Islands and Page curves of Reissner-Nordstr\"om black holes

Understand

We apply the recently proposed quantum extremal surface construction to calculate the Page curve of the eternal Reissner-Nordstr\"om 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-Nordstr\"om 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-Nordstr\"om black hole with an additional term representing the effect of the matter fields.