Page Curves and Islands in Charged Dilaton Black Holes

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.

minor corrections, references added

References in corpus (7)

• Black holes as mirrors: quantum information in random subsystems
• Inconsistency of Islands in Theories with Long-Range Gravity
• Islands in charged linear dilaton black holes
• Page Curve and the Information Paradox in Flat Space
• Page curves for a family of exactly solvable evaporating black holes
• Page Curves and Bath Deformations
• Page Curve from Defect Extremal Surface and Island in Higher Dimensions

Cited by in corpus (2)

• Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background
• Entropy of Radiation with Dynamical Gravity