Black holes Entangled by Radiation

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.