The Weyl BMS group and Einstein's equations

TL;DR

This paper introduces an extended BMS group called Weyl BMS (BMSW) that includes local Weyl rescalings and diffeomorphisms, demonstrating its algebraic structure, physical implications, and relation to Einstein's equations at null infinity.

Contribution

The paper defines the Weyl BMS group, generalizes the Barnich-Troessaert bracket, and shows the Noether charges form a centerless representation, linking asymptotic symmetries to Einstein's equations.

Findings

BMSW group includes super-translations, Weyl rescalings, and sphere diffeomorphisms.

Noether charges form a centerless algebra representation at null infinity.

BMSW elements label gravitational vacua.

Abstract

We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes, besides super-translations, local Weyl rescalings and arbitrary diffeomorphisms of the 2d sphere metric. After generalizing the Barnich-Troessaert bracket, we show that the Noether charges of the BMSW group provide a centerless representation of the BMSW Lie algebra at every cross section of null infinity. This result is tantamount to proving that the flux-balance laws for the Noether charges imply the validity of the asymptotic Einstein's equations at null infinity. The extension requires a holographic renormalization procedure, which we construct without any dependence on background fields. The renormalized phase space of null infinity reveals new pairs of conjugate variables. Finally, we show that BMSW group elements label the gravitational vacua.