Nonlinear gravitational radiation reaction: failed tail, memories & squares

A bstract 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 i 0 + -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 $$ \mathcal{O} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> </mml:math> ( 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.