Abstract 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 radiation. In the doubly holographic setup, we compute the entanglement entropy and mutual information among subsystems and obtain the dynamic phase structure of the entanglement. The formation of entanglement between these two black holes is delayed by the space which the radiation must travel through. If the black holes exchange sufficient Hawking modes, the final state is characterized by a connected entanglement wedge; otherwise, the final entanglement wedge contains two separate islands. In the former case, the entanglement wedge of the black holes forms at the time scale proportional to the size of the flat space between them. While in both cases, the unitarity of the evolution is preserved. When the sizes of the 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 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 SYK clusters is found in cases with a long Majorana chain. In particular, when the 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 particles exchanging between neighboring clusters and reproduce the features of entanglement observed in the previous models.
Abstract 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 radiation. In the doubly holographic setup, we compute the entanglement entropy and mutual information among subsystems and obtain the dynamic phase structure of the entanglement. The formation of entanglement between these two black holes is delayed by the space which the radiation must travel through. If the black holes exchange sufficient Hawking modes, the final state is characterized by a connected entanglement wedge; otherwise, the final entanglement wedge contains two separate islands. In the former case, the entanglement wedge of the black holes forms at the time scale proportional to the size of the flat space between them. While in both cases, the unitarity of the evolution is preserved. When the sizes of the 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 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 SYK clusters is found in cases with a long Majorana chain. In particular, when the 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 particles exchanging between neighboring clusters and reproduce the features of entanglement observed in the previous models.
Abstract In this note, following [1–3], we introduce and study various holographic systems which can describe evaporating black holes. The systems we consider are boundary conformal field theories for which the number of local degrees of freedom on the boundary (cbdy) is large compared to the number of local degrees of freedom in the bulk CFT (cbulk). We consider states where the boundary degrees of freedom on their own would describe an equilibrium black hole, but the coupling to the bulk CFT degrees of freedom allows this black hole to evaporate. The Page time for the black hole is controlled by the ratio cbdy/cbulk. Using both holographic calculations and direct CFT calculations, we study the evolution of the entanglement entropy for the subset of the radiation system (i.e. the bulk CFT) at a distance d > a from the boundary. We find that the entanglement entropy for this subsystem increases until time a + tPage and then undergoes a phase transition after which the entanglement wedge of the radiation system includes the black hole interior. Remarkably, this occurs even if the radiation system is initially at the same temperature as the black hole so that the two are in thermal equilibrium. In this case, even though the black hole does not lose energy, it “radiates” information through interaction with the radiation system until the radiation system contains enough information to reconstruct the black hole interior.
A bstract We investigate the evolution of entanglement within an open, strongly coupled system interacting with a heat bath as its environment, in the frameworks of both the doubly holographic model and the Sachdev-Ye-Kitaev (SYK) model. Generally, the entanglement within the system initially increases as due to internal interactions; however, it eventually dissipates into the environment. In the doubly holographic setup, we consider an end-of-the-world brane in the bulk to represent an eternal black hole coupled with its radiation and the evolution of the global thermofield double (TFD) state. For small black holes, the reflected entropy between the bipartition exhibits a ramp-plateau-slump behavior, where the plateau arises due to the phase transition of the entanglement wedge cross-section before the Page time. Similarly, the mutual information between the bipartition displays a ramp-slop-stabilizing behavior. In quantum mechanics, we consider a double copy of the SYK-plus-bath system in a global TFD state, resembling an eternal black hole interacting with an environment. The Rényi mutual information within the double-copied SYK clusters exhibits a ramp-plateau-slope-stabilizing behavior. The dynamic behaviors of the entanglement quantities observed in these two models are attributable to the competition between the internal interaction of the system and the external interaction with the baths. Our study provides a fine-grained picture of the entanglement dynamics inside black holes before their Page time.
Abstract We study a thermofield double type entangled state on two disjoint universes A and B, where one of the universes is asymptotically flat containing a black hole. As we increase the entanglement temperature, this black hole receives back-reaction from the stress–energy tensor of the state. This results in lengthening of the wormhole region in the black hole interior, and decreasing of its horizon area, both of which are key features of an evaporating black hole. We then compute the entanglement entropy in universe A through the island formula, and argue that it naturally follows the Page curve of an evaporating black hole in flat space. We also study the effects of local operations in the gravitating universe with the black hole. We find that they accelerate the evaporation of the black hole, thereby disrupting the entanglement between the two universes. Furthermore, we observe that, depending on whether the operation can be regarded as a local operation and classical communication or not, the behavior of the entanglement entropy changes. In particular, when the operation is made neither in the entanglement wedge of the radiation system nor that of the black hole, the transition between the island phase and the no-island phase can happen multiple times.
Abstract We construct a holographic map that takes the semi-classical state of an evaporating black hole and its Hawking radiation to a microscopic model that reflects the scrambling dynamics of the black hole. The microscopic model is given by a nested sequence of random unitaries, each one implementing a scrambling time step of the black hole evolution. Differently from other models, energy conservation and the thermal nature of the Hawking radiation are taken into account. We show that the QES formula follows for the entropy of multiple subsets of the radiation and black hole. We further show that a version of entanglement wedge reconstruction can be proved by computing suitable trace norms and quantum fidelities involving the action of a unitary on a subset of Hawking partners. If the Hawking partner is in an island, its unitary can be reconstructed by a unitary on the radiation. We also adopt a similar setup and analyse reconstruction of unitaries acting on an infalling system.
Hawking's black hole evaporation process suggests that we may need to choose between quantum unitarity and other basic physical principles such as no-signaling, entanglement monogamy, and the equivalence principle. We here show that the Hawking's quantum model for the black hole evaporation is consistent with the above fundamental principles. Our analysis does not involve exotic new physics, but rather uses standard quantum theory, general relativity, and the Einstein–Hilbert action including matter. We explicitly show that the whole state consisting of matter and radiation (in a joint superposition of different energy states) is pure at any stage of the evaporation process, including the particular case of 0 mass. Moreover, after full evaporation the state for radiation at infinity is pure and in one-to-one correspondence with the initial state forming the black hole. Thus there is no information loss upon full evaporation according to the quantum information theory. The original entanglement of the black hole matter (if any) gets transferred to the outgoing particles via a process similar to entanglement swapping, without violation of causality (as proved explicitly). On the other hand, if the initial state is a tensor product state, the entanglement of Hawking particles, present in the intermediate phase, is broken when the black hole evaporates completely. Therefore, the final state (entangled or tensor product depending on the nature of initial state) after the full black hole evaporation is pure without loss of information.
We study thermodynamic properties and the entanglement island of a black hole in asymptotically safe quantum gravity, analyzing key thermodynamic quantities such as the Hawking temperature, heat capacity, and entropy, as well as the mass-horizon radius relation. Unlike Schwarzschild black holes, the temperature decreases with mass near the evaporation endpoint, signaling a phase transition and possible stable remnant. The entanglement entropy of Hawking radiation is obtained both with and without island contributions. Without islands, the radiation entropy grows linearly indefinitely, leading to the information paradox. By including island contributions and extremizing the generalized entropy functional, we resolve this paradox. At late times, the radiation entropy saturates at the Bekenstein-Hawking entropy, confirming unitary evolution. From this, we derive the Page time and scrambling time by equating early- and late-time entanglement entropies. The result of this study establishes the finiteness of the radiation entropy and consistency with quantum mechanics.