Islands in charged linear dilaton black holes

Abstract

We investigate the Page curve for a nonstandard black hole which is asymptotically nonflat/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 nonextremal case and the extremal case. In the nonextremal 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 saturates to 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(Page) = 3/pi C S-BH/T-H. For the extremal case, the island prescription provides the well-defined entanglement entropy only with the island, which cannot be obtained from the continuous limit of the nonextremal case. This implies that the Page curve may not be reproduced for the extremal case and further investigation is needed.