Black-Hole Information
Black-Hole Information — Page Curve & Unitarity · Quantum Gravity
Show that black holes preserve information — recover the unitary Page curve of Hawking radiation via the island formula.
📋 The problem
Hawking's calculation implies black holes destroy information, contradicting quantum unitarity. The island / replica-wormhole prescription recovers a unitary 'Page curve' for radiation entropy. Reproducing it tests whether information survives.
🧗 Why it's a grand challenge
It requires fine-grained entanglement entropy with quantum-extremal-surface (island) contributions; analytic only in toy models; deviations diagnose where semiclassical gravity fails.
🧮 Governing model
S_rad = min ext_I [ Area(∂I)/4G_N + S_bulk(R∪I) ] (island formula)Fine-grained entropy of Hawking radiation S_rad(t) with the island/QES prescription; unitarity ⇒ Page curve that rises then falls.
Current best: Islands / replica-wormhole Page-curve derivations
🧭 Possible approaches
- Quantum-extremal-surface / island solvers for radiation entropy
- Replica-wormhole emulators
- Learning the Page transition in toy evaporating models
🎯 Build the benchmark
Recover the unitary Page curve for an evaporating model with low deviation, using the island formula.
Metric: page_dev — deviation from unitary Page curve (lower better)
Datasets to start from: Replica-wormhole entropy benchmark set, Evaporating-model entanglement series
🤖 Build an AI agent to solve it
An agent that, given an evaporation model, computes the entropy curve and locates the Page time and islands.
Once a benchmark exists, an AI4Science agent can iterate solutions against it — every verified solution earns PWM.
This is a frontier framing page — an open problem, not yet benchmarked or verified, unlike PWM's mature computational-imaging benchmarks.