Entanglement island and Page curve for one-sided charged black hole

TL;DR

This paper investigates how charge affects the entanglement entropy and Page curve of Hawking radiation in one-sided black holes, revealing geometric influences on entropy behavior for both extremal and non-extremal cases.

Contribution

It extends island formula methods to dynamic charged black holes, analyzing the impact of charge and geometry on entropy and the Page curve.

Findings

Island formation bounds entropy at late times in non-extremal black holes.

Entanglement entropy follows the Page curve when island exists.

In extremal black holes, entropy approximates Bekenstein-Hawking entropy when island is present.

Abstract

In this paper, we extend the method of calculating the entanglement entropy of Hawking radiation of black holes using the "in" vacuum state, which describes one-sided asymptotically flat neutral black hole formed by gravitational collapse, to dynamic charged black holes. We explore the influence of charge on the position of the boundary of island $\partial I$ and the Page time. Due to their distinct geometric structures, we discuss non-extremal and extremal charged black holes separately. In non-extremal cases, the emergence of island saves the bound of entropy at late times, and the entanglement entropy of Hawking radiation satisfies the Page curve. Moreover, we also find that the position of the boundary of island $\partial I$ depends on the position of the cutoff surface (observers), differing from the behavior in eternal charged black holes. In extremal black holes, when the island exists, the entanglement entropy is approximately equal to the Bekenstein-Hawking entropy, while the entanglement entropy becomes ill-defined when island is absent. Our analysis underscores how different geometric configurations significantly influence the behavior of entropy.