Abstract
We study several properties of some new charges of asymptotically flat spacetimes. These dual supertranslation charges are akin to the magnetic large $U(1)$ charges in QED. In this paper we find the symmetries associated with these charges and show that the global dual supertranslation charge is topological because it is invariant under globally defined, smooth variations of the asymptotic metric. We also exhibit spacetimes where the charge does not vanish and we find dynamical processes that interpolate between regions with different values of these charges.
Highlights
New dual gravitational charges of asymptotically flat spacetimes were introduced in [1,2]
In this paper we find the symmetries associated with these charges and show that the global dual supertranslation charge is topological because it is invariant under globally defined, smooth variations of the asymptotic metric
We have discussed several properties of the symmetry generated by the dual supertranslation charges of [1,2]; we have shown in particular that the global dual supertranslation charge is invariant under arbitrary globally defined, smooth deformation of the metric
Summary
New dual gravitational charges of asymptotically flat spacetimes were introduced in [1,2]. Matching of the boundary graviton follows from Lorentz invariance [8], but it is not enough to ensure stress-energy conservation, which we need to impose explicitly by the matching condition on the Bondi mass. To emphasize the importance of this difference, let us resort again to the analogy with electrodynamics, where the matching condition of the scalar potential follows from Lorentz invariance [3] In electrodynamics this is enough to ensure magnetic charge conservation (in the absence of magnetic sources), but electric charge conservation has to be imposed explicitly. We study the Taub-NUT metric as an example of a solution that carries a dual supertranslation charge and an imaginary boundary graviton, and use it to demonstrate the resulting topological structure. Comments and topics for future study of the new topological symmetry
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