Fonctionne avec Indico
v3.2.9
One aspect of the black hole information puzzle concerns the issue that the radiation entropy seems ever increasing. Assuming unitarity, Page showed in a toy model that the entropy must follow the Page curve that stops increasing after the black hole "half-life". In semiclassical gravity, the entropy of Hawking radiation is recently shown to be given by the "island formula", which was derived using the replica trick with replica wormhole contributions. It successfully produces the qualitative behavior of the Page curve. However, the island formula doesn't capture the radiation entropy accurately when the effect of replica symmetry breaking is significant, which could occur in presence of non-trivial entanglement spectra between the radiation and the black hole. In such scenarios, the quantum extremal surfaces and islands cannot be identified.
After reviewing the path integral method for the gravitational replica trick, we show how free probability can help us compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model of two-dimensional black holes. We observe that the relevant gravitational path integral is combinatorially matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector respectively. We then work out how the free convolution formula can be evaluated using free harmonic analysis. The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply. Using the close tie between free probability and random matrix theory, we show that the PSSY model can be described as a generalization of Page's model.
Sylvain Carrozza, Luca Lionni, Fabien Vignes-Tourneret