Page curve

The Page curve describes the time evolution of the entanglement entropy of Hawking radiation emitted by an evaporating black hole. Named after Don Page, it predicts that the entropy of the radiation should initially rise as the black hole emits thermal radiation, then reach a maximum at approximately the Page time (half the evaporation time), and finally fall to zero as the black hole disappears and the radiation becomes pure. This behavior resolves the black hole information paradox by showing that the total entropy of the black hole-plus-radiation system remains bounded and consistent with quantum unitarity.

Recent calculations using quantum extremal surfaces in the context of the holographic principle have successfully reproduced the Page curve, providing strong evidence that information is preserved in black hole evaporation. The Page curve is thus not merely a theoretical prediction; it is a diagnostic tool for distinguishing between theories of quantum gravity that preserve information and those that do not.