Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading post-Newtonian order

TL;DR

This paper advances the understanding of gravitational waves from inspiralling compact objects by calculating next-to-leading order spin-spin effects in the post-Newtonian expansion, confirming the consistency of different computational methods.

Contribution

It provides the first complete derivation of spin-spin effects at NLO in the PN expansion using the EFT framework, including dynamical invariants, fluxes, and radiative observables.

Findings

Derived spin-spin effects in orbital frequency and phase to NLO.

Calculated linear momentum fluxes and kick velocities at high PN order.

Confirmed equivalence of EFT and traditional methods for source multipoles.

Abstract

Using the gravitational potential and source multipole moments bilinear in the spins, first computed to next-to-leading order (NLO) in the post-Newtonian (PN) expansion within the effective field theory (EFT) framework, we complete here the derivation of the dynamical invariants and flux-balance equations, including energy and angular momentum. We use these results to calculate spin-spin effects in the orbital frequency and accumulated phase to NLO for circular orbits. We also derive the linear momentum and center-of-mass fluxes and associated kick-velocity, to the highest relevant PN order. We explicitly demonstrate the equivalence between the quadratic-in-spin source multipoles obtained using the EFT formalism and those rederived later with more traditional tools, leading to perfect agreement for spin-spin radiative observables to NLO among both approaches.