The $\Lambda$-BMS${}_4$ group of dS${}_4$ and new boundary conditions for AdS${}_4$

Abstract

Using the dictionary between Bondi and Fefferman-Graham gauges, we identify the analogues of the Bondi news, Bondi mass and Bondi angular momentum aspects at the boundary of generic asymptotically locally (A)dS${}_4$ spacetimes. We introduce the $\Lambda$-BMS${}_4$ group as the residual symmetry group of the metric in Bondi gauge after boundary gauge fixing. This group consists of infinite-dimensional non-abelian supertranslations and superrotations and it reduces in the asymptotically flat limit to the extended BMS${}_4$ group. Furthermore, we present new boundary conditions for asymptotically locally AdS${}_4$ spacetimes which admit $\mathbb{R}$ times the group of area-preserving diffeomorphisms as the asymptotic symmetry group. The boundary conditions amount to fix 2 components of the holographic stress-tensor while allowing 2 components of the boundary metric to fluctuate. They correspond to a deformation of a holographic CFT${}_3$ which is coupled to a fluctuating spatial metric of fixed area.

42 pages, 1 figure, attached Mathematica notebook, corrigendum version

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