Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order

TL;DR

This paper derives the next-to-next-to-leading order post-Newtonian Hamiltonian for tidal interactions in compact binary systems, including multiple multipole contributions, and confirms consistency with recent scattering amplitude results.

Contribution

It provides the NNL PN tidal Hamiltonian in various coordinate systems and variables, advancing the theoretical understanding of tidal effects at high precision.

Findings

Agreement with recent scattering amplitude results

Hamiltonian includes mass quadrupole, current quadrupole, and mass octupole interactions

Derived in multiple coordinate systems and variables

Abstract

In previous works, we obtained the leading, next-to-leading and next-to-next-to-leading (NNL) post-Newtonian (PN) corrections in the conservative tidal interactions between two compact non-spinning objects using a Lagrangian of effective field theory (EFT) in harmonic coordinates. In the present paper, we compute the corresponding NNL PN tidal effective Hamiltonian in ADM-like and isotropic coordinates, with contributions from mass quadrupole, current quadrupole and mass octupole tidal interactions, consistently included at that level. We also derive the NNL tidal Hamiltonian in Delaunay variables. We find full agreement in the overlap with recent results that were derived using tools from scattering amplitudes and the EFT to second post-Minkowskian (PM) order.