Asymptotic Flatness, Taub-NUT, and Variational Principle

TL;DR

This paper refines the understanding of asymptotically flat spacetimes by removing supertranslation ambiguities, incorporating magnetic charges, and extending the variational principle to include electric and magnetic four-momenta, with detailed metric analysis.

Contribution

It demonstrates the removal of supertranslation ambiguities with hyperbolic cut-offs and extends the variational principle to configurations with both electric and magnetic charges.

Findings

Supertranslation ambiguities can be eliminated with hyperbolic cut-offs.

Configurations with different electric and magnetic four-momenta are consistent in the variational principle.

Kerr Taub-NUT metric expressed in Beig-Schmidt form and compared with tensor harmonics.

Abstract

Using hyperbolic temporal and spatial cut-offs to define 4d asymptotically flat spacetimes, 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 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 3d de Sitter space.