Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics

In the context of the two-body problem in General Relativity, hereditary terms in the long range gravitational field depend on the history rather than the instantaneous state of the source at retarded time. We compute the next-to leading effects of such hereditary terms, that comprise tail and memory, on the two-body dynamics, within effective field theory methods, including both dissipative and conservative effects. The former confirm known results at 2.5 post-Newtonian order with respect to the leading order in the luminosity function; the conservative part is a new result and is an unavoidable ingredient for a derivation of the conservative two-body dynamics at fifth post-Newtonian order.