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

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)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.