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

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.

24 pages, 3 tables

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• Classical gravitational scattering at $\mathcal{O}(G^2{S}_1^{\infty }{S}_2^{\infty })$
• Observables from the Spinning Eikonal
• A Rutherford-like formula for scattering off Kerr-Newman BHs and subleading corrections