’…‘’› ’… ƒˆ’ 879 it possible to consider observations of bright stars near Galactic Center as a useful tool to constrain parameters of gravity theories, in particular to test General Relativity. We have shown that in the future graviton mass constraints found with analysis of trajectories of bright stars will be better than the current estimates obtained from observations of gravitational wave signals using LIGOÄVirgo interferometers. As shown in [3], similarly, we could obtain limits on the tidal charge for the black hole. Analysis of the size and shapes of shadows around the supermassive black hole at the Galactic Center (or/and at the center of M87), observed with the Event Horizon Telescope, could constrain parameters of various alternative theories of gravity, as it was discussed in [4].