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

TL;DR

This paper derives the BMS current algebra within the Newman-Penrose formalism, generalizing the Bondi mass loss formula and expressing diffeomorphisms via scalars, providing new insights into asymptotic symmetries in gravity.

Contribution

It presents a self-contained derivation of BMS current algebra using the Newman-Penrose formalism, including a generalization of the mass loss formula and analysis of gauge transformation effects.

Findings

Derived BMS current algebra in Newman-Penrose formalism

Generalized Bondi mass loss formula to all BMS generators

Analyzed gauge transformation breaking and its relation to presymplectic flux

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.