Islands in charged linear dilaton black holes

TL;DR

This paper studies the entanglement entropy and Page curve of charged linear dilaton black holes using the island prescription, revealing universal features in non-extremal cases and challenges in extremal cases.

Contribution

It applies the island prescription to non-standard charged linear dilaton black holes, analyzing entanglement entropy and revealing universal Page time behavior.

Findings

Page curve is consistent with unitarity in non-extremal case

Page time is universal across models, proportional to entropy and temperature

Extremal case requires island for well-defined entropy, but may not reproduce the Page curve

Abstract

We investigate the Page curve for a non-standard black hole which is asymptotically non-flat/AdS/dS. For this purpose, we apply the island prescription to the charged linear dilaton black holes and analyze, in detail, the entanglement entropy of Hawking radiation for both the non-extremal case and the extremal case. In the non-extremal case, we find the Page curve consistent with the unitarity principle: at early times the entanglement entropy grows linearly in time without the island and at late times it is saturated double of the Bekenstein-Hawking entropy in the presence of the island. We observe the Page time is universal for all different models studied by our method: $t_{\text{Page}}=\frac{3}{ \pi c}\frac{S_{\text{BH}}}{T_H}.$ For the extremal case, the island prescription provides the well defined entanglement entropy only with the island, which can not be obtained from the continuous limit of the non-extremal case. This implies that the Page curve may not be reproduced for the extremal case and further investigation is needed.