  We construct three models to describe the scenario where two eternal black
holes are separated by a flat space, and can eventually be entangled by
exchanging radiations. In the doubly holographic setup, we compute the
entanglement entropy and the mutual information among the subsystems and obtain
the dynamic phase structure of the entanglement. The formation of entanglement
between the two black holes is delayed by the space where the radiations must
travel through. Finally, if the two black holes exchange sufficient Hawking
modes, the final state is characterized by a connected entanglement wedge;
otherwise, the final entanglement wedge contains two separated islands. In the
former case, the entanglement wedge of the two black holes forms at the time
scale of the size of the flat space between them. While in both cases,
unitarity of the evolution is preserved. 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. In the field theory side, we consider two
Sachdev-Ye-Kitaev (SYK) clusters coupled to a Majorana chain, which resemble
two black holes connected by a radiation region. We numerically compute the
same entanglement measures, and obtain similar phase structures as the bulk
results. In general, a time delay of the entanglement between the two SYK
clusters is found in cases with a long Majorana chain. In particular, when the
two SYK clusters are different in size, similar entanglement loss between the
smaller SYK cluster and the Majorana chain is observed. Finally, we investigate
a chain model composed of EPR clusters with particle exchanges between
neighboring clusters, and reproduce the features of entanglement observed in
the other models.
