Virtual Hawking Radiation

TL;DR

This paper investigates how virtual Hawking gravitons influence gravitational scattering processes involving black holes and quantum fields, revealing a new quantum gravity effect at leading order in the semi-classical regime.

Contribution

It introduces the concept of off-shell Hawking radiation effects in scattering, providing a novel calculation of inelastic cross sections mediated by virtual Hawking gravitons.

Findings

Identifies a new leading order quantum gravity effect in black hole scattering.

Derives the inelastic cross section due to virtual Hawking gravitons.

Shows the effect is comparable to known one-loop graviton corrections.

Abstract

We consider the effects of off-shell Hawking radiation on scattering processes involving black holes coupled to quantum fields. The focus here is to the case of gravitational scattering of a scalar field mediated by the exchange of virtual Hawking gravitons from a four-dimensional Schwarzschild black hole. Our result is obtained in the context of a worldline effective field theory for the black hole, and is valid in the semi-classical limit where the Schwarzschild radius $r_s$ is larger than the Planck length $1/m_{Pl}$. In addition, we assume that four-momentum exchange $q$ is smaller than $r_s^{-1}$ and that the incoming particle has energy larger then the black hole's Hawking temperature. The inelastic cross section we obtain is a new, leading order quantum gravity effect, arising at the same order in $q^2/m_{Pl}^2$ as the well understood one-loop graviton vacuum polarization corrections to gravitational scattering between massive particles.