Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes

Abstract

The Fabbri-Russo model is a generalized model of a two-dimensional dilaton gravity theory with various parameters "$n$" describing various specific gravities. Particularly, the Russo-Susskind-Thorlacius gravity model fits the case $n=1$. In the Fabbri-Russo model, we investigate Page curves and the entanglement island. Islands are considered in eternal and evaporating black holes. Surprisingly, in any black hole, the emergence of islands causes the rise of the entanglement entropy of the radiation to decelerate after the Page time, satisfying the principle of unitarity. For eternal black holes, the fine-grained entropy reaches a saturation value that is twice the Bekenstein-Hawking entropy. For evaporating black holes, the fine-grained entropy finally reaches zero. The parameter "$n$" significantly impacts the Page curve at extremely early times. However, at late times and large distance limit, the impact of the parameter "$n$" is a subleading term and is exponentially suppressed. As a result, the shape of Page curves is "$n$"-independent in the leading order. Furthermore, we discuss the relationship between islands and firewalls. We show that the island is a better candidate than firewalls for encountering the quantum entanglement-monogamy problem. Finally, we briefly review the gravity/ensemble duality as a potential resolution to the state conundrum resulting from the island formula.

43 pages,5 figures, references added

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• Entanglement Island and Page Curve in Wedge Holography
• Mutual information of subsystems and the Page curve for Schwarzschild de-Sitter black hole
• Islands in Non-Minimal Dilaton Gravity: Exploring Effective Theories for Black Hole Evaporation
• Island of Reissner-Nordstr$\ddot{\mathbf{o}}$m anti-de Sitter black holes in the large $d$ limit
• Analogue gravity and the island prescription
• Towards bit threads in general gravitational spacetimes
• Effect of backreaction on Island, Page curve and Mutual Information
• Entanglement island and Page curve for one-sided charged black hole
• Investigating the role of mutual information in the Page curve for a functional renormalization group improved Schwarzschild black hole
• New insights on mutual information in the island approach to the Page curve