Virtual Hawking Radiation

We consider the effects of off shell Hawking radiation on scattering processes involving black holes coupled to quantum fields. The focus here is on 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 semiclassical 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.