Restoring predictability in semiclassical gravitational collapse

TL;DR

The paper argues that Hawking's information‑loss paradox can be reconciled by including semiclassical fluctuations of the gravitational background, modeled via a Gaussian shell wavefunction with width set by the inverse of the Bekenstein–Hawking entropy. This yields a corrected radiation density matrix with small but nonzero off‑diagonal elements of order $C_{BH}^{1/2}$ that encode correlations between the collapsing shell and emitted quanta, allowing information to leak gradually. Using a multi‑particle density‑matrix framework, the authors show that the information content grows from a suppressed rate before the Page time to an order‑unity rate by Page time, consistent with unitary evaporation, while maintaining near‑thermal behavior at early times. The results suggest that quantum fluctuations of the background geometry can restore information without requiring new Planck‑scale physics, though a more complete time‑dependent treatment remains to be developed.

Abstract

Hawking showed that the radiation emitted from a classical collapsing shell is thermal. Here, we show that a semiclassical collapsing shell emits radiation that is only approximately thermal, with small but significant deviations. The most important difference is the presence of small off-diagonal elements in the radiation density matrix with a magnitude of order $1/\sqrt{S_{BH}}$, $S_{BH}$ being the Bekenstein-Hawking entropy of the incipient black hole. The off-diagonal elements store the correlations between the collapsing shell and the emitted radiation and allow information to continuously leak from the collapsed body. The rate of escape of information is initially very small, increasing to order one by the Page time, when the black hole has lost half its original entropy. We show that, until the Page time, the radiation is almost exactly thermal and that, from this time on, it begins to purify at an increasing rate.