Page Curve

The Page curve describes the expected evolution of entanglement entropy between a black hole and its Hawking radiation as the black hole evaporates. Named after Don Page, who derived it in 1993, the curve predicts that the entropy initially rises as the black hole emits thermal radiation, then peaks at the Page time — approximately halfway through the evaporation — and then declines to zero as the radiation eventually encodes the full quantum state of the infalling matter.

The curve's significance is that it resolves the information paradox at the level of entropy: if the total entropy of the radiation-plus-hole system follows the Page curve, then information is not destroyed but merely redistributed. The recent derivation of the Page curve from holographic quantum gravity — using the replica trick in the path integral — is considered one of the major achievements of 21st-century theoretical physics. Yet the curve leaves open the question of how the information is encoded in the radiation, and whether the process can be described by a smooth semiclassical geometry or requires a firewall at the horizon.