Amplitudes for Hawking Radiation

TL;DR

This paper derives the Hawking radiation spectrum using a novel semiclassical scattering amplitude approach involving Feynman diagrams, including one-loop corrections that account for black hole size effects.

Contribution

It introduces a new semiclassical scattering amplitude method for Hawking radiation, incorporating in-in amplitudes and one-loop corrections related to black hole size.

Findings

Derived Hawking spectrum from Feynman diagrams

Computed one-loop correction analogous to triangle correction

Identified finite-size effects related to black hole radius

Abstract

We obtain the Hawking spectrum by exponentiating a series of Feynman diagrams describing a scalar field scattering through a collapse background. Our approach is rooted in semiclassical methods of scattering amplitudes which have recently been developed for application to gravitational-wave physics. The diagrams we encounter do not compute a standard amplitude, but rather an in-in generalisation of an amplitude which is closely connected to the Bogoliubov coefficients. We also compute the subdominant one-loop correction in our perturbative approach, analogous to the triangle correction to Schwarzschild scattering. This term can be interpreted as a finite-size correction sensitive to the radius of the black hole.