The Λ-BMS4 charge algebra

Abstract

The surface charge algebra of generic asymptotically locally (A)dS4 spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The Λ-BMS4 charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat limit then reproduces the BMS4 charge algebra of supertranslations and super-Lorentz transformations acting on asymptotically locally flat spacetimes. The BMS4 surface charges represent the BMS4 algebra without central extension at the corners of null infinity under the standard Dirac bracket, which implies that the BMS4 flux algebra admits no non-trivial central extension.

Multipole expansion of gravitational waves: from harmonic to Bondi coordinates

“…For completeness, we can now detail the boundary conditions at spatial infinity that could be imposed in order to completely fix the asymptotic frame, even though we will not enforce these conditions in the following sections since they remove the generalized BMS asymptotic symmetry group at spatial infinity [18,50,54,55]. First, upon fixing the boundary metric to be the unit sphere metric, q ab = γ ab , all proper super-Lorentz transformations are discarded and the generalized BMS algebra reduces to the original BMS algebra.…”

Conservation and integrability in lower-dimensional gravity

“…An important technical result going into this direction is the Barnich-Troessaert bracket [14] that allows one to derive mathematically consistent charge algebras for non-integrable charges. This bracket has then been used in many different contexts [15,19,21,[23][24][25][26][27] and the associated charge algebras have been shown to be physically extremely relevant since they contain all the information about the flux-balance laws of the theory [13,28,29].…”

“…Indeed, it is particularly well-adapted to investigate the interplay between radiation and symmetries [17,19,28,[34][35][36][37][38][39]. Furthermore, it allows us to consider simultaneously asymptotically locally flat spacetimes exhibiting null boundaries and asymptotically locally AdS spacetimes with timelike boundaries [26,[40][41][42][43][44][45]. The analyses of these two types of asymptotics are related through a flat limit process [40,46,47].…”

Super-Hawking radiation

“…Asymptotic symmetries have also experienced a revival due to the unveiling of unexpected connections with observable effects. On the one hand, soft theorems have been recast as Ward identities for asymptotic symmetry transformations, not only for scattering amplitudes on (asymptotically) flat spacetime [11][12][13][14][15][16][17][18][19][20][21] but also in the case of correlation functions on (anti-) de Sitter background [22][23][24][25][26][27][28][29][30]. On the other hand, directly observable counterparts of asymptotic symmetries have been identified in the so-called memory effects, permanent footprints that radiation can leave behind on a test apparatus [31][32][33][34].…”