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Using the dictionary between Bondi and Fefferman-Graham gauges, we identifythe analogues of the Bondi news, Bondi mass and Bondi angular momentum aspectsat the boundary of generic asymptotically locally (A)dS$_4$ spacetimes. Weintroduce the $\Lambda$-BMS$_4$ group as the residual symmetry group of themetric in Bondi gauge after boundary gauge fixing. This group consists ofinfinite-dimensional non-abelian supertranslations and superrotations and itreduces in the asymptotically flat limit to the extended BMS$_4$ group.Furthermore, we present new boundary conditions for asymptotically locallyAdS$_4$ spacetimes which admit $\mathbb R$ times the group of area-preservingdiffeomorphisms as the asymptotic symmetry group. The boundary conditionsamount to fix 2 components of the holographic stress-tensor while allowing 2components of the boundary metric to fluctuate. They correspond to adeformation of a holographic CFT$_3$ which is coupled to a fluctuating spatialmetric of fixed area.

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