Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics

TL;DR

This paper calculates all quadratic-in-spin interactions in spinning binaries at the third subleading post-Newtonian order, revealing new finite-size effects and a novel 'Spin Love number' as a probe for gravity and QCD.

Contribution

It provides the first complete derivation of quadratic-in-spin interactions at this order, extending effective field theory methods to generic compact objects and spin configurations.

Findings

Derived observable binding energies and gauge-invariant relations.

Identified a new finite-size effect with a 'Spin Love number'.

Extended the effective field theory approach for spinning gravitating objects.

Abstract

We obtain for the first time all quadratic-in-spin interactions in spinning binaries at the third subleading order in post-Newtonian (PN) gravity, and provide their observable binding energies and their gauge-invariant relations to the angular momentum. Our results are valid for generic compact objects, orbits, and spin orientations, and enter at the fifth PN order for maximally-rotating objects, thus pushing the state of the art. This is accomplished through an extension of the effective field theory of spinning gravitating objects, and of its computational application. We also discover a new finite-size effect which is unique to spinning objects, with a new ``Spin Love number'' as its characteristic coefficient, that is a new probe for gravity and QCD.