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The universal covering space of the Penrose diagram of the backreacted black hole. Black dots indicate that we can continue this pattern indefinitely.
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A bstract
We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy o...
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The replica wormholes are a key to the existence of the islands that play a central role in a recent proposal for the resolution of the black hole information paradox. In this paper, we study the replica wormholes in the JT gravity, a model of two-dimensional quantum gravity coupled to a non-dynamical dilaton, by making use of the 2$d$ conformal fi...
In a 1+1 dimensional QFT on a circle, we consider the von Neumann entanglement entropy of an interval for typical pure states. As a function of the interval size, we expect a Page curve in the entropy. We employ a specific ensemble average of pure states, and show how to write the ensemble-averaged Renyi entropy as a path integral on a singular rep...
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A bstract
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Citations
... The assumption of our computation was the JLMS relation and did not necessarily require AdS holography. One particular interesting application would be to study modular transport in de Sitter space, similar to studies of the entanglement entropy in cosmological spacetimes [49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. ...
Modular Berry transport is a useful way to understand how geometric bulk information is encoded in the boundary CFT: The modular curvature is directly related to the bulk Riemann curvature. We extend this approach by studying modular transport in the presence of a non-trivial quantum extremal surface. Focusing on JT gravity on an AdS background coupled to a non-gravitating bath, we compute the modular curvature of an interval in the bath in the presence of an island: the Quantum Extremal Modular Curvature (QEMC). We highlight some important properties of the QEMC, most importantly that it is non-local in general. In an OPE limit, the QEMC becomes local and probes the bulk Riemann curvature in regions behind a horizon. Our work gives a new approach to probe physics behind horizons.
... EW(R) = R ∪ I. Then according to the entanglement wedge reconstruction [20][21][22], it is possible for an observer who is restricted to region R to recover the information on the region I through sufficient complex operations. Subsequently, the entanglement island and the entanglement entropy have been widely studied in various gravitational spacetimes, such as AdS black hole spacetime coupled to non-gravitational bath [23][24][25][26][27] and gravitational baths [28,29], asymptotically flat black hole spacetime [30][31][32][33][34][35][36][37][38][39], de-Sitter spacetime [40][41][42][43], AdS spacetime dual to the BCFT [44][45][46][47][48] and so on. More importantly, these studies indicated that the gravitational entropy formula may be applied in more general spacetimes. ...
The concept of the generalized entanglement wedge was recently proposed by Bousso and Penington, which states that any bulk gravitational region $a$ possesses an associated generalized entanglement wedge $E(a) \supset a$ on a static Cauchy surface $M$ in general gravitational spacetimes, where $E(a)$ may contain an entanglement island $I(a)$. It suggests that the fine-grained entropy for bulk region $a$ is given by the generalized entropy $S_{\text{gen}}(E(a))$. Motivated by this proposal, we extend the quantum bit thread description to general gravitational spacetimes, no longer limited to the AdS spacetime. By utilizing the convex optimization techniques, a dual flow description for the generalized entropy $S_{\text{gen}}(E(a))$ of a bulk gravitational region $a$ is established on the static Cauchy surface $M$, such that $S_{\text{gen}}(E(a))$ is equal to the maximum flux of any flow that starts from the boundary $\partial M$ and ends at bulk region $a$, or equivalently, the maximum number of bit threads that connect the boundary $\partial M$ to the bulk region $a$. In addition, the nesting property of flows is also proved. Thus the basic properties of the entropy for bulk regions, i.e. the monotonicity, subadditivity, Araki-Lieb inequality and strong subadditivity, can be verified from flow perspectives by using properties of flows, such as the nesting property. Moreover, in max thread configurations, we find that there exists some lower bounds on the bulk entanglement entropy of matter fields in the region $E(a)\setminus a$, particularly on an entanglement island region $I(a) \subset (E(a)\setminus a)$, as required by the existence of a nontrivial generalized entanglement wedge. Our quantum bit thread formulation may provide a way to investigate more fine-grained entanglement structures in general spacetimes.
... More complicated setups, such as higher-dimensional spacetimes or spacetimes with no asymptotically flat subregions, are still subjects of research [31,34,[41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. As for de Sitter, the literature uses a specific setup, in which the original manifold is either initially two-dimensional or is reduced to two dimensions, and the applicability of the island formula is postulated [42,45,[58][59][60]. ...
A bstract
In this paper, we consider the entanglement entropy of conformal matter for finite and semi-infinite entangling regions, as well as the formation of entanglement islands in four-dimensional de Sitter spacetime partially reduced to two dimensions. We analyze complementarity and pure state condition of entanglement entropy of pure states as a consistency test of the CFT formulas in this geometrical setup, which has been previously used in the literature to study the information paradox in higher-dimensional de Sitter in the context of the island proposal. We consider two different types of Cauchy surfaces in the extended static patch and flat coordinates, correspondingly. For former, we found that entanglement entropy of a pure state is always bounded from below by a constant and never becomes zero, as required by quantum mechanics. In turn, the difference between the entropies for some region and its complement, which should be zero for a pure state, in direct calculations essentially depends on how the boundaries of these regions evolve with time. Regarding the flat coordinates, it is impossible to regularize spacelike infinity in a way that would be compatible with complementarity and pure state condition, as opposed, for instance, to two-sided Schwarzschild black hole. Finally, we discuss the information paradox in de Sitter and show that the island formula does not resolve it, at least in this setup. Namely, we give examples of a region with a time-limited growth of entanglement entropy, for which there is no island solution, and the region, for which entanglement entropy does not grow, but the island solution exists.
