The Λ-BMS4 group of dS4 and new boundary conditions for AdS4

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)dS₄ spacetimes. We introduce the -BMS₄ 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 BMS₄ group. Furthermore, we present new boundary conditions for asymptotically locally AdS₄ spacetimes which admit times the group of area-preserving diffeomorphisms as the asymptotic symmetry group. The boundary conditions amount to fix two components of the holographic stress-tensor while allowing two components of the boundary metric to fluctuate. They correspond to a deformation of a holographic CFT₃ which is coupled to a fluctuating spatial metric of fixed area.