Extensions of the asymptotic symmetry algebra of general relativity (Q2185234)

The authors consider a recently proposed extension of the Bondi-Metzner-Sachs algebra to include arbitrary infinitesimal diffeomorphisms on a 2-sphere. In order to realize this extended algebra as asymptotic symmetries, they work with an extended class of space-times in which the unphysical metric at null infinity is not universal. They show that the symplectic current evaluated on these extended symmetries is divergent in the limit to null infinity. They 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 a symplectic current may not need to be covariant in order to have a covariant symplectic form. The authors 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.