Conservation of asymptotic charges from past to future null infinity: Lorentz charges in general relativity

We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of spacetimes that are asymptotically-flat in the sense of Ashtekar and Hansen. Combined with the results of \cite{KP-GR-match}, this shows that \emph{all} Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacetimes, proving a relationship that was conjectured by Strominger. Assuming additional suitable conditions are satisfied at timelike infinities, this proves that the flux of all BMS charges is conserved in any classical gravitational scattering process.