Island, Page Curve and Superradiance of Rotating BTZ Black Holes

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.

22 pages, 4 figures, typos corrected, Refs added

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Cited by in corpus (6)

• The role of mutual information in the Page curve
• Page curves and Entanglement Islands for the Step-Function Vaidya Model of Evaporating Black Holes
• Phantom BTZ black holes
• Notes on solution phase space and BTZ black hole
• New insights on mutual information in the island approach to the Page curve
• Thermodynamics and information recovery of Schwarzschild AdS black holes in conformal Killing gravity