scholarly journals Defect extremal surface for reflected entropy

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Tianyi Li ◽  
Ma-Ke Yuan ◽  
Yang Zhou
Keyword(s):  
Black Hole ◽  
Mixed State ◽  
Entanglement Entropy ◽  
Quantum Defect ◽  
Entropy Measure ◽  
Extremal Surface ◽  
Decomposition Procedure ◽  
Hole Model ◽  
Quantum Defect Theory

Abstract Defect extremal surface is defined by extremizing the Ryu-Takayanagi formula corrected by the quantum defect theory. This is interesting when the AdS bulk contains a defect brane (or string). We introduce a defect extremal surface formula for reflected entropy, which is a mixed state generalization of entanglement entropy measure. Based on a decomposition procedure of an AdS bulk with a brane, we demonstrate the equivalence between defect extremal surface formula and island formula for reflected entropy in AdS3/BCFT2. We also compute the evolution of reflected entropy in evaporating black hole model and find that defect extremal surface formula agrees with island formula.

scholarly journals Islands and Page curves of Reissner-Nordström black holes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Xuanhua Wang ◽  
Ran Li ◽  
Jin Wang
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Additional Term ◽  
Current Case ◽  
Information Paradox ◽  
Extremal Surface ◽  
Four Dimensions ◽  
Black Hole Information

Abstract We apply the recently proposed quantum extremal surface construction to calculate the Page curve of the eternal Reissner-Nordström black holes in four dimensions ignoring the backreaction and the greybody factor. Without the island, the entropy of Hawking radiation grows linearly with time, which results in the information paradox for the eternal black holes. By extremizing the generalized entropy that allows the contributions from the island, we find that the island extends to the outside the horizon of the Reissner-Nordström black hole. When taking the effect of the islands into account, it is shown that the entanglement entropy of Hawking radiation at late times for a given region far from the black hole horizon reproduces the Bekenstein-Hawking entropy of the Reissner-Nordström black hole with an additional term representing the effect of the matter fields. The result is consistent with the finiteness of the entanglement entropy for the radiation from an eternal black hole. This facilitates to address the black hole information paradox issue in the current case under the above-mentioned approximations.

scholarly journals Finding pythons in unexpected places

2021 ◽  
Author(s):  
Netta Engelhardt ◽  
Geoff Penington ◽  
Arvin Shahbazi-Moghaddam
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Mixed State ◽  
Crucial Role ◽  
State Dependence ◽  
Extremal Surface ◽  
Black Hole Interior ◽  
Exponential Complexity

Abstract We argue that novel (highly nonclassical) quantum extremal surfaces play a crucial role in reconstructing the black hole interior even for isolated, single-sided, non-evaporating black holes (i.e. with no auxiliary reservoir). Specifically, any code subspace where interior outgoing modes can be excited will have a quantum extremal surface in its maximally mixed state. We argue that as a result, reconstruction of interior outgoing modes is always exponentially complex. Our construction provides evidence in favor of a strong Python’s lunch proposal: that nonminimal quantum extremal surfaces are the exclusive source of exponential complexity in the holographic dictionary. We also comment on the relevance of these quantum extremal surfaces to the geometrization of state dependence in the typicality arguments for firewalls.

scholarly journals Evaporating black holes coupled to a thermal bath

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Zhe Chen ◽  
Zachary Fisher ◽  
Juan Hernandez ◽  
Robert C. Myers ◽  
Shan-Ming Ruan
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Initial Temperature ◽  
Entanglement Entropy ◽  
Bath Temperature ◽  
Thermal Bath ◽  
Holographic Model ◽  
Extremal Surface ◽  
Holographic Entanglement Entropy ◽  
Black Hole Interior

Abstract We study the doubly holographic model of [1] in the situation where a black hole in two-dimensional JT gravity theory is coupled to an auxiliary bath system at arbitrary finite temperature. Depending on the initial temperature of the black hole relative to the bath temperature, the black hole can lose mass by emitting Hawking radiation, stay in equilibrium with the bath or gain mass by absorbing thermal radiation from the bath. In all of these scenarios, a unitary Page curve is obtained by applying the usual prescription for holographic entanglement entropy and identifying the quantum extremal surface for the generalized entropy, using both analytical and numeric calculations. As the application of the entanglement wedge reconstruction, we further investigate the reconstruction of the black hole interior from a subsystem containing the Hawking radiation. We examine the roles of the Hawking radiation and also the purification of the thermal bath in this reconstruction.

scholarly journals Island in charged black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yi Ling ◽  
Yuxuan Liu ◽  
Zhuo-Yu Xian
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Entanglement Entropy ◽  
Information Paradox ◽  
Extremal Surface ◽  
Charged Black Holes ◽  
Dimensional Spacetime ◽  
Black Hole Information ◽  
Extremal Black Holes

