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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 thehorizon, diverges. In introductory courses on General Relativity, this factgives rise to questions about the reality of this divergence, and its eventualeffect on the geometry of the black hole. We address these concerns and showthat, eventually, it is the observer at rest who may induce corrections to themetric, unless its mass is crucially small when located near the horizon.

The infalling photon, the infalling particle, and the observer at rest near the horizon of a black hole