Islands and Page curves of Reissner-Nordstrom black holes

We apply the recently proposed quantum extremal surface construction to calculate the Page curve of the eternal Reissner-Nordstrom black holes in four dimensions ignoring the backreaction and the greybody factor. Without the island, the entropy of Hawking radiation grows linearly with time, which results in the information paradox for the eternal black holes. By extremizing the generalized entropy that allows the contributions from the island, we find that the island extends to the outside the horizon of the Reissner-Nordstrom black hole. When taking the effect of the islands into account, it is shown that the entanglement entropy of Hawking radiation at late times for a given region far from the black hole horizon reproduces the Bekenstein-Hawking entropy of the Reissner-Nordstrom black hole with an additional term representing the effect of the matter fields. The result is consistent with the finiteness of the entanglement entropy for the radiation from an eternal black hole. This facilitates to address the black hole information paradox issue in the current case under the above-mentioned approximations.

Automated summary

By applying the quantum extremal surface construction, we calculated the Page curve for eternal Reissner-Nordstrom black holes, ignoring backreaction and the greybody factor. The inclusion of islands outside the horizon of the black hole results in the entanglement entropy of Hawking radiation reproducing the Bekenstein-Hawking entropy with an additional term representing the effect of matter fields, helping to address the black hole information paradox.