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

TL;DR

This paper develops a covariant phase space formalism for null boundaries in gravitational theories, revealing anomalies in charge algebras that relate to black hole entropy and holographic principles.

Contribution

It introduces a new principle fixing quasilocal charges via holographic Dirichlet flux, and derives a formula for charge algebra anomalies on null surfaces.

Findings

The anomaly in charge algebra is linked to the null normal frame fixing.

Applying the formalism to near-horizon Virasoro symmetry yields a doubled entropy.

The entropy derived is twice the Bekenstein-Hawking entropy, interpreted via entangled CFTs.

Abstract

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. This anomaly arises from having fixed a frame for the null normal, and we draw parallels between it and the holographic Weyl anomaly that occurs in AdS/CFT. As an application of this formalism, we analyze the near-horizon Virasoro symmetry considered by Haco, Hawking, Perry, and Strominger, and perform a systematic derivation of the fluxes and central charges. Applying the Cardy formula to the result yields an entropy that is twice the Bekenstein-Hawking entropy of the horizon. Motivated by the extended Hilbert space construction, we interpret this in terms of a pair of entangled CFTs associated with edge modes on either side of the bifurcation surface.