Island, Page Curve and Superradiance of Rotating BTZ Black Holes

TL;DR

This paper analyzes the information paradox and Page curve for rotating BTZ black holes using the island paradigm, highlighting the role of superradiance in resolving divergences in extremal cases.

Contribution

It introduces the consideration of superradiance in the island paradigm to address divergences in the Page time for extremal rotating black holes.

Findings

Page curve obeyed when island is outside the horizon

Superradiance reduces Page time and entropy for non-large central charge

Black hole becomes neutral after superradiance completes

Abstract

We study the Page curve and the information paradox for the BTZ black hole coupled to two thermal baths by applying the island paradigm. We prove that as the island locates outside the event horizon, the entanglement entropy of Hawking radiation for finite temperature black holes obeys the Page curve. However, for extremal rotating black holes, the Page time and the scrambling time become divergent. To avoid the ill-defined of the Page time, we consider the contribution of superradiance, which is a process that can extract rotational energy from black holes. The superradiance continues in a period much shorter than the Page time when the central charge $c$ is not too large. In this process, the Page time, the scrambling time and the black hole thermal entropy all decrease. Whenever the superradiance finishes, the black hole turn out to be a neutral black hole and the Hawking radiation dominates. The Page curve can then be well reproduced.