Local-in-time Conservative Binary Dynamics at Fourth Post-Minkowskian Order
Abstract
Leveraging scattering information to describe binary systems in generic orbits requires identifying local- and nonlocal-in-time tail effects. We report here the derivation of the universal (non-spinning) local-in-time conservative dynamics at fourth Post-Minkowskian order, i.e. . This is achieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [2112.11296,2210.05541]. Unlike the total result, the integration problem involves two scales, velocity and mass ratio, and features multiple polylogarithms, complete elliptic and iterated elliptic integrals, notably in the mass ratio. We reconstruct the local radial action, center-of-mass momentum and Hamiltonian, as well as the exact logarithmic-dependent part(s), all valid for generic orbits. We incorporate the remaining nonlocal terms for elliptic-like motion to sixth Post-Newtonian order. The combined Hamiltonian is in perfect agreement in the overlap with the Post-Newtonian state of the art. The results presented here provide the most accurate description of gravitationally-bound binaries harnessing scattering data to date, readily applicable to waveform modelling.
Cite
@article{arxiv.2403.04853,
title = {Local-in-time Conservative Binary Dynamics at Fourth Post-Minkowskian Order},
author = {Christoph Dlapa and Gregor Kälin and Zhengwen Liu and Rafael A. Porto},
journal= {arXiv preprint arXiv:2403.04853},
year = {2024}
}
Comments
5 pages + Refs + Supplemental. Two computer-readable ancillary files. Two computer-readable ancillary files. v2: Ancillary files corrected to be compatible with the split in Eq. (2) and the result quoted in Eq. (7) (unmodified) with the given h_i coefficients (unmodified). To appear in Phys. Rev. Lett