scholarly journals Dirichlet baths and the not-so-fine-grained Page curve

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kausik Ghosh ◽  
Chethan Krishnan
Keyword(s):  
Black Hole ◽  
Entanglement Entropy ◽  
Flat Space ◽  
Information Paradox ◽  
Braneworld Cosmology ◽  
Fine Grained ◽  
Link Type ◽  
Related Approach ◽  
Set Up ◽  
Weak Gravity

Abstract We present a doubly holographic prescription for computing entanglement entropy on a gravitating brane. It involves a Ryu-Takayanagi surface with a Dirichlet anchoring condition. In braneworld cosmology, a related approach was used previously in arXiv:2007.06551. There, the prescription naturally computed a co-moving entanglement entropy, and was argued to resolve the information paradox for a black hole living in the cosmology. In this paper, we show that the Dirichlet prescription leads to reasonable results, when applied to a recently studied wedge holography set up with a gravitating bath. The nature of the information paradox and its resolution in our Dirichlet problem have a natural understanding in terms of the strength of gravity on the two branes and at the anchoring location. By sliding the anchor to the defect, we demonstrate that the limit where gravity decouples from the anchor is continuous — in other words, as far as island physics is considered, weak gravity on the anchor is identical to no gravity. The weak and (moderately) strong gravity regions on the brane are separated by a “Dirichlet wall”. We find an intricate interplay between various extremal surfaces, with an island coming to the rescue whenever there is an information paradox. This is despite the presence of massless gravitons in the spectrum. The overall physics is consistent with the slogan that gravity becomes “more holographic”, as it gets stronger. Our observations strengthen the case that the conventional Page curve is indeed of significance, when discussing the information paradox in flat space. We work in high enough dimensions so that the graviton is non-trivial, and our results are in line with the previous discussions on gravitating baths in arXiv:2005.02993 and arXiv:2007.06551.

scholarly journals Failure of the split property in gravity and the information paradox

2022 ◽  
Author(s):  
Suvrat Raju
Keyword(s):  
Black Hole ◽  
Entanglement Entropy ◽  
Coarse Graining ◽  
The State ◽  
Information Paradox ◽  
Fine Grained ◽  
Theories Of Gravity ◽  
Split Property ◽  
The Common ◽  
Ordinary Quantum

Abstract In an ordinary quantum field theory, the “split property” implies that the state of the system can be specified independently on a bounded subregion of a Cauchy slice and its complement. This property does not hold for theories of gravity, where observables near the boundary of the Cauchy slice uniquely fix the state on the entire slice. The original formulation of the information paradox explicitly assumed the split property and we follow this assumption to isolate the precise error in Hawking’s argument. A similar assumption also underpins the monogamy paradox of Mathur and AMPS. Finally the same assumption is used to support the common idea that the entanglement entropy of the region outside a black hole should follow a Page curve. It is for this reason that computations of the Page curve have been performed only in nonstandard theories of gravity, which include a nongravitational bath and massive gravitons. The fine-grained entropy at I^{+} does not obey a Page curve for an evaporating black hole in standard theories of gravity but we discuss possibilities for coarse graining that might lead to a Page curve in such cases.

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.

LECTURES ON BLACK HOLE QUANTUM MECHANICS

1998 ◽  
Vol 13 (31) ◽  
pp. 5279-5372 ◽  
Author(s):  
FRANK WILCZEK
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Flat Space ◽  
Elementary Particles ◽  
The Other ◽  
Semiclassical Physics ◽  
Quantum Numbers ◽  
Set Up ◽  
Physical Consequences ◽  
Dilaton Black Holes

The lectures that follow were originally given in 1992, and written up only slightly later. Since then there have been dramatic developments in the quantum theory of black holes, especially in the context of string theory. None of these are reflected here. The concept of quantum hair, which is discussed at length in the lectures, is certainly of permanent interest, and I continue to believe that in some generalized form it will prove central to the whole question of how information is stored in black holes. The discussion of scattering and emission modes from various classes of black holes could be substantially simplified using modern techniques, and from currently popular perspectives the choice of examples might look eccentric. On the other hand fashions have changed rapidly in the field, and the big questions as stated and addressed here, especially as formulated for "real" black holes (nonextremal, in four-dimensional, asymptotically flat space–time, with supersymmetry broken), remain pertinent even as the tools to address them may evolve. The four lectures I gave at the school were based on two lengthy papers that have now been published, "Black Holes as Elementary Particles," Nuclear PhysicsB380, 447 (1992) and "Quantum Hair on Black Holes," Nuclear PhysicsB378, 175 (1992). The unifying theme of this work is to help make plausible the possibility that black holes, although they are certainly unusual and extreme states of matter, may be susceptible to a description using concepts that are not fundamentally different from those we use in describing other sorts of quantum-mechanical matter. In the first two lectures I discussed dilaton black holes. The fact that apparently innocuous changes in the "matter" action can drastically change the properties of a black hole is already very significant: it indicates that the physical properties of small black holes cannot be discussed reliably in the abstract, but must be considered with due regard to the rest of physics. (The macroscopic properties of large black holes, in particular those of astrophysical interest, are presumably well described by the familiar Einstein–Maxwell action which governs the massless fields. Heavy fields will at most provide Yukawa tails to the field surrounding the hole.) I will show how perturbations may be set up and analyzed completely, and why doing this is crucial for understanding the semiclassical physics of the hole including the Hawking radiation quantitatively. It will emerge that there is a class of dilaton black holes which behave as rather straightforward elementary particles. In the other two lectures I discussed the issue of hair on black holes, in particular the existence of hair associated with discrete gauge charges and its physical consequences. This hair is particularly interesting to analyze because it is invisible classically and to all order in ℏ. Its existence shows that black holes can have some "internal" quantum numbers in addition to their traditional classification by mass, charge, and angular momentum. The text that follows, follows the original papers closely.

