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

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.

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