Anomalies in gravitational charge algebras of null boundaries and black hole entropy

Understand

We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal.

• To fix the ambiguity inherent in the Wald-Zoupas definition of quasilocal charges, we propose a new principle, based on holographic reasoning, that the flux be of Dirichlet form.
• This also produces an expression for the analog of the Brown-York stress tensor on the null surface.
• Defining the algebra of charges using the Barnich-Troessaert bracket for open subsystems, we give a general formula for the central -- or more generally, abelian -- extensions that appear in terms of the anomalous transformation of the boundary term in the gravitational action.