Charged particle scattering near the horizon

Abstract

We study Maxwell theory, in the presence of charged scalar sources, near the black hole horizon in a partial wave basis. We derive the gauge field configuration that solves Maxwell equations in the near-horizon region of a Schwarzschild black hole when sourced by a charge density of a localised charged particle. This is the electromagnetic analog of the gravitational Dray-'t Hooft shockwave near the horizon. We explicitly calculate the S-matrix associated with this shockwave in the first quantised $1\to 1$ formalism. We develop a theory for scalar QED near the horizon using which we compute the electromagnetic eikonal S-matrix from elastic $2\to 2$ scattering of charged particles exchanging soft photons in the black hole eikonal limit. The resulting ladder resummation agrees perfectly with the result from the first quantised formalism, whereas the field-theoretic formulation allows for a computation of a wider range of amplitudes. As a demonstration, we explicitly compute sub-leading corrections that arise from four-vertices.

23 pages + appendices. v2: typos corrected, some clarifications added. v3: fixed an incorrect Feynman diagram. v4: further typos fixed and clarifications added

References in corpus (2)

• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• From Shockwaves to the Gravitational Memory Effect

Cited by in corpus (2)

• Celestial Eikonal Amplitudes in the Near-Horizon Region
• All near-horizon symmetries of the Schwarzschild black hole in linearised gravity