Holography and the Page curve of an evaporating black hole

Abstract

The Page curve exhibits a sharp peak at the Page time corresponding to a phase transition from an empty quantum extremal surface to a non-empty one. This study delves into the impact of this phase transition on the informational content of black hole radiation through constructing a smooth Page curve which represents a gradual transition instead. We utilize replica trick, apply holography in a specific form, and introduce mathematical identities inherent to the curve's smoothness. Our results suggest that a gradual transition could lead to a significant increase in the informational content of the radiation.