  In this paper we derive exact analytical formulas for the evolution of the
photon sphere and for the angular radius of the shadow in a special Vaidya
spacetime. The Vaidya metric describes a spherically symmetric object that
gains or loses mass, depending on a mass function $m(v)$ that can be freely
chosen. Here we consider the case that $m(v)$ is a linearly increasing or
decreasing function. The first case can serve as a simple model for an
accreting black hole, the second case for a (Hawking) radiating black hole.
With a linear mass function the Vaidya metric admits a conformal Killing vector
field which, together with the spherical symmetry, gives us enough constants of
motion for analytically calculating the light-like geodesics. Both in the
accreting and in the radiating case, we first calculate the light-like
geodesics, the photon sphere, the angular radius of the shadow, and the
red-shift of light in coordinates in which the metric is manifestly conformally
static, then we analyze the photon sphere and the shadow in the original
Eddington-Finkelstein-like Vaidya coordinates.
