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By using the quantum extremal island formula, we perform a simple calculationof the generalized entanglement entropy of Hawking radiation from the twodimensional Liouville black hole. No reasonable island was found whenextremizing the generalized entropy. We explain qualitatively the reason whythe page curve cannot be reproduced in the present model. This suggests thatthe islands may not necessarily save the information paradox for the Liouvilleblack holes.

Island may not save the information paradox of Liouville black holes