  We analytically calculate the influence of a plasma on the shadow of a black
hole (or of another compact object). We restrict to spherically symmetric and
static situations, where the shadow is circular. The plasma is assumed to be
non-magnetized and pressure-less. We derive the general formulas for a
spherically symmetric plasma density on an unspecified spherically symmetric
and static spacetime. The formalism applies not only to black holes but also,
e.g., to wormholes. As examples for the underlying spacetime model, we consider
the Schwarzschild spacetime and the Ellis wormhole. In particular, we treat the
case that the plasma is in radial free fall from infinity onto a Schwarzschild
black hole. The perspectives of actually observing the influence of a plasma on
the shadows of supermassive black holes are discussed.
