Supertranslations call for superrotations

TL;DR

This paper reviews recent developments in the symmetries of asymptotically flat spacetimes, highlighting the role of supertranslations and superrotations in different dimensions and their algebraic structures.

Contribution

It provides a classification of central extensions of the BMS3 and BMS4 algebras and discusses the implications of superrotations in the symmetry structure.

Findings

In higher dimensions, the symmetry algebra is Poincaré.

In 3 and 4 dimensions, superrotations extend supertranslations.

Classification of central extensions of BMS algebras.

Abstract

We review recent results on symmetries of asymptotically flat spacetimes at null infinity. In higher dimensions, the symmetry algebra realizes the Poincar\'e algebra. In three and four dimensions, besides the infinitesimal supertranslations that have been known since the sixties, the algebras are evenly balanced because there are also infinitesimal superrotations. We provide the classification of central extensions of the bms3 and bms4 algebras. Applications and consequences as well as directions for future work are briefly indicated.