A note on the Newman-Unti group and the BMS charge algebra in terms of Newman-Penrose coefficients

TL;DR

This paper revisits the symmetry algebra of asymptotically flat spacetimes at null infinity, showing its structure and including local conformal transformations, with explicit construction of surface charges and their algebra.

Contribution

It demonstrates the isomorphism of the Newman-Unti algebra to a BMS algebra extended by local conformal transformations and details the Newman-Penrose coefficients' conformal properties.

Findings

The symmetry algebra is isomorphic to the BMS algebra plus conformal rescalings.

Surface charges are constructed and their algebra derived.

Local conformal transformations can be consistently incorporated.

Abstract

The symmetry algebra of asymptotically flat spacetimes at null infinity in four dimensions in the sense of Newman and Unti is revisited. As in the Bondi-Metzner-Sachs gauge, it is shown to be isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with bms4. The latter algebra is the semi-direct sum of infinitesimal supertranslations with the conformal Killing vectors of the Riemann sphere. Infinitesimal local conformal transformations can then consistently be included. We work out the local conformal properties of the relevant Newman-Penrose coefficients, construct the surface charges and derive their algebra.