Entanglement Islands in Generalized Two-dimensional Dilaton Black Holes

TL;DR

This paper explores entanglement islands in a generalized two-dimensional dilaton black hole model, analyzing their effects on entropy and unitarity, and discusses implications for firewalls and gravity/ensemble duality.

Contribution

It extends the understanding of entanglement islands in a generalized dilaton gravity model with parameter n, analyzing their impact on Page curves and black hole entropy.

Findings

Islands cause entropy to decelerate after Page time, ensuring unitarity.

For eternal black holes, entropy saturates at twice the Bekenstein-Hawking value.

For evaporating black holes, entropy eventually drops to zero.

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.