# Charged test-particle scattering and effective one-body metrics with spin

## TL;DR

This paper advances the understanding of test-particle scattering in charged and spinning black hole spacetimes, providing new calculations and frameworks that connect scattering angles with effective one-body metrics, including spin effects.

## Contribution

It presents novel scattering angle calculations for charged particles in Kerr-Newman spacetime and constructs an effective one-body metric for spinning binaries up to second order in G.

## Key findings

- Scattering angles computed up to fourth order in G for charged particles.
- Re-derivation of the Darwin scattering formula via resummation.
- Construction of an effective one-body metric incorporating spin effects.

## Abstract

Using recently developed techniques, we consider weak-field test-particle scattering angle calculations in two distinct settings: Charged test-particles in spacetimes of charged sources and Effective One-Body theory with spin. We present scattering angle calculations up to $\mathcal O(G^4)$ of charged particles in the Kerr-Newman metric, including electromagnetic interactions up to second order in charge. Coulomb scattering is also discussed, and the well-known Darwin scattering formula is rederived by resummation. An Effective One-Body metric for a Kerr-Schwarzschild binary is constructed in a post-Minkowskian framework up to $\mathcal O(G^2)$ and first order in spin. Facilitated by explicit scattering calculations, our approach is equivalent with existing literature through gauge-like transformations. Finally, we investigate if the Newman Janis Algorithm applied to an Effective One-Body metric of non-spinning binaries represents a binary system with spin.