A supplementary radiation-reaction force between two binaries

TL;DR

This paper introduces a new gravitational radiation-reaction force between two binaries, affecting their orbital decay and dependent on retarded time, which extends traditional post-Newtonian models for N-body systems.

Contribution

It presents the first derivation of a supplementary binary-binary radiation-reaction force using Effective Field Theory, generalizing existing post-Newtonian estimates.

Findings

The new force can be comparable to the standard 2.5PN force in certain regimes.

The force depends on retarded time even at low velocities.

The formula interpolates between different physical limits.

Abstract

Radiation-reaction forces originating from the emission of gravitational waves (GW) bring binaries to close proximity and are thus responsible for virtually all the mergers that we can observe in GW interferometers. We show that there exists a supplementary radiation-reaction force between two binaries interacting gravitationally, changing in particular the decay rate of the semimajor axis under the emission of GW. This new binary-binary force is in some settings of the same order-of-magnitude than the usual 2.5PN force for an isolated binary and presents some striking features such as a dependence on retarded time even in the post-Newtonian regime where all velocities are arbitrarily small. Using Effective Field Theory tools, we provide the expression of the force in generic configurations and show that it interpolates between several intuitive results in different limits. In particular, our formula generalizes the standard post-Newtonian estimates for radiation-reaction forces in $N$-body systems which are valid only in the limit where the GW wavelength goes to infinity.