The Reissner-Nordström-Tangherlini solution from scattering amplitudes of charged scalars

Abstract

The metric and the electromagnetic potential generated by a static, spherically symmetric charged massive object in any dimension are given by the Reissner-Nordström-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.

45 pages, 16 figures, typos corrected, version published on JHEP

References in corpus (4)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• A worldsheet for Kerr
• Graviton-Photon Scattering
• Kerr-Newman from Minimal Coupling

Cited by in corpus (5)

• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections
• Classical off-shell currents
• Conservative Scattering of Reissner-Nordström Black Holes at Third Post-Minkowskian Order
• Observables and Unconstrained Spin Tensor Dynamics in General Relativity from Scattering Amplitudes
• Gravitational multipoles from scattering amplitudes in higher dimensions