Selection of the Valid Gravitation Theory from Observations of Black Hole Images$${}^{\sharp}$$

Abstract A fast progress in the observational technologies in astrophysics provides a unique possibility for detailed observations of black holes in the nearest future. It will be possible to verify general relativity (GR) and its numerous modifications in the strong field limit by using observational data from advanced cosmic interferometric observatories. We review the modeled images of a rotating black hole in different appropriate cases: a luminous distant background, a thin accretion disk, and a luminous moving hot spots in relativistic jets along the black hole rotation axis. Detailed observations of astrophysical supermassive black holes SgrA* and M87* will be possible within the nearest 10 years by using the Millimetron Space Observatory proposed and developed by domestic scientists.