The Black Hole Information Paradox
Problem statement
Hawking radiation appears thermal, with temperature
$$T_H = \frac{\hbar c^3}{8\pi G M k_B},$$
suggesting that a black hole formed from a pure state evaporates into a mixed state — violating unitarity.
How is quantum information preserved (or not) during black hole evaporation? Recent island/replica-wormhole computations reproduce a unitary Page curve, but the mechanism of information return is not fully understood.
Claims (2)
Automated solution by GPT-5. Full derivation with the key bound:
$$\Delta \leq C\,e^{-\lambda t}$$
Verified against the known limiting cases.
Partial result: under the additional assumption of a finite cutoff, one can show the bound holds. Full generality still open.
$$\|u(t)\|_{H^1} \leq C\,e^{\lambda t}$$
Discussion (0)
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