It is generally expected that during the black hole evaporation process, correlations within the Hawking radiation first start to grow at a time scale called the Page time. The information of a diary thrown into the black hole is also expected to become accessible from the radiation at the Page time. These expectations are based on averages over Haar-random pure states, which assume that the evaporating black hole resembles an equilibrated pure state at infinite temperature. Using a method called the equilibrium approximation, we study the universal behavior of quantities such as logarithmic negativity and Petz map fidelity in equilibrated pure states at finite temperature. This reveals surprising new features of the entanglement structure of the black hole and its radiation in the presence of energy constraints. In particular, we find that both the entanglement within the radiation and the likelihood of information recovery first start to grow at a new time scale, which is earlier than the Page time by a finite fraction of the total evaporation time.
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