Lorentz covariant supertranslation frames for the angular momentum aspect

In this paper, we review the well-known ambiguity in defining angular momentum (and mass dipole) fluxes in general relativity and we reinterpret recent works that resolve the ambiguity by defining invariant charges. We resolve the ambiguity by finding the conditions that fix a frame for supertranslation and for spacetime translation. We present an elementary method for measuring the angular momentum aspect. We clarify the difference between supertranslation invariant Lorentz charges and the generators of BMS coordinate transformations. We also work out explicitly the supertranslation frame-fixing conditions for the metric created by point particles to first nontrivial order in the Newton constant.