Black hole shadow with a cosmological constant for cosmological observers

We investigate the effect of the cosmological constant on the angular size of a black hole shadow. It is known that the accelerated expansion which is created by the cosmological constant changes the angular size of the black hole shadow for static observers. However, the shadow size must be calculated for the appropriate cosmological observes. We calculate the angular size of the shadow measured by cosmological comoving observers by projecting the shadow angle to this observer rest frame. We show that the shadow size tends to zero as the observer approaches the cosmological horizon. We estimate the angular size of the shadow for a typical supermassive black hole, e.g M87. It is found that the angular size of the shadow for cosmological observers and static observers is approximately the same at these scales of mass and distance. We present a catalog of supermassive black holes and calculate the effect of the cosmological constant on their shadow size and find that the effect could be $3\; precent$ for distant known sources like the Phoenix Cluster supermassive black hole.Comment: 8 pages, 2 figures, a few typos in table numbers and text correcte