Local in Time Conservative Binary Dynamics at Fourth Post-Minkowskian Order

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 (nonspinning) local in time conservative dynamics at fourth post-Minkowskian order, i.e., O(G^{4}). This is achtieved by computing the nonlocal-in-time contribution to the deflection angle, and removing it from the full conservative value in [C. Dlapa et al., Phys. Rev. Lett. 128, 161104 (2022).PRLTAO0031-900710.1103/PhysRevLett.128.161104; C. Dlapa et al., Phys. Rev. Lett. 130, 101401 (2023).PRLTAO0031-900710.1103/PhysRevLett.130.101401]. 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 ellipticlike 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 modeling.