Frames and slicings for angular momentum in post-Minkowski scattering

In relativistic physics, angular momentum is paired with a lesser known conserved quantity, the "mass moment,"which appears as the time-space components of the angular momentum tensor. Calculations of mass moment in electromagnetic and gravitational scattering of point particles have led to some puzzling behavior in which the radiated mass moment does not appear to match the corresponding mechanical change. We review the issues and show how the freedoms of time slicing and asymptotic frame may be used to bring all known results into agreement. The key points are to use hyperboloidal time slices and to allow the perturbative and asymptotic frames to differ by an independent Bondi-Metzner-Sachs (BMS) transformation at early and late times. The relevant BMS transformation involves a translation found recently by Riva et al. Building on this work, we conjecture a flux balance law for all orders in the post-Minkowski expansion.