Asymptotically flat spacetimes with BMS$_3$ symmetry

TL;DR

This paper constructs a consistent phase space for 3D asymptotically flat spacetimes that carries a single copy of the $BMS_3$ symmetry, realized both at the boundary and in the bulk. By imposing Neumann boundary conditions with a boundary lightcone structure and employing a hyperbolic foliation, it derives a four-function phase space of null boundary fields and computes integrable charges for superrotations and supertranslations, reproducing the $BMS_3$ algebra with a possible central extension in the translational sector. The analysis shows that null boundary fields impose antipodal identifications between $ ext{I}^+$ and $ ext{I}^-$ (modulo a conical defect), and introduces the concept of a BMS horizon for charge screening. The results provide a concrete 3D model as a stepping stone toward understanding the infrared structure and holographic aspects of higher-dimensional asymptotically flat spacetimes, with implications for symplectic symmetries and bulk-boundary correspondences.

Abstract

We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy of the BMS group at both null infinities and spatial infinity. The BMS phase space obeys a notion of holographic causality and can be parametrized by boundary null fields. This automatically leads to the antipodal identification of bulk fields between past and future null infinity in the absence of a global conical defect.

Figures (1)

• Figure 1: Penrose diagram illustrating null geodesic motion on the $dS_2$ boundary in the absence or presence of a global conical defect.