  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.

High Energy Physics - Theory