# Radiation reaction for spinning bodies in effective field theory II: Spin-spin effects

## TL;DR

This paper calculates the leading quadratic-in-spin radiation-reaction effects on binary systems at four-and-a-half PN order, including finite-size spin effects, using effective field theory, and shows these effects influence spin evolution.

## Contribution

It introduces the first computation of finite-size spin effects on radiation reaction at quadratic order in spins within the effective field theory framework.

## Key findings

- Finite-size spin effects are included at 4.5 PN order.
- Radiation reaction influences spin evolution when spin-spin effects are considered.
- Energy loss matches the total emitted power, confirming consistency.

## Abstract

We compute the leading Post-Newtonian (PN) contributions at quadratic order in the spins to the radiation-reaction acceleration and spin evolution for binary systems, entering at four-and-a-half PN order. Our calculation includes the back-reaction from finite-size spin effects, which is presented for the first time. The computation is carried out, from first principles, using the effective field theory framework for spinning extended objects. At this order, nonconservative effects in the spin-spin sector are independent of the spin supplementary conditions. A non-trivial consistency check is performed by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone. We find that, in contrast to the spin-orbit contributions (reported in a companion paper), the radiation reaction affects the evolution of the spin vectors once spin-spin effects are incorporated.