Natural Page curve on the full AdS boundary for evaporating small black holes

Determine whether there exists a natural, physically motivated fine-grained entropy on the entire AdS boundary—i.e., an algebra of boundary observables that does not artificially discard the Hamiltonian or restrict to subregions—whose time dependence during the evaporation of a small AdS black hole follows a Page curve.

Background

In standard gravity, the fine-grained entropy of the full asymptotic algebra remains constant during black hole formation and evaporation because the Hamiltonian is a boundary term, implying completeness of asymptotic observables and invalidating a traditional Page curve measured at infinity. In AdS, unlike at null infinity in flat space, dropping the Hamiltonian is not natural because it reappears via the operator product expansion of local operators, which complicates attempts to obtain a Page-curve-like behavior without artificial truncations.

The authors analyze coarse- and fine-grained boundary entropies for small AdS black holes. Coarse-grained entropies follow a Hawking-like monotonic increase, whereas the fine-grained entropy of the full boundary algebra is time-independent. They then pose the explicit question of whether a natural definition—avoiding artificial restrictions or blind spots—can yield a Page curve on the full boundary during evaporation, noting several obstacles, including OPE-induced regeneration of the Hamiltonian and the tight link between gravitational coupling and black hole entropy.