Conformal Carroll groups and BMS symmetry

TL;DR

This work reframes the asymptotic symmetry problem of four-dimensional asymptotically flat spacetimes by treating the future null boundary ${\cal I}^{+}$ as a Carroll manifold and showing that its conformal symmetries reproduce the BMS group. It introduces conformal Carroll transformations ${\mathrm{CCarr}}_N$ as the symmetry group preserving $g\otimes\xi^{\otimes N}$ up to a conformal factor, with the case $N=2$ yielding the BMS group on the celestial sphere and $z=1$ for $d=1$ relevant to Conformal Galilei structures. The Newman-Unti (NU) group is presented as a broader extension preserving the conformal class of $g$, and for the light-cone it becomes ${\mathrm{Conf}}(S^d)\ltimes C^{\infty}(C,\mathbb{R})$, illustrating a nested hierarchy NU_1 ⊂ BMS ⊂ NU_2 ... with ${\mathrm{NU}}_1={\mathrm{CCarr}}_\infty$. The paper thus unifies BMS, NU, and Carrollian geometry within a common conformal Carroll framework, clarifying the nature of supertranslations and the role of the celestial sphere in asymptotic symmetries.

Abstract

The Bondi-Metzner-Sachs (BMS) group is shown to be the conformal extension of Levy-Leblond's "Carroll" group. Further extension to the Newman-Unti (NU) group is also discussed in the Carroll framework.