A canonical bracket for open gravitational system

TL;DR

This paper demonstrates that an extended gravitational Lagrangian yields a canonical bracket representing the extended corner algebra, integrating symplectic flux into the Lagrangian and forming a representation of the extended corner symmetry algebra.

Contribution

It introduces a canonical bracket for an extended gravitational Lagrangian that captures the extended corner algebra and symplectic flux reabsorption.

Findings

The generalized Barnich-Troessaert bracket is obtained as a canonical bracket.

The extended Lagrangian allows symplectic flux to be absorbed into the Lagrangian.

The canonical Poisson bracket of charges represents the extended corner symmetry algebra.

Abstract

This paper shows that the generalization of the Barnich-Troessaert bracket recently proposed to represent the extended corner algebra can be obtained as the canonical bracket for an extended gravitational Lagrangian. This extension effectively allows one to reabsorb the symplectic flux into the dressing of the Lagrangian by an embedding field. It also implies that the canonical Poisson bracket of charges forms a representation of the extended corner symmetry algebra.