A general framework for gravitational charges and holographic renormalization

Understand

We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques.

• This framework encompasses both localized charges associated with spacetime subregions, as well as global conserved charges of the full spacetime.
• Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries.
• The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles.