Double copy, Kerr–Schild gauges and the effective-one-body formalism

We look for a classical double-copy-inspired relation between gravity and electrodynamics by connecting the descriptions of the scattering of two point masses, and of two point charges, in terms of perturbative (post-Minkowskian or post-Lorentzian) expansions. We do so by recasting available analytical information within the effective-one-body formalism using Kerr–Schild gauges in both cases. Working at the third perturbative level, we find that the usual linear relation (holding in the probe limit) between the adimensionalized electric potential, , and the Schwarzschild-like gravitational one, , is deformed, in the comparable-mass, comparable-charge, case, into a nonlinear relation which becomes universal in the high energy limit: .