Asymptotic flatness, Taub-NUT metric, and variational principle

Using hyperbolic temporal and spatial cutoffs to define four-dimensional asymptotically flat space-times, we show that supertranslation ambiguities in the asymptotic fields can all be removed even in the presence of gravitational magnetic charges. We then show that configurations with different electric and magnetic four-momenta can be consistently considered in the Mann-Marolf variational principle. This generalizes the previous result where variations over asymptotically flat configurations with fixed magnetic four-momenta were considered. We also express the Kerr Taub-NUT metric to the leading and next-to-leading order in the Beig-Schmidt form, and compare the asymptotic form with the tensor harmonics on three-dimensional de Sitter space.