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We study the information paradox of Reissner-Nordstr${\ddot{o}}$m anti-deSitter (RN-AdS$_{d+1}$) black holes in the large dimension limit by using theisland formula. The entanglement entropy of Hawking radiation is calculatedboth for the non-extremal and the extremal cases, in which the boundary of theradiation region is close to the outer horizon. For the non-extremal case, theentanglement entropy of Hawking radiation obeys the Page curve, i.e. theentanglement entropy of Hawking radiation increases with time and reachessaturation about twice Bekenstein-Hawking entropy at the Page time. For theextremal case, the entanglement entropy of Hawking radiation becomesill-defined in the absence of the island due to the appearance of thesingularity at the origin of the radial coordinate, while when the islandexists, the entanglement entropy is found to be equal to the Bekenstein-Hawkingentropy. In addition, for the case where the boundary of the radiation regionis close to the horizon, there are some obvious constraints required by theexistence of island solution for both non-extremal and extremal cases, whichcan be utilized to put constraints on the size of the black hole. These resultsreveal new features of the semi-classical large $d$ black holes from the islandperspective.

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