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.
Highlights
Remarkable progress was made in studying the information paradox of the black holes, which is caused by Hawking radiation [1]
It was shown that the island proposed to be in the entanglement wedge of the radiation should be taken into account when calculating entanglement entropy of Hawking radiation [2,3,4,5]
We investigate whether the quantum extremal island formula can be applied to resolve the information paradox of the eternal Liouville black hole in the two-dimensional dilaton gravity with the exponential potential
Summary
Remarkable progress was made in studying the information paradox of the black holes, which is caused by Hawking radiation [1]. We investigate whether the quantum extremal island formula can be applied to resolve the information paradox of the eternal Liouville black hole in the two-dimensional dilaton gravity with the exponential potential. This type of model was initially introduced by Mann [44]. We explain qualitatively the reason why the Page curve cannot be reproduced in the present model This implies that the island formula may not necessarily save the information paradox for the Liouville black holes
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