Scattering Gravitons off General Spinning Compact Objects to $\mathcal{O}(G^2 S^4)$

TL;DR

This paper calculates the one-loop gravitational scattering amplitude for spinning compact objects, including high-order spin effects, providing insights into their dynamics relevant for gravitational wave physics.

Contribution

It extends previous work by including quartic spin terms and finite-size effects up to hexadecapolar order in the classical scattering amplitude.

Findings

Derived the scattering phase for spinning objects at second post-Minkowskian order.

Linked the eikonal limit to scalar probe dynamics in Kerr backgrounds.

First complete one-loop Compton scattering description for generic spinning objects at this order.

Abstract

We compute the classical one-loop gravitational Compton amplitude describing the scattering of a graviton off a massive spinning compact object at the second post-Minkowskian order, including terms through the quartic order in spin. Our analysis includes spin-induced finite-size effects up to the hexadecapolar order, and extends recent results obtained for minimal couplings at the quadratic order in spin. From the amplitude, we determine the scattering phase in momentum space, applicable in both the eikonal and wave regimes. In the eikonal limit, we then isolate the spin-independent contribution of the graviton field, explicitly linking it to the dynamics of a massless scalar probe in a Kerr background. This constitutes the first complete description of classical one-loop Compton scattering for generic spinning compact objects at the second post-Minkowskian and hexadecapolar orders.