Scattering Radiation Emitted Near a Black Hole Horizon

Abstract

We study a family of outgoing electromagnetic radiation states prepared outside but arbitrarily close to the horizon of a Schwarzschild black hole, with frequencies that remain uniformly bounded in the local source frame. As the preparation point approaches the horizon, gravitational redshift drives this radiation toward zero Killing frequency and into a controlled soft regime at any fixed exterior scattering radius. The radiation considered here may be viewed as part of the Hawking radiation spectrum. After including transmission through the Schwarzschild potential, we obtain the leading soft response in a localized region of weak curvature and formulate an inclusive scattering probability that is infrared safe. Through the infrared triangle, this response is related to electromagnetic memory at future null infinity. The conditioned memory record probes angular projections of the zero-frequency component of the transmitted radiation, together with their correlations with the accompanying hard scattering outcome. It can therefore provide an additional asymptotic constraint and a partial fingerprint of the radiation source.

20 pages, 3 figures, substantially revised and expanded