Fourth Post-Minkowskian Local-in-Time Conservative Dynamics of Binary Systems

TL;DR

This paper calculates the local-in-time conservative dynamics of two-body gravitational systems at the fourth post-Minkowskian order, providing gauge-invariant results relevant for understanding relativistic binary interactions.

Contribution

It introduces a novel computation of the fourth post-Minkowskian local dynamics using the Tutti Frutti approach and recent advances, with explicit gauge-invariant expressions.

Findings

Derived the local-in-time contribution to the on-shell action.

Provided the Effective One Body Hamiltonian at this order.

Achieved gauge-invariant expressions for hyperbolic and elliptic motions.

Abstract

We compute the purely local-in-time (scale-free and logarithm-free) part of the conservative dynamics of gravitationally interacting two-body systems at the fourth post-Minkowskian order, and at the thirtiest order in velocity. The gauge-invariant content of this fourth post-Minkowskian local dynamics is given in two ways: (i) its contribution to the on-shell action (for both hyperboliclike and ellipticlike motions); and (ii) its contribution to the Effective One Body Hamiltonian (in energy gauge). Our computation capitalizes on the Tutti Frutti approach [Phys. Rev. Lett. \textbf{123}, no.23, 231104 (2019)], and on recent post-Minkowskian advances [Phys. Rev. Lett. \textbf{128}, no.16, 161103 (2022)], [Phys. Rev. Lett. \textbf{128}, no.16, 161104 (2022)], and [Phys. Rev. Lett. \textbf{132}, no.22, 221401 (2024)].