Note on the symplectic structure of asymptotically flat gravity and BMS symmetries

TL;DR

The paper addresses the infrared structure of asymptotically flat gravity by formulating a covariant phase-space description that splits the gravitational data at null infinity into bulk and boundary degrees of freedom. This decomposition yields the correct bulk–bulk and boundary–boundary Poisson brackets without ad hoc boundary terms and shows that BMS charges canonically generate their transformations on the gravitational phase space, including both supertranslations and superrotations. The analysis identifies hard and soft components in the charges for each sector and demonstrates that the integrable parts properly implement the corresponding transformations. The results clarify the phase-space structure at null infinity and have potential implications for soft-theorem–holography connections and celestial conformal field theories in flat space.

Abstract

The Poisson brackets of the gravitational field at null infinity play a pivotal role in establishing the equivalence between the Ward identities involving BMS charges and the soft graviton theorem. In recent literature it was noticed that, in order to reproduce the action of BMS transformations via such Poisson brackets, one needs to add "ad-hoc" boundary terms in the symplectic form. In this note we show that, introducing a suitable splitting of the gravitational field in bulk and boundary degrees of freedom and using techniques of covariant phase space formalism, it is possible to obtain the correct Poisson brackets between the boundary fields without any additional assumption. The same Poisson brackets are used to show that BMS charges canonically generate BMS transformations on the gravitational phase space.