Abstract We study the information paradox for the eternal black hole with charges on a doubly-holographic model in general dimensions, where the charged black hole on a Planck brane is coupled to the baths on the conformal boundaries. In the case of weak tension, the brane can be treated as a probe such that its backreaction to the bulk is negligible. We analytically calculate the entanglement entropy of the radiation and obtain the Page curve with the presence of an island on the brane. For the near-extremal black holes, the growth rate is linear in the temperature. Taking both Dvali-Gabadadze-Porrati term and nonzero tension into account, we obtain the numerical solution with backreaction in four-dimensional spacetime and find the quantum extremal surface at t = 0. To guarantee that a Page curve can be obtained in general cases, we propose two strategies to impose enough degrees of freedom on the brane such that the black hole information paradox can be properly described by the doubly-holographic setup.

scholarly journals Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons

2021 ◽  
Author(s):  
Abhishek Mathur ◽  
Sumati Surya ◽  
Nomaan X
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Density Matrix ◽  
Mixed State ◽  
Entanglement Entropy ◽  
Spatial Density ◽  
De Sitter Spacetime ◽  
Cosmological Horizon ◽  
De Sitter ◽  
Sitter Spacetime

Abstract We calculate Sorkin's manifestly covariant, spacetime entanglement entropy (SSEE) for a massive and massless minimally coupled free Gaussian scalar field for the de Sitter horizon and Schwarzschild de Sitter horizons, respectively, in d > 2. In de Sitter spacetime we restrict the Bunch-Davies vacuum in the conformal patch to the static patch to obtain a mixed state. The finiteness of the spatial L2 norm in the static patch implies that the SSEE is well defined for each mode. We find that for this mixed state it is independent of the effective mass of the scalar field and matches results obtained by Higuchi and Yamamoto, where, a spatial density matrix was used to calculate the horizon entanglement entropy. Using a cut-off in the angular modes we show that the SSEE is proportional to the area of the de Sitter cosmological horizon. Our analysis can be carried over to the black hole and cosmological horizon in Schwarzschild de Sitter spacetime, which also has finite spatial L2 norm in the static regions. Although the explicit form of the modes is not known in this case, we use appropriate boundary conditions for a massless minimally coupled scalar field, to find the mode-wise SSEE for both the black hole and de Sitter cosmological horizons. As in the de Sitter calculation we see that SSEE is proportional to the horizon area in each case after taking a cut-off in the angular modes.

scholarly journals Islands and stretched horizon

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Yoshinori Matsuo
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Total System ◽  
Island Rule ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
Ads Spacetime ◽  
Hole Geometry

Abstract Recently it was proposed that the entanglement entropy of the Hawking radiation contains the information of a region including the interior of the event horizon, which is called “island.” In studies of the entanglement entropy of the Hawking radiation, the total system in the black hole geometry is separated into the Hawking radiation and black hole. In this paper, we study the entanglement entropy of the black hole in the asymptotically flat Schwarzschild spacetime. Consistency with the island rule for the Hawking radiation implies that the information of the black hole is located in a different region than the island. We found an instability of the island in the calculation of the entanglement entropy of the region outside a surface near the horizon. This implies that the region contains all the information of the total system and the information of the black hole is localized on the surface. Thus the surface would be interpreted as the stretched horizon. This structure also resembles black holes in the AdS spacetime with an auxiliary flat spacetime, where the information of the black hole is localized at the interface between the AdS spacetime and the flat spacetime.

scholarly journals First law of entanglement entropy in AdS black hole backgrounds

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Akihiro Ishibashi ◽  
Kengo Maeda
Keyword(s):  
Black Hole ◽  
Entanglement Entropy

scholarly journals Islands in linear dilaton black holes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Georgios K. Karananas ◽  
Alex Kehagias ◽  
John Taskas
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Two Dimensional ◽  
Extremal Case ◽  
Von Neumann ◽  
Dimensional Black Hole ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We derive a novel four-dimensional black hole with planar horizon that asymptotes to the linear dilaton background. The usual growth of its entanglement entropy before Page’s time is established. After that, emergent islands modify to a large extent the entropy, which becomes finite and is saturated by its Bekenstein-Hawking value in accordance with the finiteness of the von Neumann entropy of eternal black holes. We demonstrate that viewed from the string frame, our solution is the two-dimensional Witten black hole with two additional free bosons. We generalize our findings by considering a general class of linear dilaton black hole solutions at a generic point along the σ-model renormalization group (RG) equations. For those, we observe that the entanglement entropy is “running” i.e. it is changing along the RG flow with respect to the two-dimensional worldsheet length scale. At any fixed moment before Page’s time the aforementioned entropy increases towards the infrared (IR) domain, whereas the presence of islands leads the running entropy to decrease towards the IR at later times. Finally, we present a four-dimensional charged black hole that asymptotes to the linear dilaton background as well. We compute the associated entanglement entropy for the extremal case and we find that an island is needed in order for it to follow the Page curve.

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