We address the problem of the physical relevance of the "trans-Planckian" frequencies which occur in Hawking radiation. We first show that these frequencies characterize the fluctuations of the energy-momentum tensor around its regular mean value. These fluctuations are isolated, and their properties obtained, by considering the energy density correlated to a specific final state of the Hawking radiation. This conditional energy density is expressed in terms of an off-diagonal matrix element and is complex. The dynamical relevance of these conditional fluxes is then proven in the context of perturbation theory in a $S$ matrix formulation. In particular, we show how this analysis can be used to study back reaction effects to the production of a single quantum. Furthermore these conditional fluxes offer a historical description of the emergence of Hawking quanta from vacuum fluctuations. It is shown that initially these fluctuations are located around the lightlike geodesic that shall generate the horizon and have exponentially large energy densities. Upon exiting from the star they break up into two pieces. The external one is red shifted and becomes an on mass shell quantum, the other, its "partner," ends up in the singularity.

• Received 27 March 1996

DOI:https://doi.org/10.1103/PhysRevD.54.7444