  We propose an extension of the BMS group, which we refer to as Weyl BMS or
BMSW for short, that includes, besides super-translation, local Weyl rescaling
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.
