Next to Leading Order Spin(1)Spin(1) Effects in the Motion of Inspiralling Compact Binaries

TL;DR

This paper calculates the next-to-leading order spin-spin effects in the motion of inspiraling compact binaries at 3PN order using effective field theory, completing the spin potential calculations needed for accurate modeling.

Contribution

It provides the last missing spin potential terms at 3PN order, including self-induced finite size effects, enabling precise equations of motion for spinning binaries.

Findings

Derived next-to-leading order Spin(1)Spin(1) potential at 3PN order

Included sub-leading self-induced finite size effects

Provided the precession equations for spinning binaries

Abstract

Using effective field theory techniques we compute the next to leading order Spin(1)Spin(1) terms in the potential of spinning compact objects at third Post-Newtonian order, including sub-leading self-induced finite size effects. This result represents the last ingredient to complete the relevant spin potentials to 3PN order from which the equations of motion follow via a canonical formalism. As an example we include the precession equation.