<p>The black hole information paradox arises from Hawking’s semiclassical analysis showing that evaporating black holes emit only thermal radiation, leading to apparent loss of information. Unitarity demands that the radiation’s von Neumann entropy follow a Page curve, first rising and then eventually falling to zero. Here we propose a model in which the black hole interior is stratified into concentric layers of distinct quantum degrees of freedom. We apply the quantum extremal surface (island) prescription to compute the entanglement entropy of the Hawking radiation in this layered geometry. We find a staircase-shaped Page curve: after an initial rise, the entropy reaches successive plateaus and then drops each time a new island, associated with an inner layer, becomes dominant. Each drop corresponds to the transfer of information from one layer to the radiation, yielding sequential purification of the black hole. This multi-step Page curve realizes unitary evaporation in discrete stages and implies a cascade of entanglement-wedge reconstructions that progressively include deeper layers. These results highlight how black hole microstructure can be unveiled through entanglement dynamics, with broad implications for holography and semiclassical gravity.</p>

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Stratified Black Hole Interiors and Time-Resolved Page Curves for Information Recovery

  • Alberto Miró Morán

摘要

The black hole information paradox arises from Hawking’s semiclassical analysis showing that evaporating black holes emit only thermal radiation, leading to apparent loss of information. Unitarity demands that the radiation’s von Neumann entropy follow a Page curve, first rising and then eventually falling to zero. Here we propose a model in which the black hole interior is stratified into concentric layers of distinct quantum degrees of freedom. We apply the quantum extremal surface (island) prescription to compute the entanglement entropy of the Hawking radiation in this layered geometry. We find a staircase-shaped Page curve: after an initial rise, the entropy reaches successive plateaus and then drops each time a new island, associated with an inner layer, becomes dominant. Each drop corresponds to the transfer of information from one layer to the radiation, yielding sequential purification of the black hole. This multi-step Page curve realizes unitary evaporation in discrete stages and implies a cascade of entanglement-wedge reconstructions that progressively include deeper layers. These results highlight how black hole microstructure can be unveiled through entanglement dynamics, with broad implications for holography and semiclassical gravity.