  When a massive test particle or a photon fall radially into a black hole,
their energy, as measured by a static observer located very close to the
horizon, diverges. In introductory courses on General Relativity, this fact
gives rise to questions about the reality of this divergence, and its eventual
effect on the geometry of the black hole. We address these concerns and show
that, eventually, it is the observer at rest who may induce corrections to the
metric, unless its mass is crucially small when located near the horizon.
