The Bondi-Metzner-Sachs group in five spacetime dimensions

TL;DR

This paper explores the structure of asymptotic symmetries in five-dimensional flat spacetimes, revealing a nonlinear algebra involving multiple arbitrary functions and nontrivial central charges, extending the understanding of BMS symmetries.

Contribution

It uncovers the nonlinear algebra of asymptotic symmetries in five dimensions, including multiple functions and central charges, which was not previously known.

Findings

The asymptotic symmetry algebra is a nonlinear deformation of the BMS algebra.

The algebra involves four independent functions on the 3-sphere at infinity.

Nontrivial central charges appear in the algebra.

Abstract

We study asymptotically flat spacetimes in five spacetime dimensions by Hamiltonian methods, focusing on spatial infinity and keeping all asymptotically relevant nonlinearities in the transformation laws and in the charge-generators. Precise boundary conditions that lead to a consistent variational principle are given. We show that the algebra of asymptotic symmetries, which had not been uncovered before, is a nonlinear deformation of the semi-direct product of the Lorentz algebra by an abelian algebra involving four independent (and not just one) arbitrary functions of the angles on the $3$-sphere at infinity, with non trivial central charges. The nonlinearities occur in the Poisson brackets of the boost generators with themselves and with the other generators. They would be invisible in a linearized treatment of infinity.