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

## TL;DR

This paper identifies the $\Lambda$-BMS$_4$ group as the residual symmetry of asymptotically (A)dS$_4$ spacetimes in Bondi gauge, introduces new boundary conditions for AdS$_4$, and explores their holographic implications.

## Contribution

It defines the $\Lambda$-BMS$_4$ group for (A)dS$_4$ and proposes new boundary conditions for AdS$_4$ with specific asymptotic symmetries and holographic deformations.

## Key findings

- $\Lambda$-BMS$_4$ group includes supertranslations and superrotations.
- New boundary conditions admit area-preserving diffeomorphisms as asymptotic symmetry.
- Boundary conditions correspond to a holographic CFT$_3$ coupled to a fluctuating boundary metric.

## 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.