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Using hyperbolic temporal and spatial cut-offs to define 4d asymptoticallyflat spacetimes, we show that supertranslation ambiguities in the asymptoticfields can all be removed even in the presence of gravitational magneticcharges. We then show that configurations with different electric and magneticfour-momenta can be consistently considered in the Mann-Marolf variationalprinciple. This generalizes the previous result where variations overasymptotically flat configurations with fixed magnetic four-momenta wereconsidered. We also express Kerr Taub-NUT metric to the leading and next toleading order in the Beig-Schmidt form, and compare the asymptotic form withthe tensor harmonics on 3d de Sitter space.

Asymptotic Flatness, Taub-NUT, and Variational Principle