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

Understand

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.