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In this paper, we consider the entanglement entropy and entanglement islands in the two-sided generalization of the Schwarzschild black hole in a cavity. We find that entanglement entropy saturates at some constant value thus for some values avoiding information paradox (in the Page curve formulation). Also we find, that inclusion of the entanglement islands leads to a universal effect induced by the boundary presence, which we call ``blinking island". For some time the entanglement island inevitably disappears, thus leading to a short-time information paradox.
Dmitry S. Ageev (Thu,) studied this question.