  We study the perception of Hawking radiation by different observers outside a
black hole. The analysis is done in terms of an effective-temperature function
that varies along the trajectory of each observer. The vacuum state of the
radiation field is chosen to be non-stationary, so as to mimic the switching-on
of Hawking radiation that would appear in a real black hole collapse. We
analyse how this vacuum is perceived by observers staying at a fixed radius, by
observers coming in free-fall from radial infinity at different times, and by
observers in free-fall released from finite radial positions. Results found
have a compelling physical interpretation. One main result, at first
unexpected, is that in general free-falling observers do perceive particle
emission by the black hole when crossing the event horizon. This happens
because of a diverging Doppler shift at the event horizon.
