Subleading BMS charges and fake news near null infinity

Abstract

In this paper we establish a relation between the non-linearly conserved Newman-Penrose charges and certain subleading terms in a large-r expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a 1/r-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. 1/r 0 , one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. At subleading orders, analogous terms in general provide obstructions to the integrability of the corresponding charges. Since the subleading terms are defined close to null infinity, but vanish actually at infinity, the analogous obstructions are not associated with genuine Bondi news. One may instead describe them as corresponding to "fake news." At order r −3 , we find that a set of integrable charges can be defined and that these are related to the ten non-linearly conserved Newman-Penrose charges.

BMS current algebra in the context of the Newman–Penrose formalism

“…Examples include for instance asymptotically flat or anti-de Sitter spacetimes in three dimensions in Fefferman-Graham or BMS gauge with fixed conformal factor. In this case, the co-dimension 2 forms are closed for all residual gauge transformations, they are conserved and r-independent (see for instance [57,58]), so that they may be computed at any finite r. It also follows from (2.49) and (2.54) that subleading charges recently considered for instance in [31,59,60] are controlled by W 0 δL{δφ rφ, Rf s|φ.…”

Taub-NUT from the Dirac monopole

“…As can be verified from the form of the BMS transformations in the notation of Ref. [11] that we are using here, under a supertranslation with diffeomorphism parameter ξ = s(θ, φ) ∂u+ · · · , we have…”

“…One of the hypersurface equations, arising at order 1/r 3 of the ℓ µ m ν G µν = 0 equation (see equation (2.16) of Ref. [11]), gives 5…”

“…Thus F 0 , C I 0 and C I 1 constitute the data determining the Bondi mass, NUT charge and angular momentum. Furthermore, the other data given by terms at higher powers in the 1/r expansion of h IJ correspond to subleading BMS charges [11], [5]. For example, D IJ determines the BMS charge at order 1/r 2 .…”

Asymptotic structure of Einstein-Maxwell-dilaton theory and its five dimensional origin

“…In recent years, physics near null infinity has obtained renewed interest from several aspects, e.g. holography [2][3][4][5][6], asymptotic symmetries [7][8][9][10][11][12], infrared physics [13][14][15][16][17][18][19][20][21][22], memory effect [23][24][25], and gravitational conserved quantities [26][27][28][29][30][31]. The Bondi gauge plays a central role in all the relevant research.…”