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<p>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 <i>conservative</i> sector through Feynman’s <i>i</i>0<sup>+</sup>-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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25924_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O} \)</EquationSource> </InlineEquation>(<i>G</i><sup>4</sup>) 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.</p>

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Nonlinear gravitational radiation reaction: failed tail, memories & squares

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月8日

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  • Rafael A. Porto,
  • Massimiliano M. Riva,
  • Zixin Yang

摘要

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 O \( \mathcal{O} \) (G4) 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.