Nonlinear Gravitational Radiation Reaction: Failed Tail, Memories & Squares

TL;DR

This paper advances the understanding of nonlinear gravitational radiation reaction effects at 5PN order using EFT, revealing boundary memory effects, conservative contributions, and resolving previous discrepancies with Post-Minkowskian results.

Contribution

It completes the 5PN nonlinear radiation-reaction analysis within the EFT framework, including nonlocal memory effects and conservative terms, and reconciles previous inconsistencies with Post-Minkowskian calculations.

Findings

Identification of boundary memory effects in the effective action.

Derivation of the ${ m O}(G^4)$ 5PN scattering angle.

Resolution of discrepancies with prior EFT and Post-Minkowskian results.

Abstract

Using the Schwinger-Keldysh "in-in" effective field theory (EFT) framework, we complete the knowledge of nonlinear gravitational radiation-reaction effects in the (relative) dynamics of binary systems at fifth Post-Newtonian (5PN) order. Diffeomorphism invariance plays a key role guaranteeing that the Ward identities are obeyed (in background-field gauge). Nonlocal-in-time (memory) effects appear in the soft-frequency limit as boundary terms in the effective action, consistently with the loss of (canonical) angular momentum. We identify a conservative sector through Feynman's $i0^+$-prescription. Notably, terms at second order in the (linear) radiation-reaction force also produce conservative-like effects (as we likewise demonstrate in electromagnetism). For the sake of comparison, we derive the ${\cal O}(G^4)$ contribution to the total (even-in-velocity) 5PN relative scattering angle. We find perfect agreement in the overlap with the state of the art in the Post-Minkowskian expansion, both in the conservative and dissipative sectors, resolving the (apparent) discrepancy with previous EFT results. We will return to the full conservative part of the 5PN dynamics elsewhere.