Island of Reissner-Nordström anti–de Sitter black holes in the large D limit

Abstract

We study the information paradox of Reissner-Nordström anti–de Sitter black holes in the large dimension limit by using the island formula. The entanglement entropy of Hawking radiation is calculated both for the nonextremal and the extremal cases, in which the boundary of the radiation region is close to the outer horizon. For the nonextremal 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 the island solution for both nonextremal and extremal cases, which can be utilized to put constraints on the size of the black hole. These results reveal new features of the semiclassical large D black holes from the island perspective. Published by the American Physical Society 2024