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Radiation reaction at 3.5 post-Newtonian order in effective field theory

Chad R. Galley, Adam K. Leibovich

TL;DR

The paper derives radiation-reaction forces through $3.5$PN for compact binary inspirals using an effective field theory framework augmented by a rigorous dissipative variational principle. It computes contributions from mass quadrupole, mass octupole, and current quadrupole via Feynman diagrams and confirms agreement with the established Iyer–Will results, providing a non-trivial validation of the extended variational method. The work, together with prior EFT results, nearly completes the spinning-binary equations of motion at $3.5$PN, leaving only the spin–orbit piece of the $3.5$PN potential. This approach also sets the stage for future higher-order radiation-reaction calculations and tail-term corrections at $4$PN and beyond.

Abstract

We derive the radiation reaction forces on a compact binary inspiral through 3.5 order in the post-Newtonian expansion using the effective field theory approach. We utilize a recent formulation of Hamilton's variational principle that rigorously extends the usual Lagrangian and Hamiltonian formalisms to dissipative systems, including the inspiral of a compact binary from the emission of gravitational waves. We find agreement with previous results, which thus provides a non-trivial confirmation of the extended variational principle. The results from this work nearly complete the equations of motion for the generic inspiral of a compact binary with spinning constituents through 3.5 post-Newtonian order, as derived entirely with effective field theory, with only the spin-orbit corrections to the potential at 3.5 post-Newtonian remaining.

Radiation reaction at 3.5 post-Newtonian order in effective field theory

TL;DR

The paper derives radiation-reaction forces through PN for compact binary inspirals using an effective field theory framework augmented by a rigorous dissipative variational principle. It computes contributions from mass quadrupole, mass octupole, and current quadrupole via Feynman diagrams and confirms agreement with the established Iyer–Will results, providing a non-trivial validation of the extended variational method. The work, together with prior EFT results, nearly completes the spinning-binary equations of motion at PN, leaving only the spin–orbit piece of the PN potential. This approach also sets the stage for future higher-order radiation-reaction calculations and tail-term corrections at PN and beyond.

Abstract

We derive the radiation reaction forces on a compact binary inspiral through 3.5 order in the post-Newtonian expansion using the effective field theory approach. We utilize a recent formulation of Hamilton's variational principle that rigorously extends the usual Lagrangian and Hamiltonian formalisms to dissipative systems, including the inspiral of a compact binary from the emission of gravitational waves. We find agreement with previous results, which thus provides a non-trivial confirmation of the extended variational principle. The results from this work nearly complete the equations of motion for the generic inspiral of a compact binary with spinning constituents through 3.5 post-Newtonian order, as derived entirely with effective field theory, with only the spin-orbit corrections to the potential at 3.5 post-Newtonian remaining.

Paper Structure

This paper contains 10 sections, 59 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Overview of effective field theory and dissipative mechanics
  3. Effective field theory of compact binary inspirals
  4. Classical mechanics for dissipative systems
  5. Radiation reaction through 3.5PN
  6. Feynman diagrams
  7. Radiation reaction force
  8. Conclusion
  9. Acknowledgments
  10. Radiation reaction at 2.5PN

Figures (2)

  • Figure 1: The Feynman diagram giving the contribution to the radiation reaction from the mass quadrupole. $A$ and $B$ label worldlines that have been doubled in the extended variational principle.
  • Figure 2: The Feynman diagram giving the contributions to the radiation reaction from the mass octupole (left) and the current quadrupole (right).