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Subleading Spin-Orbit Correction to the Newtonian Potential in Effective Field Theory Formalism

Delphine L. Perrodin

TL;DR

The paper computes the next-to-leading order spin-orbit correction to the Newtonian potential in NRGR, targeting the 2.5PN level for inspiralling compact binaries. It systematically aggregates contributions from single-graviton exchange, propagator corrections, quadratic (seagull) diagrams, and 3-graviton diagrams, using the NRGR lagrangian framework and spin formalism. The final 2.5PN spin-orbit potential, $V_{2.5PN}^{so}$, is presented as a sum of these diagrammatic pieces with explicit dependence on spin tensors $S_1^{0k}, S_1^{ik}$, particle velocities, and accelerations, while noting gauge-related subtleties and ongoing cross-checks with other approaches. This work advances the NRGR methodology for spin effects in binary dynamics and sets the stage for gauge-invariant comparisons of spin-orbit terms at high PN orders.

Abstract

We study the gravitational dynamics in the early inspiral phase of coalescing compact binaries using Non-Relativistic General Relativity (NRGR) - an effective field theory formalism based on the post-newtonian expansion, but which provides a consistent lagrangian framework and a systematic way in which to study binary dynamics and gravitational wave emission. We calculate in this framework the spin-orbit correction to the newtonian potential at 2.5 PN.

Subleading Spin-Orbit Correction to the Newtonian Potential in Effective Field Theory Formalism

TL;DR

The paper computes the next-to-leading order spin-orbit correction to the Newtonian potential in NRGR, targeting the 2.5PN level for inspiralling compact binaries. It systematically aggregates contributions from single-graviton exchange, propagator corrections, quadratic (seagull) diagrams, and 3-graviton diagrams, using the NRGR lagrangian framework and spin formalism. The final 2.5PN spin-orbit potential, , is presented as a sum of these diagrammatic pieces with explicit dependence on spin tensors , particle velocities, and accelerations, while noting gauge-related subtleties and ongoing cross-checks with other approaches. This work advances the NRGR methodology for spin effects in binary dynamics and sets the stage for gauge-invariant comparisons of spin-orbit terms at high PN orders.

Abstract

We study the gravitational dynamics in the early inspiral phase of coalescing compact binaries using Non-Relativistic General Relativity (NRGR) - an effective field theory formalism based on the post-newtonian expansion, but which provides a consistent lagrangian framework and a systematic way in which to study binary dynamics and gravitational wave emission. We calculate in this framework the spin-orbit correction to the newtonian potential at 2.5 PN.

Paper Structure

This paper contains 5 sections, 8 equations, 4 figures.

Table of Contents

  1. Potential from single-graviton exchange
  2. Potential from propagator corrections
  3. Potential from quadratic diagrams
  4. Potential from 3-graviton diagrams
  5. Spin-orbit potential at 2.5PN

Figures (4)

  • Figure 1: Diagrams with single-graviton exchange. The blobs represent spin insertions. The leading order spin vertex introduces a $o(v^2)$ correction.
  • Figure 2: Single-graviton diagrams with propagator corrections, which scale as $o(v^2)$. There are different ways to calculate this term.
  • Figure 3: Quadratic "seagull" diagrams with double-graviton exchange. The leading order quadratic spin vertex scales as $o(v^4)$.
  • Figure 4: 3-graviton diagrams. The leading order 3-graviton vertex scales as $o(v^2)$, while crosses correspond to $o(v)$ - corrections to the 3-graviton vertex. 3-graviton vertices were computed with the help of Rothstein's 3-graviton code code.