Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling

TL;DR

This paper derives equations of motion for spinning binary systems including radiation reaction and spin-spin effects at high post-Newtonian orders, revealing spin precession caused by radiation damping and confirming energy and angular momentum conservation.

Contribution

It introduces the first detailed derivation of radiation-reaction effects on spin-spin interactions in binary systems at 3.5PN order.

Findings

Radiation damping causes spin precession at 3.5PN order.

Spin-spin effects influence the evolution of individual spins.

Energy and angular momentum loss balance radiative flux calculations.

Abstract

Using post-Newtonian equations of motion for fluid bodies that include radiation-reaction terms at 2.5 and 3.5 post-Newtonian (PN) order O[(v/c)^5] and O[(v/c)^7] beyond Newtonian order), we derive the equations of motion for binary systems with spinning bodies, including spin-spin effects. In particular we determine the effects of radiation-reaction coupled to spin-spin effects on the two-body equations of motion, and on the evolution of the spins. We find that radiation damping causes a 3.5PN order, spin-spin induced precession of the individual spins. This contrasts with the case of spin-orbit coupling, where there is no effect on the spins at 3.5PN order. Employing the equations of motion and of spin precession, we verify that the loss of total energy and total angular momentum induced by spin-spin effects precisely balances the radiative flux of those quantities calculated by Kidder et al.