Gravitational Faraday effect from on-shell amplitudes

TL;DR

This paper investigates how the spin of a massive object influences classical scattering with massless particles, revealing higher-order gravitational Faraday effects and confirming universality and symmetry properties at second order in the gravitational constant.

Contribution

It computes the eikonal phase and spin effects in scattering up to 14th order in spin at second order in G, extending understanding of gravitational Faraday effects beyond linear order.

Findings

Gravitational Faraday effect appears at second order in G.

Universality holds up to NLO for spinning bodies.

Absence of certain spin structures in black hole limit confirmed.

Abstract

Effects of massive object's spin on massive-massless $2 \to 2$ classical scattering is studied. Focus is set on the less-considered dimensionless expansion parameter $\lambda/b$, where $\lambda$ is the massless particle's wavelength and $b$ is the impact parameter. Corrections in $\lambda/b$ start to appear from $\mathcal{O}(G^2)$, with leading correction terms tied to the gravitational Faraday effect, which is a special case of the Lense-Thirring effect. We compute the eikonal phase up to $\mathcal{O}(G^2)$ and extract spin effect on the scattering angle and time delay up to 14th order in spin. The gravitational Faraday effect at linear order in spin is reproduced by $\lambda/b$ correction terms, which we compute to higher orders in spin. We find that the equivalence principle, or universality, holds up to NLO for general spinning bodies, i.e. away from geometric optics limit. Furthermore, in the black hole limit, we confirm the absence of particular spin structure observed, along with the associated shift symmetry, and argue that it holds to arbitrary spin order at $\mathcal{O}(G^2)$ in the massless probe limit.