Classical gravitational scattering at $\mathcal{O}(G^{2} S_{1}^{\infty} S_{2}^{\infty})$

TL;DR

This paper computes the classical gravitational scattering amplitude of two rotating Kerr black holes at second order in Newton's constant, including all relevant spin-induced multipoles and contact terms, providing a comprehensive framework for high-spin black hole interactions.

Contribution

It introduces a complete calculation of Kerr black hole scattering at (G^2) order with all spin effects and contact terms, enabling detailed analysis of their scattering properties.

Findings

Derived the scattering amplitude including all contact terms.

Provided a template for high-spin gravitational scattering calculations.

Facilitated exploration of special properties for specific contact-term values.

Abstract

We calculate the scattering of two rotating objects with the linear-in-curvature spin-induced multipoles of Kerr black holes at $\mathcal{O}(G^2)$ and all orders in the spins of both objects. This is done including the complete set of contact terms potentially relevant to Kerr-black-hole scattering at $\mathcal{O}(G^2)$. As such, Kerr black holes should be described by this scattering amplitude for a specific choice of values for the contact-term coefficients. The inclusion of all potential contact terms means this amplitude allows for a comprehensive search for structures emerging for certain values of the coefficients, and hence special properties that might be exhibited by Kerr-black-hole scattering. Our result can also act as a template for comparison for future computations of classical gravitational high-spin scattering.