Island of Reissner-Nordström anti-de Sitter black holes in the large d limit
arxiv(2023)
Abstract
We study the information paradox of Reissner-Nordström 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.
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