Radiative 3.5 post-Newtonian ADM Hamiltonian for many-body point-mass systems

We calculate to ${\mathrm{post}}^{3.5}$-Newtonian order of approximation of general relativity the radiation-reaction part of the ADM Hamiltonian for a many-body system of nonspinning point masses. The Hamiltonian is applied to the derivation of the gravitational energy loss of a gravitationally bound two-body system in quasielliptic motion. Agreement with the known result for the time-averaged energy loss is obtained to order ${\mathrm{}(v/c)\mathrm{}}^7$.