Einstein-Planck Formula, Equivalence Principle and Black Hole Radiance

TL;DR

This paper explores how gravity affects the Einstein-Planck formula and suggests that black holes must emit thermal radiation to resolve frequency blueshift divergences, linking the equivalence principle to black hole radiance.

Contribution

It demonstrates that gravitational corrections to the Einstein-Planck formula imply black holes emit thermal radiation, connecting the equivalence principle to Hawking radiation.

Findings

Gravity modifies the Einstein-Planck relation near black holes

Black holes emit thermal radiation to prevent frequency divergence

The equivalence principle supports black hole thermality

Abstract

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.