Barnich–Troessaert bracket as a Dirac bracket on the covariant phase space

Abstract The Barnich–Troessaert bracket is a proposal for modified Poisson on the covariant phase space general relativity. new allows us to compute charges, which are otherwise not integrable. Yet there catch. There clear prescription how evaluate any such charge, but little known extend entire space. This problem, because every gravitational observable also charge. In this paper, we propose an extension. basic idea remove radiative data from requires second-class constraints. Given few assumptions, show that resulting Dirac constraint surface nothing BT bracket. A heuristic argument given can only contain edge modes.