Gravitational Poisson brackets at null infinity compatible with smooth superrotations

TL;DR

This paper derives a consistent Poisson bracket structure at null infinity that incorporates smooth superrotations, extending the gravitational phase space to include celestial metric variables and boundary terms.

Contribution

It introduces a novel Poisson bracket algebra that includes the celestial metric and boundary effects, enabling a canonical realization of smooth superrotations.

Findings

Derived Poisson brackets including boundary terms.

Established relations between celestial metric and radiative variables.

Extended gravitational phase space to accommodate superrotations.

Abstract

Superrotations are local extensions of the Lorentz group at null infinity that have been argued to be symmetries of gravitational scattering. In their smooth version, they can be identified with the group of diffeomorphisms on the celestial sphere. Their canonical realization requires treating the celestial metric as a variable in the gravitational phase space, along with the news and shear tensors. In this paper, we derive the resulting Poisson brackets (PB). The standard PB algebra of the news and shear tensors is augmented by distributional terms at the boundaries of null infinity, including novel PB relations between the celestial metric and the radiative variables.