Abstract
Starting from an action principle adapted to the Newman–Penrose formalism, we provide a self-contained derivation of BMS current algebra, which includes the generalization of the Bondi mass loss formula to all BMS generators. In the spirit of the Newman–Penrose approach, infinitesimal diffeomorphisms are expressed in terms of four scalars rather than a vector field. In this framework, the on-shell closed co-dimension two forms of the linearized theory associated with Killing vectors of the background are constructed from a standard algorithm. The explicit expression for the breaking that occurs when using residual gauge transformations instead of exact Killing vectors is worked out and related to the presymplectic flux.
Highlights
The importance of the Bondi mass loss formula [1, 2] in the context of early research on gravitational waves has recently been stressed
Starting from an action principle adapted to the Newman–Penrose formalism, we provide a self-contained derivation of BMS current algebra, which includes the generalization of the Bondi mass loss formula to all BMS generators
Starting from classification results [11,12,13] on conserved co-dimension 2 forms in gauge field theories, a BMS charge algebra [14] has been constructed in the metric formulation in terms of which the non-conservation of BMS charges can be understood as a particular case
Summary
The importance of the Bondi mass loss formula [1, 2] in the context of early research on gravitational waves has recently been stressed (see e.g. [3,4,5]). The variant we are using here is tensorial (rather than spinorial as in [33, 34]) It is a first order action principle of Cartan type that uses as variables vielbeins, the Lorentz connection in a non-holonomic frame, and a suitable set of auxiliary fields. In four dimensions, it can be directly expressed in terms of the quantities of the NP formalism. In this paper, we work out all details in the case of a generic first order gauge theory In this case, a full understanding of the appropriate homotopy operators is not needed because the main statement on (non-)conservation of the constructed co-dimension 2 forms will be checked by explicit computation. The results of [27] are generalized to the case of an arbitrary time-dependent conformal factor
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