Beyond islands: A free probabilistic approach

Understand

We give a free probabilistic proposal to compute the fine-grained radiation entropy for an arbitrary bulk radiation state, in the context of the Penington-Shenker-Stanford-Yang (PSSY) model where the gravitational path integral can be implemented with full control.

• We observe that the replica trick gravitational path integral is combinatorially matching the free multiplicative convolution between the spectra of the gravitational sector and the matter sector respectively.
• The convolution formula computes the radiation entropy accurately even in cases when the island formula fails to apply.
• It also helps to justify this gravitational replica trick as a soluble Hausdorff moment problem.