Classical gravitational spinning-spinless scattering at $\mathcal{O}(G^{2} S^{\infty})$

TL;DR

This paper computes the classical gravitational scattering amplitude involving a spinning and a spinless object at second order in Newton's constant, incorporating all spin orders, and derives the eikonal phase for aligned spins.

Contribution

It introduces a method to calculate all-spin gravitational scattering amplitudes at second order in G, fixing parameters using ultrarelativistic limits, and resumming spin effects into hypergeometric functions.

Findings

Derived the all-spin scattering amplitude at (G^2) order.

Fixed amplitude parameters using ultrarelativistic limit considerations.

Resummed spin dependence into hypergeometric functions.

Abstract

Making use of the recently-derived, all-spin, opposite-helicity Compton amplitude, we calculate the classical gravitational scattering amplitude for one spinning and one spinless object at $\mathcal{O}(G^{2})$ and all orders in spin. By construction, this amplitude exhibits the spin structure that has been conjectured to describe Kerr black holes. This spin structure alone is not enough to fix all deformations of the Compton amplitude by contact terms, but when combined with considerations of the ultrarelativistic limit we can uniquely assign values to the parameters remaining in the even-in-spin sector. Once these parameters are determined, much of the spin dependence of the amplitude resums into hypergeometric functions. Finally, we derive the eikonal phase for aligned-spin scattering.