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arXiv:1912.00909 · Journal of High Energy Physics

A quantum circuit interpretation of evaporating black hole geometry

Ying Zhao

Published Jul 1, 2020• 15 citations
arXivHTMLPDF

Abstract

Abstract We give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double. If Alice perturbs thermofield double and waits for scrambling time, she will have a one-sided black hole with interior of her own. We argue that by similar mechanism the radiation gets access to the interior (island forms) after Page time. The growth of the island happens as a result of the constant transitions from two-sided to one-sided black holes.

DOI
10.1007/jhep07(2020)139

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Abstract We give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double. If Alice perturbs thermofield double and waits for scrambling time, she will have a one-sided black hole with interior of her own. We argue that by similar mechanism the radiation gets access to the interior (island forms) after Page time. The growth of the island happens as a result of the constant transitions from two-sided to one-sided black holes.
We give a quantum circuit interpretation of evaporating black hole geometry. We make an analogy between the appearance of island for evaporating black hole and the transition from two-sided to one-sided black hole in the familiar example of perturbed thermofield double. If Alice perturbs thermofield double and waits for scrambling time, she will have a one-sided black hole with interior of her own. We argue that by similar mechanism the radiation gets access to the interior (island forms) after Page time. The growth of the island happens as a result of the constant transitions from two-sided to one-sided black holes.
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.
The Island Formula for Quantum Extremal Surfaces of large AdS black holes, which are made to evaporate by coupling the CFT of the AdS/CFT correspondence to an external system, demonstrates that the space time picture can reproduce the quantum mechanically required Page curve of the CFT/bath system if a region in the interior of the black hole has become entangled with the external radiation by the Page time. In an effective quantum field theory (EFT) description in ``nice slice" coordinates, this appears to imply paradoxical entanglement between degrees of freedom that have been causally disconnected since long before the Page time. We will give two arguments that all of the quantum information in the island is in fact concentrated in a tiny space-like portion of the island very close to the black hole horizon at the Page time. The first applies the covariant entropy bound\cite{fsb} (CEB) to the causal diamonds of geodesics originating on the space-like region that becomes the island, but on a time slice just before the Page time. All points on the island except those in a stretched horizon region very close to the horizon have entropy bounds that are tiny fractions of the black hole entropy. The second argument uses standard quantum statistical mechanics combined with the tensor network renormalization group regularization of CFT to argue that the wave function of a typical pure state in the microcanonical evaporating black hole always has most of its probability concentrated in a small range of wavelengths corresponding to a small range of radii in the dual tensor network/AdS slice.
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.
A bstract In recent years, there is a huge progress in understanding the black hole information problem, and the key is that the black hole entropy of radiation should be calculated by the island formula, which describes the Page curve to ensure the unitarity of black hole evaporation. In the paper, we find that the black hole evaporation interpreted by the island formula can be understood in the language of approximate quantum error correction. Furthermore, the Page transition, as a special property of the Page curve, should be understood as the property of approximate quantum error correction itself, i.e. a general class of quantum systems under certain conditions from approximate quantum error correction can also exhibit phenomenon similar to the Page transition.
Analyses suggest that the quantum RT construction can be effectively extended beyond the asymptotically AdS spacetime for the calculation of the entanglement entropy. We study the entanglement entropy of a one-parameter family of exactly solvable gravities in the 2-dimensional asymptotically-flat space, and investigate the evaporating and the bath-removed black hole solutions including both the RST and the BPP black holes as two special cases. We generalize the results on the Page curves of evaporating (dynamical) black holes to this family of gravities and compute the corresponding entanglement entropy explicitly. The Page curves and the configuration of islands directly follow from the calculation. In the case of evaporating black holes formed by collapsing matter shells, the Page time is around a third of the black hole evaporating time and the island lies inside the horizon. In the bath-removed black hole case, the position of the islands is discontinuous across two different spacetime geometries and two transition points are witnessed in this model. We analyze the island configurations and the Page curves in the large-N limit in both cases and restore the unitary Page curves.