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 Islands and Page curves in charged dilaton black holes

2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Ming-Hui Yu ◽  
Xian-Hui Ge
Keyword(s):  
Black Holes ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Von Neumann Entropy ◽  
Extremal Case ◽  
Von Neumann ◽  
Asymptotically Flat ◽  
Flat Spacetime ◽  
The Impact ◽  
Dilaton Black Holes

AbstractWe study the Page curve for eternal Garfinkle–Horowitz–Strominger dilaton black holes in four dimensional asymptotically flat spacetime by using the island paradigm. The results demonstrate that without the island, the entanglement entropy of Hawking radiation is proportional to time and becomes divergent at late times. While taking account of the existence of the island outside the event horizon, the entanglement entropy stops growing at late times and eventually reaches a saturation value. This value is twice of the Bekenstein–Hawking entropy and consistent with the finiteness of the von Neumann entropy of eternal black holes. Moreover, we discuss the impact of the stringy coefficient n and charge Q on the Page time and the scrambling time respectively. For the non-extremal case, the influence of the coefficient n on them is small compared to the influence of the charge Q. However, for the extremal case, the Page time and the scrambling time become divergent or near vanishing. This implies the island paradigm needs further investigation.

scholarly journals Entanglement entropy of asymptotically flat non-extremal and extremal black holes with an island

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Wontae Kim ◽  
Mungon Nam
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Entanglement Entropy ◽  
Heat Bath ◽  
Extremal Black Hole ◽  
Curvature Singularity ◽  
Island Rule ◽  
Generalized Entropy ◽  
Asymptotically Flat ◽  
Extremal Black Holes

AbstractThe island rule for the entanglement entropy is applied to an eternal Reissner–Nordström black hole. The key ingredient is that the black hole is assumed to be in thermal equilibrium with a heat bath of an arbitrary temperature and so the generalized entropy is treated as being off-shell. Taking the on-shell condition to the off-shell generalized entropy, we find the generalized entropy and then obtain the entanglement entropy following the island rule. For the non-extremal black hole, the entanglement entropy grows linearly in time and can be saturated after the Page time as expected. The entanglement entropy also has a well-defined Schwarzschild limit. In the extremal black hole, the island prescription provides a logarithmically growing entanglement entropy in time and a constant entanglement entropy after the Page time. In the extremal black hole, the boundary of the island hits the curvature singularity where the semi-classical approximations appear invalid. To avoid encountering the curvature singularity, we apply this procedure to the Hayward black hole regular at the origin. Consequently, the presence of the island in extremal black holes can provide a finite entanglement entropy, which might imply non-trivial vacuum configurations of extremal black holes.

scholarly journals Island in the presence of higher derivative terms

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Mohsen Alishahiha ◽  
Amin Faraji Astaneh ◽  
Ali Naseh
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Hawking Radiation ◽  
Entanglement Entropy ◽  
Asymptotically Flat ◽  
Higher Derivative ◽  
Ads Black Holes ◽  
Dimensional Models ◽  
Black Hole Solutions

Abstract Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.

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 Gravitational lensing effect on the Hawking radiation of dyonic black holes

2014 ◽  
Vol 11 (08) ◽  
pp. 1450074 ◽  
Author(s):  
Izzet Sakalli ◽  
Ali Ovgun ◽  
Seyedeh Fatemeh Mirekhtiary
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Refractive Index ◽  
Coordinate System ◽  
Gravitational Lensing ◽  
Hawking Radiation ◽  
Hawking Temperature ◽  
Tunneling Rate ◽  
Asymptotically Flat ◽  
Lensing Effect

In this paper, we analyze the Hawking radiation (HR) of a non-asymptotically flat (NAF) dyonic black hole (dBH) in four-dimensional (4D) Einstein–Maxwell–Dilaton (EMD) gravity by using one of the semiclassical approaches which is the so-called Hamilton–Jacobi (HJ) method. We particularly motivate on the isotropic coordinate system (ICS) of the dBH in order to highlight the ambiguity to be appeared in the derivation of the Hawking temperature (TH) via the HJ method. Besides, it will be shown that the ICS allows us to write the metric of the dBH in form of the Fermat metric, which renders possible of identification of the refractive index (n) of the dBH. It is unraveled that the value of n and therefore the gravitational lensing effect is decisive on the tunneling rate of the HR. We also uncloak how one can resolve the discrepancy about the TH of the dBH in spite of that lensing effect.

