Mutual information, islands in black holes and the Page curve

TL;DR

This paper investigates how mutual information influences the Page curve in black hole physics, revealing that the vanishing of mutual information signals the onset of the Page time and leads to a consistent entropy evolution.

Contribution

It demonstrates that the vanishing mutual information between subsystems corresponds to the Page time and provides corrected entropy expressions with logarithmic and inverse power law terms.

Findings

Vanishing mutual information indicates the Page time.

Derived corrected entropy expressions with specific logarithmic and inverse power law forms.

Established a connection between entanglement wedge phases and the Page curve.

Abstract

The role played by the mutual information of subsystems on the Page curve is explored in this paper. With the total system consisting of the black hole and radiation, together with the inclusion of island, we observe that the vanishing of mutual information between $B_+$ and $B_-$ which in turn means the disconnected phase of the entanglement wedge corresponding to $B_+\cup B_-$, yields a time scale of the order of scrambling time. This results in a time independent expression for the fine grained entropy of Hawking radiation consistent with the correct Page curve. We also find corrections to this entropy and Page time which are logarithmic and inverse power law in form.