Hawking Radiation from Feynman Diagrams

TL;DR

This paper uses Feynman diagrams to analyze Hawking radiation, showing how quantum scattering processes relate to classical descriptions and identifying conditions under which Hawking radiation ceases.

Contribution

It introduces a quantum field theoretic approach to Hawking radiation using Feynman diagrams and clarifies the transition from quantum to classical regimes.

Findings

Hawking radiation is recovered for low photon energies

Thermal photon production stops when partner energies reach the infalling particle's mass

The approach links scattering amplitudes to Hawking radiation phenomena

Abstract

The aim of this letter is to clarify the relationships between Hawking radiation and the scattering of light by matter falling into a black hole. To this end we analyze the S-matrix elements of a model composed of a massive infalling particle (described by a quantized field) and the radiation field. These fields are coupled by current-current interactions and propagate in the Schwarzschild geometry. As long as the photons energy is much smaller than the mass of the infalling particle, one recovers Hawking radiation since our S-matrix elements identically reproduce the Bogoliubov coefficients obtained by treating the trajectory of the infalling particle classically. But after a brief period, the energy of the `partners' of Hawking photons reaches this mass and the production of thermal photons through these interactions stops. The implications of this result are discussed.