Entropy bound and the non-universality of entanglement islands

Abstract

The island prescription reproduces the Page curve and avoids the Almheiri--Marolf--Polchinski--Sully (AMPS) monogamy conflict for suitable radiation subsystems by placing the corresponding interior partners in their entanglement wedges. This mechanism is intrinsically region-dependent. We define a common compact semiclassical support as a finite semiclassical domain that contains representatives of the interior partners of a chosen family of late Hawking modes, while each radiation subsystem need reconstruct only its own partner. We ask whether these separate mode-by-mode reconstructions can be represented within such a common support at a fixed evaporation epoch. The physical motivation is that horizon normalcy---the requirement that the horizon remain smooth for an infalling observer and that semiclassical effective field theory remain valid across it---is a local property, whereas the island condition that resolves AMPS for a given late mode depends on the radiation subsystem used for reconstruction. Using a bounded null realization of the common support together with the quantum Bousso bound, we show that no regular common compact semiclassical support can realize all of the relevant AMPS partner sectors once the support enters the hyperentropic regime. The argument is formulated entirely within the semiclassical region in which the AMPS setup is valid and does not require extending the null surface to the Planckian singularity.

9 pages, two-column format. Substantially revised. Replaced the strong universal-island condition by a weaker common compact partner-support formulation, reformulated the obstruction using conditional entropy and the quantum Bousso bound, and substantially improved the presentation, organization, and clarity of the manuscript