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 → 1 formalism. We develop a theory for scalar QED near the horizon using which we compute the electromagnetic eikonal S-matrix from elastic 2 → 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.
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Acknowledgments
We are grateful to Gerard ’t Hooft for various helpful conversations over the years. We acknowledge the support of the Netherlands Organisation for Scientific Research (NWO) and the Delta-Institute for Theoretical Physics (D-ITP) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). Nava G. is currently supported by project RTI4001 of the Department of Atomic Energy, Govt. of India.
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Feleppa, F., Gaddam, N. & Groenenboom, N. Charged particle scattering near the horizon. J. High Energ. Phys. 2024, 148 (2024). https://doi.org/10.1007/JHEP02(2024)148
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DOI: https://doi.org/10.1007/JHEP02(2024)148