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 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.
Highlights
Introduction and motivational remarksSoft theorems characterise scattering processes in any theory of gravity with d ≥ 4 flat noncompact dimensions [1, 2]
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 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
Summary
Soft theorems characterise scattering processes in any theory of gravity with d ≥ 4 flat noncompact dimensions [1, 2]. We discuss the most general, non-linear, Ricci flat configuration space at null infinity in any number of spacetime dimensions with appropriate boundary conditions supporting consistent actions of superrotation-like and supertranslation-like transformations. The postfix “like” is mandatory because we show (subsections 3.1, 3.2.1) that to accommodate smooth diffeomorphisms of the cross sections of null infinity (CL-superrotations) among the asymptotic Killing fields, the boundary conditions need to be further extended beyond the conditions proposed by Campiglia and Laddha in four spacetime dimensions: the interpretation of these transformations as enhancements of translations and rotations/Lorentz boosts is in general lost These boundary conditions are discussed in 3.1 and are shown to serve our purposes in subsection 3.2.1 via the claims C.1, C.2, C.3, to which the experienced reader can immediately turn. In the subsections we explicitly show that such metrics must not satisfy the Einstein condition, and in the linearised approach of [70], the perturbation of γ is such that γ + is not Einstein
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