The 2PM Hamiltonian for binary Kerr to quartic in spin

TL;DR

This paper derives a 2PM Hamiltonian for binary Kerr black holes including spin effects up to quartic order, using scattering amplitudes and verifying with known results and test particle calculations.

Contribution

It introduces a novel method to obtain the conservative potential for spinning black holes up to quartic spin order from scattering amplitudes.

Findings

Derived the 2PM Hamiltonian including quartic spin terms.

Validated the Hamiltonian against lower-order results and test black hole scattering.

Provided a framework for incorporating high-order spin effects in binary black hole dynamics.

Abstract

From the S-matrix of spinning particles, we extract the 2 PM conservative potential for binary spinning black holes up to quartic order in spin operators. An important ingredient is the exponentiated gravitational Compton amplitude in the classical spin-limit for all graviton helicity sectors. The validity of the resulting Hamiltonian is verified by matching to known lower spin order results, as well as direct computation of the 2PM impulse and spin kicks from the eikonal phase and that from the test black hole scattering based on Mathisson-Papapetrou-Dixon equations.