Shadow of a black hole at cosmological distances

Cosmic expansion is expected to influence the size of a black hole shadow observed by a comoving observer. Except for the simplest case of the Schwarzschild black hole in the de Sitter universe, an analytical approach for the calculation of shadow size in an expanding universe is still not developed. In this paper, we present the approximate method based on using the angular size redshift relation. This approach is appropriate for the general case of any multicomponent universe (with matter, radiation, and dark energy). In particular, we show that supermassive black holes at large cosmological distances in the Universe with matter may give a shadow size approaching the shadow size of the black hole in the center of our Galaxy, and present sensitivity limits.