Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries

TL;DR

This paper derives and analyzes cubic-in-spin effects in the dynamics and gravitational wave emission of compact binaries at leading post-Newtonian order, highlighting their significance for rapidly spinning black hole systems.

Contribution

It extends the Lagrangian formalism to cubic order in spins, deriving equations of motion, precession, and stress-energy tensor, and computes their impact on gravitational wave energy flux.

Findings

Cubic-in-spin effects enter at 3.5PN order in gravitational wave flux.

Derived covariant equations for spin precession and motion including cubic effects.

Simplified results provided for spin-aligned, circular orbits.

Abstract

We investigate cubic-in-spin effects for inspiralling compact objects binaries, both in the dynamics and the energy flux emitted in gravitational waves, at the leading post-Newtonian order. We use a Lagrangian formalism to implement finite-size effects, and extend it at cubic order in the spins, which corresponds to the octupolar order in a multipolar decomposition. This formalism allows us to derive the equation of motion, equations of precession for the spin, and stress-energy tensor of each body in covariant form, and admits a formal generalization to any multipolar order. For spin-induced multipoles, i.e. in the case where the rotation of the compact object is sole responsible for the additional multipole moments, we find a unique structure for the octupolar moment representing cubic-in-spin effects. We apply these results to compute the associated effects in the dynamics of compact binary systems, and deduce the corresponding terms in the energy loss rate due to gravitational waves. These effects enter at the third-and-a-half post-Newtonian order, and can be important for binaries involving rapidly spinning black holes. We provide simplified results for spin-aligned, circular orbits, and discuss the quantitative importance of the new contributions.