Page Curves and Islands in Charged Dilaton Black Holes

TL;DR

This paper investigates the entanglement entropy evolution in charged dilaton black holes, demonstrating the role of islands in resolving the information paradox and analyzing how charge and parameters affect the Page curve.

Contribution

It applies the quantum extremal surface prescription to charged dilaton black holes, revealing how islands influence the Page curve and entropy saturation, with detailed analysis of parameter effects.

Findings

Entanglement entropy saturates due to islands, reaching twice the Bekenstein-Hawking entropy.

Charge significantly affects the Page time, especially near extremality.

Without islands, entropy diverges at late times.

Abstract

We study the Page curve in the four dimensional asymptotically flat eternal Garfinkle-Horowitz-Strominger dilaton black holes by applying the "quantum extremal surface" prescription. The results demonstrate that without island, the entanglement entropy of Hawking radiation is proportional to time and divergent at late times. While taking account of the emergence of the island extending slightly outside the event horizon, the entanglement entropy of Hawking radiation stops growing and eventually reaches a saturation value, which is twice of the Bekenstein-Hawking entropy and consistent with the finiteness of the von Neumann entropy of eternal black holes. Moreover, we discuss the impact of the parameter $n$ and charge $Q$ on the Page time. The influence of $n$ on it can neglected when the ratio of the charge $Q$ to the black hole mass $M$ is sufficiently small, but the charge $Q$ has a significant impact on Page time. Importantly, at the extremal case, the Page time becomes divergent or vanishing, in which the semiclassical theory needs further investigation.