Kerr-Newman from Minimal Coupling

TL;DR

This paper demonstrates that all four-dimensional asymptotically flat black hole solutions at 1PN order can be derived from minimal coupling amplitudes, with rotating solutions obtained via a spin-factor deformation, linking on-shell amplitudes to classical black hole metrics.

Contribution

It introduces a novel method to derive Kerr-Newman and Reissner-Nordstr"om solutions from minimal coupling amplitudes using spin-factor deformations, connecting scattering amplitudes to classical black hole solutions.

Findings

Derived black hole metrics from scattering amplitudes at 1PN order.

Showed rotating solutions via spin-factor deformation of non-rotating amplitudes.

Linked impact parameter deformations to the Janis-Newman algorithm.

Abstract

We show that at 1PN all four-dimensional black hole solutions in asymptotically flat spacetimes can be derived from leading singularities involving minimally coupled three-particle amplitudes. Furthermore, we show that the rotating solutions can be derived from their non-rotating counterparts by a spin-factor deformation of the relevant minimally coupled amplitudes. To show this, we compute the tree-level and one-loop leading singularities for a heavy charged source with generic spin s. We compute the metrics both with and without a spin factor and show that we get both the Kerr-Newman and Reissner-Nordstr\"om solutions respectively. We then go on to compute the impulse imparted to the probe particle in the infinite spin limit and show that the spin factor induces a complex deformation of the impact parameter, as was recently observed for Kerr black holes in a recent paper by Arkani-Hamed et al. We interpret these observations as being the on-shell avatar of the Janis-Newman algorithm for charged black holes.