Island of Reissner-Nordstr$\mathbf{\ddot{o}}$m anti-de Sitter black holes in the large $d$ limit

TL;DR

This paper investigates the information paradox for large-dimensional Reissner-Nordström anti-de Sitter black holes using the island formula, revealing how entanglement entropy behaves in non-extremal and extremal cases and providing new insights into semi-classical large $d$ black holes.

Contribution

It applies the island formula to large $d$ RN-AdS black holes, analyzing entanglement entropy and constraints near the horizon, which is novel in the context of high-dimensional black hole physics.

Findings

Entanglement entropy follows the Page curve in non-extremal cases.

In extremal cases, entropy is ill-defined without the island but equals Bekenstein-Hawking entropy when the island exists.

Constraints on black hole size are derived from the existence of island solutions.

Abstract

We study the information paradox of Reissner-Nordstr${\ddot{o}}$m anti-de Sitter (RN-AdS$_{d+1}$) black holes in the large dimension limit by using the island formula. The entanglement entropy of Hawking radiation is calculated both for the non-extremal and the extremal cases, in which the boundary of the radiation region is close to the outer horizon. For the non-extremal case, the entanglement entropy of Hawking radiation obeys the Page curve, i.e. the entanglement entropy of Hawking radiation increases with time and reaches saturation about twice Bekenstein-Hawking entropy at the Page time. For the extremal case, the entanglement entropy of Hawking radiation becomes ill-defined in the absence of the island due to the appearance of the singularity at the origin of the radial coordinate, while when the island exists, the entanglement entropy is found to be equal to the Bekenstein-Hawking entropy. In addition, for the case where the boundary of the radiation region is close to the horizon, there are some obvious constraints required by the existence of island solution for both non-extremal and extremal cases, which can be utilized to put constraints on the size of the black hole. These results reveal new features of the semi-classical large $d$ black holes from the island perspective.