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

TL;DR

The paper extends Bondi-type asymptotics to spacetimes with a cosmological constant by defining the $\Lambda$-BMS$_4$ residual symmetry at future infinity and identifying the analog of Bondi news as the symplectic pair $(g_{AB}^{(0)}, J^{AB})$. It derives the Bondi-like evolution equations for $M^{(\Lambda)}$ and $N_A^{(\Lambda)}$ from a controlled Bondi gauge analysis and connects these data to the holographic stress-tensor via a Fefferman–Graham dictionary. It then constructs new mixed Dirichlet-Neumann boundary conditions for AdS$_4$ that yield a finite, integrable, nontrivial charge algebra with asymptotic symmetry $\mathbb{R}\times\mathcal{A}$ (area-preserving diffeomorphisms), and discusses stationary solutions within this framework. Collectively, these results provide a covariant, holographically consistent generalization of BMS-like symmetries in (A)dS$_4$ and introduce boundary conditions with potentially rich holographic duals.

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 $Λ$-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.

Figures (1)

• Figure 1: On scales $r \ll 1/\vert\Lambda\vert$, the gravitational field can be described without the cosmological constant. One can therefore consider approximately (general) asymptotically flat regions of any locally asymptotically (A)dS$_4$ spacetime. Lines of constant $u$ (depicted with an arrow in the positive $r$ direction) map the respective boundary $\mathscr I^+_{\text{dS}}$ or $\mathscr I^0_{\text{AdS}}$ to the future null boundary $\mathscr I^+$. The residual $\Lambda$-BMS symmetries are defined in the bulk and admit a smooth flat limit. Since energy flows in the bulk of spacetime, there is no smooth flat limit to $\mathscr I^+$ of the Bondi news and mass defined on $\mathscr I^+_{\text{dS}}$ and $\mathscr I^0_{\text{AdS}}$.