Einstein-Planck Formula, Equivalence Principle and Black Hole Radiance

The presence of gravity implies corrections to the Einstein-Planck formula $E=h \nu$. This gives hope that the divergent blueshift in frequency, associated to the presence of a black hole horizon, could be smoothed out for the energy. Using simple arguments based on Einstein's equivalence principle we show that this is only possible if a black hole emits, in first approximation, not just a single particle, but thermal radiation.