Generate the page curve for the Kerr black hole near the horizon limit

Abstract

We study the Page curve and the information paradox for the rotating black hole. For this purpose, we apply the island prescription to the Kerr black hole near the horizon limit and analyze the behavior of the entan glement entropy at early and late times. The results demonstrate that the Page curve is consistent with the unitarity principle: without the island, the entanglement entropy grows linearly in time, and in the presence of the island, it is saturated twice the Bekenstein Hawking entropy. We observe the Page time is universal for all di↵erent models studied by our method: tP age = 3SBH ⇡THc . However, for extremal rotating black holes, the Page time be comes divergent or vanishing, which the semi-classical theory needs further investigation.