We propose an extension of the BMS group, which we refer to as Weyl BMS or BMSW for short, that includes 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.

我们提出了 BMS 组的扩展，我们将其简称为 Weyl BMS 或 BMSW，其中包括超平移、局部 Weyl 重新缩放和二维球度量的任意微分同胚。在推广 Barnich-Troessaert 括号之后，我们证明了 BMSW 群的 Noether 电荷在每个零无穷大截面处提供了 BMSW 李代数的无心表示。这个结果相当于证明了诺特电荷的通量平衡定律暗示了渐近爱因斯坦方程在零无穷远处的有效性。扩展需要一个全息重整化过程，我们在不依赖背景场的情况下构建它。零无穷大的重整化相空间揭示了新的共轭变量对。最后，我们表明 BMSW 群元素标记了引力真空。