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Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach

Adam K. Leibovich, Natália T. Maia, Ira Z. Rothstein, Zixin Yang

TL;DR

The work addresses the 2PN radiative dynamics of inspiralling compact binaries within the NRGR EFT framework, deriving the 2PN corrections to the mass quadrupole $I^{ij}$ and the 2PN equation of motion in the linearized harmonic gauge. It develops the radiation-sector formalism, computes higher-order stress-energy tensor components $T^{00}$, $T^{0i}$, and $T^{ii}$ via NRGR Feynman diagrams, and assembles the 2PN mass quadrupole by summing contributions and applying center-of-mass shifts, enabling the 2PN power loss computation through multipole radiation. The results are cross-validated against established BD I and Epstein-W Wagoner formalisms, up to a coordinate transformation that reconciles gauge-dependent differences, and they supply essential building blocks for future higher-order EFT calculations and spinning template development. Overall, this paper strengthens the NRGR EFT approach to gravitational-wave modeling by delivering the explicit 2PN radiative ingredients and clarifying gauge-related comparisons, paving the way for next-to-next-to-leading order radiation-reaction analyses.

Abstract

We use the Effective Field Theory (EFT) framework to compute the mass quadrupole moment, the equation of motion, and the power loss of inspiralling compact binaries at the second order in the Post-Newtonian (PN) approximation. We present expressions for the stress-energy pseudo-tensor components of the binary system in higher PN orders. The 2PN correction to the mass quadrupole moment as well as to the acceleration computed in the linearized harmonic gauge presented here are the ingredients needed for the calculation of the next-to-next-to leading order radiation reaction force, which will be presented elsewhere. While this paper reproduces known results, it supplies the building blocks necessary for future higher order calculations in the EFT methodology.

Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the Effective Field Theory approach

TL;DR

The work addresses the 2PN radiative dynamics of inspiralling compact binaries within the NRGR EFT framework, deriving the 2PN corrections to the mass quadrupole and the 2PN equation of motion in the linearized harmonic gauge. It develops the radiation-sector formalism, computes higher-order stress-energy tensor components , , and via NRGR Feynman diagrams, and assembles the 2PN mass quadrupole by summing contributions and applying center-of-mass shifts, enabling the 2PN power loss computation through multipole radiation. The results are cross-validated against established BD I and Epstein-W Wagoner formalisms, up to a coordinate transformation that reconciles gauge-dependent differences, and they supply essential building blocks for future higher-order EFT calculations and spinning template development. Overall, this paper strengthens the NRGR EFT approach to gravitational-wave modeling by delivering the explicit 2PN radiative ingredients and clarifying gauge-related comparisons, paving the way for next-to-next-to-leading order radiation-reaction analyses.

Abstract

We use the Effective Field Theory (EFT) framework to compute the mass quadrupole moment, the equation of motion, and the power loss of inspiralling compact binaries at the second order in the Post-Newtonian (PN) approximation. We present expressions for the stress-energy pseudo-tensor components of the binary system in higher PN orders. The 2PN correction to the mass quadrupole moment as well as to the acceleration computed in the linearized harmonic gauge presented here are the ingredients needed for the calculation of the next-to-next-to leading order radiation reaction force, which will be presented elsewhere. While this paper reproduces known results, it supplies the building blocks necessary for future higher order calculations in the EFT methodology.

Paper Structure

This paper contains 12 sections, 111 equations, 17 figures.

Table of Contents

  1. Introduction
  2. EFT setup
  3. Radiation sector
  4. Higher order stress-energy tensors
  5. 2PN correction to $T^{00}$
  6. 1PN correction to $T^{0i}$
  7. 1PN correction to $T^{ii}$
  8. Lower order stress-energy tensors
  9. Consistency tests
  10. Mass quadrupole moment at 2PN order
  11. Final remarks
  12. Acknowledgements

Figures (17)

  • Figure 1: No graviton exchange between the two particles, one external $\bar{h}^{00}$ momentum.
  • Figure 2: One-graviton exchange with external $\bar{h}^{00}$ momentum.
  • Figure 3: Diagrams with two potential gravitons coupled to $\bar{h}_{00}$.
  • Figure 4: Two-potential-graviton exchange with external $\bar{h}^{00}$ momentum.
  • Figure 5: Three-potential-graviton exchange with external $\bar{h}^{00}$ momentum.
  • ...and 12 more figures