Virtual Hawking Radiation

Understand

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.