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Mutual information, islands in black holes and the Page curve
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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.
Forward citations
Cited by 2 Pith papers
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New insights on mutual information in the island approach to the Page curve
At scrambling time I(B+:B−)=0 forces I(I:R)→∞, interpreted as conservation of geometric correlation, while I(I:R+:R−) is shown always negative via Cauchy-slice identities.
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Phase transition in a doubly holographic model of closed $\mathbf{dS_{2} }$ spacetime
A doubly holographic dS2 model has a third extremal surface whose dominance creates a phase transition, but the surface's geodesic length can be negative.
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