The Reissner-Nordstr\"om-Tangherlini solution from scattering amplitudes of charged scalars

TL;DR

This paper derives the Reissner-Nordström-Tangherlini solution in arbitrary dimensions using scattering amplitudes of charged scalars, connecting quantum amplitude calculations with classical gravitational and electromagnetic fields.

Contribution

It introduces a novel method to obtain the classical charged black hole solution from quantum scattering amplitudes up to third post-Minkowskian order.

Findings

Amplitudes develop UV divergences in 4 and 5 dimensions, canceled by higher-derivative counterterms.

Logarithmic terms in the solution match the post-Minkowskian expansion in de Donder gauge.

The approach generalizes previous chargeless case results to charged scenarios.

Abstract

The metric and the electromagnetic potential generated by a static, spherically symmetric charged massive object in any dimension are given by the Reissner-Nordstr\"om-Tangherlini solution. We derive the expansion of this solution up to third post-Minkowskian order by computing the classical contribution of scattering amplitudes describing the emission of either a graviton or a photon from a massive charged scalar field up to two loops. In four and five dimensions these amplitudes develop ultraviolet divergences that are cancelled by higher-derivative counterterms in a way that generalises what was recently shown to happen in the chargeless case. This renormalisation procedure produces logarithmic terms that match exactly those produced in the post-Minkowskian expansion of the classical solution in de Donder gauge.