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 Free fermion entanglement with a semitransparent interface: the effect of graybody factors on entanglement islands

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Jorrit Kruthoff ◽  
Raghu Mahajan ◽  
Chitraang Murdia
Keyword(s):  
Black Hole ◽  
Reflection Coefficient ◽  
Entanglement Entropy ◽  
Flat Space ◽  
Free Fermion ◽  
Zero Temperature ◽  
Island Region ◽  
Free Fermions ◽  
Single Interval ◽  
Transmitting Boundary

We study the entanglement entropy of free fermions in 2d in the presence of a partially transmitting interface that splits Minkowski space into two half-spaces. We focus on the case of a single interval that straddles the defect, and compute its entanglement entropy in three limits: Perturbing away from the fully transmitting and fully reflecting cases, and perturbing in the amount of asymmetry of the interval about the defect. Using these results within the setup of the Poincaré patch of AdS_22 statically coupled to a zero temperature flat space bath, we calculate the effect of a partially transmitting AdS_22 boundary on the location of the entanglement island region. The partially transmitting boundary is a toy model for black hole graybody factors. Our results indicate that the entanglement island region behaves in a monotonic fashion as a function of the transmission/reflection coefficient at the interface.

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 Bra-ket wormholes in gravitationally prepared states

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yiming Chen ◽  
Victor Gorbenko ◽  
Juan Maldacena
Keyword(s):  
Hyperbolic Space ◽  
Path Integral ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
De Sitter ◽  
Euclidean Case ◽  
Fine Grained ◽  
Entropy Formula ◽  
First Case

Abstract We consider two dimensional CFT states that are produced by a gravitational path integral.As a first case, we consider a state produced by Euclidean AdS2 evolution followed by flat space evolution. We use the fine grained entropy formula to explore the nature of the state. We find that the naive hyperbolic space geometry leads to a paradox. This is solved if we include a geometry that connects the bra with the ket, a bra-ket wormhole. The semiclassical Lorentzian interpretation leads to CFT state entangled with an expanding and collapsing Friedmann cosmology.As a second case, we consider a state produced by Lorentzian dS2 evolution, again followed by flat space evolution. The most naive geometry also leads to a similar paradox. We explore several possible bra-ket wormholes. The most obvious one leads to a badly divergent temperature. The most promising one also leads to a divergent temperature but by making a projection onto low energy states we find that it has features that look similar to the previous Euclidean case. In particular, the maximum entropy of an interval in the future is set by the de Sitter entropy.

scholarly journals Black hole hair removal for N = 4 CHL models

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Subhroneel Chakrabarti ◽  
Suresh Govindarajan ◽  
P. Shanmugapriya ◽  
Yogesh K. Srivastava ◽  
Amitabh Virmani
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Degrees Of Freedom ◽  
Microscopic Analysis ◽  
Flat Space ◽  
Special Care ◽  
Hair Removal ◽  
Partition Functions ◽  
Rotating Black Holes

Abstract Although BMPV black holes in flat space and in Taub-NUT space have identical near-horizon geometries, they have different indices from the microscopic analysis. For K3 compactification of type IIB theory, Sen et al. in a series of papers identified that the key to resolving this puzzle is the black hole hair modes: smooth, normalisable, bosonic and fermionic degrees of freedom living outside the horizon. In this paper, we extend their study to N = 4 CHL orbifold models. For these models, the puzzle is more challenging due to the presence of the twisted sectors. We identify hair modes in the untwisted as well as twisted sectors. We show that after removing the contributions of the hair modes from the microscopic partition functions, the 4d and 5d horizon partition functions agree. Special care is taken to present details on the smoothness analysis of hair modes for rotating black holes, thereby filling an essential gap in the literature.

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