Kavli Affiliate: Cheng Peng
| First 5 Authors: Wen-Hao Jiang, Cheng Peng, Yun-Song Piao, ,
| Summary:
Double holography has been proved to be a powerful method in comprehending
the spacetime entanglement. In this paper we investigate the doubly holographic
construction in ${mathrm{dS_{2}} }$ spacetime. We find that in this model
there exists a new extremal surface besides the Hartman-Maldacena surface and
the island surface, which could lead to a more complex phase structure. We then
propose a generalized mutual entropy to interpret the phase transition.
However, this extremal surface has a subtle property that the length of a part
of the geodesic is negative when this saddle is dominant. This is because the
negative part of the geodesic is within the horizon of the bulk geometry. We
move to the ${mathrm{AdS_{2}} }$ spacetime and find this subtlety still
exists. We purpose a simple solution to this issue.
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