Dynamics of Spinning Binary at 2PM

TL;DR

This paper develops a covariant approach to compute the gravitational scattering amplitude for spinning black holes, expanding in spin and comparing with existing results, advancing understanding of binary black hole dynamics.

Contribution

It introduces a covariant method for calculating the classical one-loop amplitude for Kerr black holes at all spin orders, incorporating unitarity and contact terms from Teukolsky solutions.

Findings

Agreement with existing literature on one-loop amplitudes

Classical eikonal computed for aligned spins at high order

Expanded amplitude up to order G^2 a^8 in spin

Abstract

We consider the covariant proposal for the gravitational Compton amplitude for a Kerr black hole. Employing the covariant three- and four-point Compton amplitudes, we assemble the classical one-loop integrand on the maximal cut at all orders in spin, utilizing the method of unitarity. Expanding in powers of spin, we evaluate the one-loop amplitude up to $\mathcal O(G^2 a^8)$. Supplemented with extra contact contributions derived from the far-zone data of the Teukolsky solutions, the one-loop amplitude is in agreement with results available in the literature. We showcase the classical eikonal in the aligned-spin case at $\mathcal O(G^2 a^7)$.