Quantum metric fluctuations and Hawking radiation

In this Rapid Communication we study the gravitational interactions between outgoing configurations giving rise to Hawking radiation and in-falling configurations. We exploit the fact that the fluctuations of the in-falling flux of energy across the horizon do not vanish in the vacuum state. This leads to interactions with outgoing quanta which grow near the horizon and prevent the appearance of trans-Planckian frequencies. These interactions express themselves in terms of metric fluctuations and lead to a description of Hawking radiation which is similar to that obtained from sound propagation in condensed matter models.