Extensions of the asymptotic symmetry algebra of general relativity
Éanna É. Flanagan, Kartik Prabhu, Ibrahim Shehzad
TL;DR
The paper tests whether enlarging the BMS symmetry to include all smooth 2-sphere diffeomorphisms yields well-defined asymptotic charges in vacuum GR. Using the covariant symplectic formalism, it shows the symplectic current diverges at null infinity for extended generators, implying ill-defined charges and fluxes, with local covariant renormalizations unable to cure the divergence. It argues that there is no universal Bondi four-momentum in the extended algebra and that the extended extension CL relies on noncovariant choices, leaving a potential loophole but lacking covariance. A final assessment is that the extended BMS proposal is not realizable on GR's null infinity phase space under covariant assumptions, reinforcing the special role of the standard BMS structure and highlighting open questions about how to formulate observables in any extended framework.
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.