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.
Highlights
The black hole information is one of the fundamental problems in many areas of physics such as quantum mechanics, thermodynamics, and the theory of general relativity [1–5]
Anti–de Sitter (AdS) space is not a necessary condition for the island formula. This island prescription is first suggested in the context of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence by Ryu and Takayanagi [19] and its further developments [6,9–11,16,20–22], it can be applied to any quantum system coupled to gravity
The extremal case is addressed in [28], but we find that we need to revisit the analysis for two reasons
Summary
The black hole information is one of the fundamental problems in many areas of physics such as quantum mechanics, thermodynamics, and the theory of general relativity [1–5]. This island prescription is first suggested in the context of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence by Ryu and Takayanagi [19] and its further developments [6,9–11,16,20–22], it can be applied to any quantum system coupled to gravity This is further supported by the fact that the entanglement entropy has been found to follow the Page curve in all the examples (e.g., asymptotically flat or dS) studied in the literature so far with the island prescription. Motivation of this paper: the island structure and the Page curve are investigated with the various black hole geometries in higher dimensions, to our knowledge, most of them considered the black holes in asymptotically flat/AdS/dS.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
