Scooting through Post-Minskowskian Scattering

In Post-Minkowskian Scattering, two particles are approaching each other from infinity, with impact parameter b, where the energy of the system is much much less than the impact parameter, E << b. In the analogous EM problem, using the EM ``2PM" trajectories, we find that the angular momentum lost in the system precisely matches the angular momentum radiated by electromagnetic waves. The gravitational case is more subtle because of gauge issues, and there is a naive mismatch in the time-space components of the angular momentum tensor (the part corresponding to a change in center of mass, or a ``scoot"). We show at 2PM that a recently proposed notion of "mechanical" angular momentum at null infinity [Riva, Vernizzi and Wong] does agree with the change in mechanical angular momentum of the particles (defined using their coordinate positions), when the bulk and boundary gauges are identified in a natural way.