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)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 R 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 CFT 3 which is coupled to a fluctuating spatial metric of fixed area.

The Λ-BMS4 charge algebra

“…In appendix C, we provide a derivation of the explicit Λ-BMS 4 generators. Finally, in appendices D and E, we summarize useful results obtained in [49] concerning the flat limit.…”

“…(iii) It allows for field-dependent diffeomorphism generators ξ a (0) and σ, which will be the case when considering the boundary conditions leading to the Λ-BMS 4 asymptotic symmetry algebra [49], as we will discuss in section 3.…”

“…As we will show in the next section 2.4, it is the unique definition of the Hamiltonian that leads to a charge algebra without central term. This definition also leads to the canonical conserved surface charges for all derived boundary conditions in AlAdS 4 spacetimes namely Dirichlet [70], Neumann [78] and Dirichlet-Neumann [49] boundary conditions.…”

“…Partial reviews include [38][39][40][41]. In cosmology, such relationships have also been described [42][43][44][45][46][47] which relate symmetries [42,44,[48][49][50], memory effects [47,[51][52][53][54][55][56][57] and consistency conditions for correlation functions [42,44,[58][59][60][61]. In this context, the main motivation of this work is to increase the understanding of symmetries in cosmological spacetimes with the aim to better understand their infrared structure.…”

“…In our previous work [49], we found how to embed the (often called generalized) BMS 4 symmetry algebra [5,6,18,19,62] within asymptotically locally anti-de Sitter or de Sitter spacetimes in four-dimensional Einstein gravity. Two ingredients are necessary: a foliation of the codimension one asymptotic boundary manifold, and a measure on the codimension two manifolds induced by the foliation.…”