Island may not save the information paradox of Liouville black holes

TL;DR

This paper investigates whether the quantum extremal island formula can resolve the information paradox in two-dimensional Liouville black holes, finding that islands do not appear to save the paradox in this model.

Contribution

The study applies the quantum extremal island formula to Liouville black holes and shows that no suitable islands are found, challenging the universality of the island proposal.

Findings

No reasonable islands found when extremizing generalized entropy.

The Page curve cannot be reproduced in this model.

Islands may not resolve the information paradox for Liouville black holes.

Abstract

By using the quantum extremal island formula, we perform a simple calculation of the generalized entanglement entropy of Hawking radiation from the two dimensional Liouville black hole. No reasonable island was found when extremizing the generalized entropy. We explain qualitatively the reason why the page curve cannot be reproduced in the present model. This suggests that the islands may not necessarily save the information paradox for the Liouville black holes.