  We propose taking advantage of the simplicity of the Vaidya metric to
introduce time-dependent gravitational fields in classroom, i.e., to go beyond
the consideration of static or stationary situations. Exploration of the
ingoing Vaidya metric is motivated by its capturing certain properties of black
holes with growing or shrinking event horizon. In particular, a Vaidya metric
with infalling negative energy density will give a decent model, in the
vicinity of the horizon, for a Schwarzschild black hole emitting Hawking
radiation. It may be employed as a toy model for the complete spacetime of an
evaporating black hole, becoming less realistic with increasing distance from
the horizon. Several interesting predictions are developed: First, particles
dropped early enough before complete evaporation of the black hole cross its
horizon as easily as with an eternal black hole. Second, the Schwarzschild
radius takes on the properties of an apparent horizon, and the true event
horizon of the black hole is inside of it, as light can escape from the
shrinking apparent horizon. Third, a particle released from rest close enough
to, but outside, the apparent horizon, is strongly repelled and may escape to
infinity. An interpretation is given that demonstrates such a particle to be
able to compete, for a short time, in a race with a photon.
