Gravitating binaries at 5PN in the post-Minkowskian approximation

TL;DR

This work computes the conservative two-body dynamics at $O(G v^{10})$, i.e. $5\mathrm{PN}$, in the post-Minkowskian framework using an Effective Field Theory approach. By deriving an acceleration-free PM Lagrangian in KK variables and relating it to the ADM Hamiltonian, the authors obtain the center-of-mass energy at $5\mathrm{PN}$ and extract the $\nu^5$ contribution to the circular-orbit energy–frequency relation, including logarithmic terms and unknown high-order coefficients. The results bridge PM and PN formalisms, validating the approach against gauge and canonical transformations, and provide a pathway to determine remaining high-order coefficients through complementary methods such as self-force and ADM/EFT techniques. These findings have potential implications for precision gravitational-wave modeling and for probing the internal structure of compact objects at high PN order.

Abstract

The energy of a compact binary system at the fifth post-Newtonian order is explicitly computed in the post-Minkowskian approximation by means of the Effective Field Theory approach. This result allows to determine, for the first time beyond the test particle limit, one coefficient of the energy expression for binary point masses on circular orbit as a function of the orbital angular frequency.

Figures (1)

• Figure 1: The three diagrams giving the post-Minkowskian dynamics. The $\phi$, $A$ and $\sigma$ propagators are represented respectively by blue dashed, red dotted and green solid lines.