Classical potential for general spinning bodies

TL;DR

This paper derives the leading-order gravitational potential for spinning bodies using an on-shell scattering amplitude approach, revealing simplifications and cancellations that reproduce known Kerr black hole results.

Contribution

It introduces a method to compute spin-dependent gravitational potentials for general bodies at all spins, including novel insights into Wilson coefficient cancellations and factorization in the chiral basis.

Findings

Reproduced Kerr black hole potential at all spins.

Discovered cancellations of finite-spin deviations in Wilson coefficients.

Demonstrated factorization of spin dependence in the chiral basis.

Abstract

In this paper we compute the spin-dependent terms of the gravitational potential for general spinning bodies at the leading Newton's constant $G$ and to all orders in spin. We utilize the on-shell approach, which extracts the classical potential directly from the scattering amplitude. For spinning particles, extra care is required due to the fact that the spin space of each particle is independent. Once the appropriate matching procedures are applied, taking the classical-spin limit we obtain the potential for general spinning bodies. When the Wilson coefficients are set to unity, we successfully reproduced the potential for the Kerr black hole. Interestingly, for finite spins, we find that the finite-spin deviations from Kerr Wilson coefficients cancel with that in the matching procedure, reproducing the Kerr potential without the need for taking the classical-spin limit. Finally, we find that when cast into the chiral basis, the spin-dependence of minimal coupling exhibits factorization, allowing us to take the classical-spin limit straight forwardly.