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.
Peng Chen (Wed,) studied this question.