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.

Some clarifications added, conclusion unchanged. Comments are welcome

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• The $S$- and $P$-wave fully charmed tetraquark states and their radial excitations
• Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes
• Planar Black Holes in Holographic Axion Gravity: Islands, Page Times, and Scrambling Times
• Cosmological and black hole islands in multi-event horizon spacetimes
• Defect extremal surfaces for entanglement negativity
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• What can we learn about islands and state paradox from quantum information theory?
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions
• Retrieving black hole information from the main Lorentzian saddle point