Reflecting Baths and Black Hole Interior Islands in JT Gravity

Abstract

We study the evolution of entanglement entropy within the island prescription in Jackiw-Teitelboim gravity coupled to finite non-gravitating baths bounded by reflecting walls. For free massless Dirac matter, we study the evolution of entanglement entropy, explicitly accounting for correlations induced by the reflecting boundaries. For sufficiently short baths, the no-island entropy saturates below the thermodynamic black hole entropy, avoiding the usual information paradox associated with its unbounded growth. For larger baths, reflected correlations drive the exterior quantum extremal surface toward the future horizon, leading to a temporary disappearance of the the near-horizon exterior island branch. We find that this branch first appears at a scrambling-like scale, and it reappears at a time that is proportional to the size of the bath. We extend the extremization across the horizon using regular Kruskal coordinates and identify real quantum extremal surfaces in the black hole interior. We show that, in the parameter regime studied, interior island configurations provide the dominant contribution to the radiation entropy during the exterior disappearance time interval, resolving the reappearance of the information paradox in an exterior-only description.