Charged particle scattering near the horizon

TL;DR

This paper investigates electromagnetic interactions near a black hole horizon, deriving solutions for Maxwell fields with charged sources, and computes scattering matrices showing how charged particles interact via soft photons in this extreme environment.

Contribution

It introduces a detailed analysis of Maxwell theory near the horizon, deriving gauge field configurations and computing the electromagnetic S-matrix using both first quantised and field-theoretic formalisms.

Findings

Derived near-horizon gauge field solutions for charged sources.

Calculated the electromagnetic S-matrix for charged particle scattering.

Confirmed the ladder resummation matches between formalisms and included sub-leading corrections.

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 $1\rightarrow 1$ formalism. We develop a theory for scalar QED near the horizon using which we compute the electromagnetic eikonal S-matrix from elastic $2\rightarrow 2$ 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.