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.
