Fourth post-Minkowskian local-in-time conservative dynamics of binary systems

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 thirtieth 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 [D. Bini et al., Novel approach to binary dynamics: Application to the fifth post-Newtonian level, Phys. Rev. Lett. 123, 231104 (2019)] and on recent post-Minkowskian advances [Z. Bern et al., Scattering amplitudes, the tail effect, and conservative binary dynamics at O(G4), Phys. Rev. Lett. 128, 161103 (2022); C. Dlapa et al., Conservative dynamics of binary systems at fourth post-Minkowskian order in the large-eccentricity expansion, Phys. Rev. Lett. 128, 161104 (2022); C. Dlapa et al., Local in time conservative binary dynamics at fourth post-Minkowskian order, 132, 221401 (2024)].