Extensions of the asymptotic symmetry algebra of general relativity

TL;DR

This paper investigates an extended algebra of asymptotic symmetries in general relativity, revealing divergences in the symplectic current that challenge the realization of these symmetries at null infinity.

Contribution

It demonstrates that the proposed extension of the BMS algebra leads to divergences in the symplectic current, questioning its role as a symmetry algebra in vacuum GR.

Findings

Symplectic current diverges at null infinity for extended symmetries.

Extended algebra lacks a universal Bondi 4-momentum.

Divergences cannot be removed by local covariant redefinitions.

Abstract

We consider a recently proposed extension of the Bondi-Metzner-Sachs algebra to include arbitrary infinitesimal diffeomorphisms on a (2)-sphere. To realize this extended algebra as asymptotic symmetries, we work with an extended class of spacetimes in which the unphysical metric at null infinity is not universal. We show that the symplectic current evaluated on these extended symmetries is divergent in the limit to null infinity. We also show that this divergence cannot be removed by a local and covariant redefinition of the symplectic current. This suggests that such an extended symmetry algebra cannot be realized as symmetries on the phase space of vacuum general relativity at null infinity, and that the corresponding asymptotic charges are ill-defined. However, a possible loophole in the argument is the possibility that symplectic current may not need to be covariant in order to have a covariant symplectic form. We also show that the extended algebra does not have a preferred subalgebra of translations and therefore does not admit a universal definition of Bondi 4-momentum.