Page Curves and Islands in Charged Dilaton Black Holes
arXiv:2107.03031
Abstract
We study the Page curve in the four dimensional asymptotically flat eternal Garfinkle-Horowitz-Strominger dilaton black holes by applying the "quantum extremal surface" prescription. The results demonstrate that without island, the entanglement entropy of Hawking radiation is proportional to time and divergent at late times. While taking account of the emergence of the island extending slightly outside the event horizon, the entanglement entropy of Hawking radiation stops growing and eventually reaches a saturation value, which is twice of the Bekenstein-Hawking entropy and consistent with the finiteness of the von Neumann entropy of eternal black holes. Moreover, we discuss the impact of the parameter and charge on the Page time. The influence of on it can neglected when the ratio of the charge to the black hole mass is sufficiently small, but the charge has a significant impact on Page time. Importantly, at the extremal case, the Page time becomes divergent or vanishing, in which the semiclassical theory needs further investigation.
arXiv commentminor corrections, references added
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