Gravitational radiation contributions to the two-body scattering angle

We compute the contribution to the two-body scattering angle of a specific class of interactions involving the exchange of gravitational radiative degrees of freedom, including the nonlinear memory process and square of radiation reaction effects. Our computation is performed directly from the equations of motion, thus computing the overall effect of both conservative and dissipative processes. Such contributions provide in principle the last missing ingredients to compute the scattering angle at fifth post-Newtonian and fourth post-Minkowskian order.

Figure 1

Processes giving rise to memorylike contributions in the 5PN equations of motion. Arrows indicate the orientation of the retarded propagators used in the in-in formalism. Top line: simple emission and memory. Bottom line: “double self-energy” diagrams involving one nonlinear GW-quadrupole coupling.