Entanglement island and Page curve of Hawking radiation in rotating Kerr black holes

TL;DR

This paper demonstrates that entanglement islands can resolve the information paradox in rotating Kerr black holes by showing the Page curve behavior of Hawking radiation entropy in a 2D effective theory.

Contribution

It extends the island rule framework to Kerr black holes, analyzing the entropy and Page curve in the small angular momentum limit.

Findings

Hawking radiation entropy follows the Page curve for Kerr black holes.

Entanglement entropy saturates the Bekenstein-Hawking entropy at late times.

Rotation affects the Page and scrambling times.

Abstract

We initiate the study of the information paradox of rotating Kerr black holes by employing the recently proposed island rule. It is known that the scalar field theory near the Kerr black hole horizon can be reduced to the 2-dimensional effective theory. Working within the framework of the 2-dimensional effective theory and assuming the small angular momentum limit, we demonstrate that the entanglement entropy of Hawking radiation from the non-extremal Kerr black hole follows the Page curve and saturates the Bekenstein-Hawking entropy at late times. In addition, we also discuss the effect of the black hole rotation on the Page time and scrambling time. For the extreme Kerr black hole, the entanglement entropy at late times also approximates the Bekenstein-Hawking entropy of the extreme Kerr black hole. These results imply that entanglement islands can provide a semi-classical resolution of the information paradox for rotating Kerr black holes.