Kavli Affiliate: Cheng Peng
| First 5 Authors: Yuxuan Liu, Zhuo-Yu Xian, Cheng Peng, Yi Ling,
| Summary:
We construct several models to describe the scenario where two eternal black
holes are entangled by exchanging radiations. The increasing entanglement
between two black holes is reflected in the emergence of a wormhole phase,
which could be considered as an incarnation of $ER=EPR$ conjecture. In double
holography, we compute the entanglement entropy and mutual information among of
various partitions and obtain the phase structure of the entanglement. We find
that two black holes can be entangled as long as they are not far apart; in
general, the formation of a wormhole needs to overcome the distance between two
black holes, and unitarity is preserved by either the formation of a wormhole
or the emergence of islands. When the sizes of two black holes are not equal,
we observe a loss of entanglement between the smaller black hole and the
radiation at late times. On the field theory side, we consider a coupled SYK
model at finite $N$, where two SYK models are applied as two black holes and a
Majorana chain connecting them resembles the radiation region. We explicitly
compute the entanglement among subsystems, and obtain the similar phase
structure. In general, a time delay of entanglement between two SYK sites is
found in cases with longer Majorana chains. In particular, when two SYK sites
are different in size, similar entanglement loss between the smaller SYK
cluster and the radiation region are observed. To have a more intuitive
understanding on the evolution of the entanglement, we further investigate a
chain model composed of EPR clusters where exchanging particles are only
allowed between neighbouring clusters. In this model, the outermost clusters
serve as two black holes, and all inner clusters serve as the radiation.
Despite the drastic simplification, the main features observed in previous
models persist.
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