  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.