scholarly journals BLACK HOLE GEOMETRIES IN NONCOMMUTATIVE STRING THEORY

2006 ◽  
Vol 21 (30) ◽  
pp. 6087-6114 ◽  
Author(s):  
SUPRIYA KAR ◽  
SUMIT MAJUMDAR
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Gauge Theory ◽  
String Theory ◽  
Hawking Radiation ◽  
Effective Theory ◽  
Effective Gravity ◽  
Noncommutative Gauge Theory ◽  
Em Field ◽  
Hole Geometry

We obtain a generalized Schwarzschild (GS) and a generalized Reissner–Nordstrom (GRN) black hole geometries in 3+1 dimensions, in a noncommutative string theory. In particular, we consider an effective theory of gravity on a curved D3-brane in presence of an electromagnetic (EM) field. Two different length scales, inherent in its noncommutative counterpart, are exploited to obtain a theory of effective gravity coupled to an U(1) noncommutative gauge theory to all orders in Θ. It is shown that the GRN-black hole geometry, in the Planckian regime, reduces to the GS-black hole. However in the classical regime it may be seen to govern both the Reissner–Nordstrom and the Schwarzschild geometries. The emerging notion of 2D black holes evident in the framework are analyzed. It is argued that the D-string in the theory may be described by the near horizon 2D black hole geometry, in the gravity decoupling limit. Finally, our analysis explains the nature of the effective force derived from the nonlinear EM-field and accounts for the Hawking radiation phenomenon in the formalism.

scholarly journals Uptunneling to de Sitter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Mehrdad Mirbabayi
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
False Vacuum ◽  
De Sitter ◽  
Dimensional Theory ◽  
Hole Geometry ◽  
Horizon Geometry ◽  
Two Sides ◽  
Extremal Black Holes

Abstract We propose a Euclidean preparation of an asymptotically AdS2 spacetime that contains an inflating dS2 bubble. The setup can be embedded in a four dimensional theory with a Minkowski vacuum and a false vacuum. AdS2 approximates the near horizon geometry of a two-sided near-extremal Reissner-Nordström black hole, and the two sides can connect to the same Minkowski asymptotics to form a topologically nontrivial worm- hole geometry. Likewise, in the false vacuum the near-horizon geometry of near-extremal black holes is approximately dS2 times 2-sphere. We interpret the Euclidean solution as describing the decay of an excitation inside the wormhole to a false vacuum bubble. The result is an inflating region inside a non-traversable asymptotically Minkowski wormhole.

scholarly journals Replica wormholes for an evaporating 2D black hole

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Kanato Goto ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Path Integral ◽  
Island Rule ◽  
Technical Challenge ◽  
Local Boundary ◽  
Lorentzian Signature ◽  
Special Cases ◽  
Non Local ◽  
Non Local Equations

Abstract Quantum extremal islands reproduce the unitary Page curve of an evaporating black hole. This has been derived by including replica wormholes in the gravitational path integral, but for the transient, evaporating black holes most relevant to Hawking’s paradox, these wormholes have not been analyzed in any detail. In this paper we study replica wormholes for black holes formed by gravitational collapse in Jackiw-Teitelboim gravity, and confirm that they lead to the island rule for the entropy. The main technical challenge is that replica wormholes rely on a Euclidean path integral, while the quantum extremal islands of an evaporating black hole exist only in Lorentzian signature. Furthermore, the Euclidean equations for the Schwarzian mode are non-local, so it is unclear how to connect to the local, Lorentzian dynamics of an evaporating black hole. We address these issues with Schwinger-Keldysh techniques and show how the non-local equations reduce to the local ‘boundary particle’ description in special cases.

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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