Island may not save the information paradox of 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.