Layered Quantum Extremal Surfaces and Multidimensional Page Curves in Stratified Black Holes
摘要
We extend stratified black hole evaporation by systematically analyzing the quantum extremal surfaces (islands) associated with each interior layer and their dynamical role in information recovery. In this framework, every concentric shell supports its own quantum extremal surface, which becomes dominant at a distinct Page time. This layered island structure gives rise to a generalized staircase Page curve, where entropy decreases occur sequentially as deeper layers are reconstructed. We solve for these layer-resolved quantum extremal surfaces explicitly in a multi-layer Jackiw–Teitelboim gravity model and show that the entanglement wedge of the Hawking radiation advances inward one layer at a time. We further generalize the analysis to multiple radiation channels and compute the full multipartite entropy using inclusion–exclusion formulas. Each radiation subsystem exhibits its own stepwise Page curve, while the total multipartite entropy remains finite even after all individual entropies vanish. This residual contribution signals an irreducible secret-sharing entanglement structure in the final radiation state, characterized by a nonzero Markov gap. Our results extend the island prescription to nested, multi-layer geometries and reveal new patterns of holographic redundancy and multipartite entanglement in black hole evaporation.