Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited

TL;DR

This paper revisits the symmetry algebra of asymptotically flat 4D spacetimes at null infinity, proposing it as a semi-direct sum involving local conformal transformations rather than Lorentz algebra, highlighting the importance of 2D conformal techniques.

Contribution

It proposes a new structure for the asymptotic symmetry algebra, emphasizing local conformal transformations over Lorentz symmetries in 4D flat spacetimes.

Findings

Symmetry algebra is a semi-direct sum of supertranslations and local conformal transformations.

Two-dimensional conformal field theory techniques are fundamental in this context.

Revises the traditional understanding of asymptotic symmetries in 4D spacetimes.

Abstract

It is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two dimensional conformal field theory techniques will play as fundamental a role in this context of direct physical interest as they do in three dimensional anti-de Sitter gravity.