General null asymptotics and superrotation-compatible configuration spaces in $d\ge4$

TL;DR

This work investigates higher-dimensional generalizations of asymptotic symmetries by solving the non-linear Bondi-Sachs vacuum Einstein equations with broadly generalized boundary conditions at null infinity. It demonstrates that to realize supertranslation-like and superrotation-like transformations one must relax standard asymptotic flatness—either by allowing time-dependent boundary metrics or by letting the leading cross-section metric be non-Einstein—leading to maximally polyhomogeneous metric expansions in even dimensions and posing challenges for a well-posed phase space and scattering framework. The analysis links the resulting boundary structures to potential holographic interpretations, drawing parallels with AlAdS Fefferman–Graham expansions and Ricci-flat holography, while clarifying the limits of KLPS-type configurations for higher-dimensional supertranslations and the conditions under which CL-like superrotations may exist. Overall, the paper provides a detailed, non-linear construction of higher-dimensional configuration spaces that accommodate extended BMS-like symmetries, highlighting both the potential and the obstacles for connecting these symmetries to soft theorems and holographic duals.

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 that the time-independent boundary metric on the cuts of $\mathscr{I}$ is not fixed to be 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.