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

TL;DR

The paper delivers a self-contained derivation of the BMS current algebra in the Newman-Penrose formalism by formulating gravity as a first-order Cartan-type theory with NP-compatible variables. It constructs on-shell closed codimension-2 forms from reducibility parameters and analyzes the breaking caused by residual gauge transformations through the presymplectic flux, yielding explicit NP expressions for the BMS currents and their cocycle structure. By applying this framework to asymptotically flat four-dimensional gravity, the authors extend the Bondi mass loss picture to the full BMS algebra, including time-dependent conformal factors and a detailed action on the NU solution space. The work solidifies the link between covariant phase space methods and NP gravity, providing a robust platform to explore current algebras in more general gravitational theories and asymptotic settings.

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.