Properties of dual supertranslation charges in asymptotically flat spacetimes

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.

Dual gravitational charges and soft theorems

“…As has been emphasised recently in Ref. [6], and in older works [7,8], the existence of non-trivial dual charges (at least globally) is intrinsically related to the non-trivial topological structure of spacetime, in the same way that a gauge connection in electromagnetism can lead to a non-trivial magnetic monopole charge.…”

“…The dual gravitational charges are given by twisted fields, defined using the Levi-Civita on the 2-sphere, and as such do not appear in components of the Einstein equation; rather, they are related to NUT charges [2,6], and may be viewed as the gravitational analogues of magnetic monopoles. As has been emphasised recently in Ref.…”

“…Furthermore, we investigate the consequence of the existence of such charges for the gravitational phase space at null infinity, which has been discussed in Refs. [11], [6], and for the Weinberg soft theorems [12], whose relation to asymptotic symmetries has attracted much recent attention [11,. We shall, mainly, focus on (dual) supertranslation charges in this paper.…”

Taub-NUT from the Dirac monopole

“…Asymptotically flat spacetimes have been extensively studied over the last 50 years, particularly, recently, in the context of gravitational wave detections [1] and asymptotic symmetry groups [2,3]. In this paper, motivated by recent work on dual gravitational charges [4][5][6][7], we show how treating asymptotically flat spacetimes in terms of a characteristic value problem [8] provides an intriguing way of viewing the Dirac magnetic monopole as a progenitor of the Taub-NUT spacetime. 1 Our starting point is to consider a general class of asymptotically flat metrics, written in a Bondi coordinate system (u, r, x I = {θ, φ}), such that the metric takes the form 2…”

Asymptotic structure of Einstein-Maxwell-dilaton theory and its five dimensional origin

“…In recent years, physics near null infinity has obtained renewed interest from several aspects, e.g. holography [2][3][4][5][6], asymptotic symmetries [7][8][9][10][11][12], infrared physics [13][14][15][16][17][18][19][20][21][22], memory effect [23][24][25], and gravitational conserved quantities [26][27][28][29][30][31]. The Bondi gauge plays a central role in all the relevant research.…”