Scattering Hawking Radiation

We analyze the physical consequences of scattering Hawking radiation emitted in the vicinity of the horizon of a Schwarzschild black hole. The Hawking radiation from the horizon becomes soft at a large distance away from the horizon due to the gravitational redshift, and the above process is exactly the soft theorem in curved spacetime. For an observer located at infinity, such a scattering process introduces a large gauge transformation, which can be regarded as a memory effect. The large gauge transformation is expected to encode more information about the radiation and might shed light on the black hole information paradox.