Definition
The Page curve is the time-dependence of the fine-grained entanglement entropy of Hawking radiation predicted by unitary evaporation of a black hole: rising from zero, peaking at the Page time (when radiation entropy equals remaining black-hole entropy), then falling back to zero as the black hole fully evaporates. Reproducing it from a semiclassical gravity calculation requires the quantum extremal surface / island prescription, with replica wormholes responsible for the descending branch.
Role in Research
The Page curve is a central object of the second semester of the holography course: Lecture 24 derives it in finite quantum mechanics, and Lecture 26 obtains it from an island in the JT model. Its derivation from semiclassical gravity — via quantum-extremal-surfaces and replica wormholes — is one of the main results of the modern black-hole information program.
Relations
- quantum-extremal-surfaces — the QES / island prescription reproduces the Page curve from semiclassical gravity.
- replica-trick-gravity — replica wormholes are responsible for the descending branch of the curve.
- jt-gravity — JT gravity + bath is the simplest system in which the Page curve can be derived explicitly.
Papers
- Page 1993, Average entropy of a subsystem, arXiv:gr-qc/9305007.
- Penington 2019, arXiv:1905.08255.
- Almheiri–Engelhardt–Marolf–Maxfield 2019, arXiv:1905.08762.
Notes
Course coverage: Lecture 24, Lecture 26 and Lecture 27.