General null asymptotics and superrotation-compatible configuration spaces in d ≥ 4

Abstract

We address the problem of consistent Campiglia-Laddha superrotations in d > 4 by solving Bondi-Sachs gauge vacuum Einstein equations at the non-linear level with the most general boundary conditions preserving the null nature of infinity. We discuss how to generalise the boundary structure to make the configuration space compatible with supertanslation-like and superrotation-like transformations. One possibility requires the time-independent boundary metric on the cuts of "Image missing" to be non-Einstein, while the other sticks to Einstein but time-dependent metrics. Both are novel features with respect to the four dimensional case, where time-dependence of the two-dimensional cross-sectional metric is not required and the Einstein condition is trivially satisfied. Other cases are also discussed. These conditions imply that the configuration spaces are not asymptotically flat in the standard sense. We discuss the implications on the construction of the phase space and the relationship with soft scattering theorems. We show that in even spacetime dimensions, the initial data compatible with such asymptotic symmetries produce maximally polyhomogeneous expansions of the metric and we advance a potential interpretation of this structure in terms of AdS/CFT and realizations of Ricci-flat holography.

Charge and Antipodal Matching across Spatial Infinity

“…Connected to this, but not only tied to it, the assumption that the large u expansion is polynomial both for C AB and the other metric functions that we consider, as well as for all r-subleading terms of the metric, does not hold in general [61,62]. While polyhomogeneous asymptotic expansions in r are believed to be a generic feature of physically relevant asymptotically flat systems (of which CK spacetimes are an example) [63][64][65], although contrasting results exist (see [66] and references therein), the polyhomogeneous behaviour in u is less understood. The potential interconnection of the two sources of polyhomogeneity has been briefly recognised in [61].…”

Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis

“…Second, while there is an enlargement on the supertranslation side, our analysis does not include the superrotations [82,83] as asymptotic symmetries. How to include these and their higher dimensional generalization [25] in a Hamiltonian treatment at spatial infinity remains an open question.…”

“…The status of the supertranslations, which are the characteristic feature of the BMS 4 enlargement of the Poincaré algebra, was in particular questioned in some work, leading to a tension with the validity of soft theorems in any D [15][16][17][18]. This question was clarified in the articles [19][20][21][22][23][24][25], which gave boundary conditions at null infinity that accomodated supertranslations (mostly in even spacetime dimensions, except for reference [25], which also considers odd spacetime dimensions).…”

Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis

“…The status of the supertranslations, which are the characteristic feature of the BMS 4 enlargement of the Poincaré algebra, was in particular questioned in some work, leading to a tension with the validity of soft theorems in any D [15][16][17][18]. This question was clarified in the articles [19][20][21][22][23][24][25], which gave boundary conditions at null infinity that accomodated supertranslations (mostly in even spacetime dimensions, except for reference [25], which also considers odd spacetime dimensions).…”