  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.
