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Register a new userCharges in the Extended BMS Algebra: Definitions and Applications
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Authors
M. Porrati
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This is a review of selected topics from recent work on symmetry charges in asymptotically flat spacetime done by the author in collaboration with U. Kol and R. Javadinezhad. First we reinterpret the reality constraint on the boundary graviton as the gauge fixing of a new local symmetry, called dual supertranslations. This symmetry extends the BMS group and bears many similarities to the dual (magnetic) gauge symmetry of electrodynamics. We use this new gauge symmetry to propose a new description of the TAUB-NUT space that does not contain closed time-like curves. Next we summarize progress towards the definition of Lorentz and super-Lorentz charges that commute with supertranslations and with the soft graviton mode.
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We classify the asymptotic charges of a class of polyhomogeneous asymptotically-flat spacetimes with finite shear, generalising recent results on smooth asymptotically-flat spacetimes. Polyhomogenous spacetimes are a formally consistent class of spacetimes that do not satisfy the well-known peeling property. As such, they constitute a more physical class of asymptotically-flat spacetimes compared to the smooth class. In particular, we establish that the generalised conserved non-linear Newman-Penrose charges that are known to exist for such spacetimes are a subset of asymptotic BMS charges.
We supplement the recently found dual gravitational charges with dual charges for the whole BMS symmetry algebra. Furthermore, we extend the dual charges away from null infinity, defining subleading dual charges. These subleading dual charges complement the subleading BMS charges in the literature and together account for all the Newman-Penrose charges.
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 group (and its various generalizations) at null infinity have been studied extensively in the literature as the symmetry group of asymptotically flat spacetimes. The intricate relationship between soft theorems and the BMS symmetries have also motivated the definition of such asymptotic symmetries to time-like infinity. Although the vector fields that generate the (generalized) BMS algebra at time-like infinity was defined in the literature, the algebra has not been investigated. In this paper, we fill this gap. We show that the super-translations and vector fields that generate sphere diffeomorphisms close under the modified Lie bracket proposed by Barnich et al.
Using the expressions for generalized ADT current and potential in a self consistent manner, we derive the asymptotic symmetry algebra on AdS$_3$ and the near horizon extremal BTZ spacetimes. The structure of symmetry algebra among the conserved charges for asymptotic killing vectors matches exactly with the known results thus establishing the algebraic equivalence between the well known existing formalisms for obtaining the conserved charges and the generalized ADT charges.
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