... The appearance of the island region is regarded as an indication of the global effects of quantum gravity. In the context of the de Sitter spacetime, there are approaches leveraging quantum information concepts to study the effects of quantum gravity, such as the dS/CFT correspondence [6,[12][13][14][15][16]. However, to study the effects of quantum gravity in de Sitter spacetime from the quantum information perspective, there is currently no guiding principle equivalent to the Page curve adopted in black hole cases. ...
We analyze the entropy behavior of the de Sitter spacetime during the inflationary phase. In the de Sitter spacetime, a cosmological horizon that constrains the causal accessible region of an observer, exhibits thermal properties analogous to the event horizon of a black hole. From the principle of holography, the entropy within the causally connected region for an observer is constrained by the area of its boundary. This entropy bound is violated in the late stage of inflation. To address the issue of entropy bound violation from a perspective of quantum information, we adopt the stochastic approach to cosmic inflation. To reformulate the issue of entropy bound in the inflation, we follow the derivation of the Page curve in the black hole context. By adopting the volume-weighted probability distribution for the inflaton field, we obtain a meaningful entropy behavior in the de Sitter spacetime.
... There have been also interesting attempts to apply it in the context of cosmology, see e.g. [29][30][31][32][33][34][35][36][37][38][39][40]. Recently, it has also been applied in the context of static patch holography for de Sitter space [41][42][43][44] in order to compute the fine grained entropy of subsystems of the dual holographic theory [45][46][47][48]. 1 Recall that the static patch holographic proposal for de Sitter space entails anchoring holographic screens on the two cosmological horizons associated with comoving observers at antipodal points of the spatial sphere. ...
A bstract
We extend a recent de Sitter holographic proposal and entanglement entropy prescription to generic closed FRW cosmologies in arbitrary dimensions, and propose that for large classes of bouncing and Big Bang/Big Crunch cosmologies, the full spacetime can be encoded holographically on two holographic screens, associated to two antipodal observers. In the expanding phase, the two screens lie at the apparent horizons. In the contracting phase, there is an infinite number of possible trajectories of the holographic screens, which can be grouped in equivalence classes. In each class the effective holographic theory can be derived from a pair of “parent” screens on the apparent horizons. A number of cases including moduli dominated cosmologies escape our discussion, and it is expected that two antipodal observers and their associated screens do not suffice to reconstruct these cosmologies. The leading contributions to the entanglement entropy between the screens arise from a minimal extremal trapped or anti-trapped surface lying in the region between them. This picture entails a time-dependent realization of the ER=EPR conjecture, where an effective geometrical bridge connecting the screens via the minimal extremal surface emerges from entanglement. For the Big Crunch contracting cases, the screens disentangle and the geometrical bridge closes off when the minimal extremal trapped sphere hits the Big Crunch singularity at a finite time before the collapse of the Universe. Semiclassical, thermal corrections are incorporated in the cases of radiation dominated cosmologies.
... Conversely, it would be interesting to study aspects which have been studied recently in bottom-up models in the top-down models, e.g. additional information-theoretic quantities [53][54][55][56][57][58][59][60][61][62][63], charged black holes [64][65][66][67], connections to bootstrap conditions [68][69][70][71][72][73] and effective brane description [74][75][76][77][78][79][80][81], more general dynamics [82][83][84][85][86], and connections to de Sitter space and cosmology [87][88][89][90][91][92][93][94][95][96][97]. ...
A bstract
We construct Type IIB string theory setups which, via double holography, realize two gravitational systems in separate AdS spaces which interact with each other and with a non-gravitational bath. We employ top-down string theory solutions with concrete field theory duals in the form of 4d $$\mathcal{N}$$ = 4 SYM BCFTs and a first-principles notion of double holography. The setups are used to realize pairs of ‘near’ and ‘far’ black holes from the perspective of the bath, which exchange Hawking radiation with each other and radiate into the bath. We identify three phases for the entropy in the bath characterized as no island, partial island and full island, and discuss the entropy curves. The setups differ from the black hole binaries observed in gravitational wave experiments but may capture certain aspects.
... The first one is a Z 2 -orbifold of dS 2 , and the second one is a two-dimensional reduction of Schwarzschild-de Sitter space. These models have been investigated in the literature [31][32][33][34][35][36][37][38][39][40] to study islands and information recovery in dS. We first review them in classical gravity, and then include in section 2.2 semiclassical corrections by coupling gravity to a two-dimensional CFT with central charge c. ...
A bstract
We prove the Strominger-Thompson quantum Bousso bound in the infinite class of conformal vacua in semiclassical JT gravity, with postive or negative cosmological constant. The Bousso-Fisher-Leichenauer-Wall quantum Bousso bound follows from an analogous derivation, requiring only initial quantum non-expansion. In this process, we show that the quantity $$2\pi {k}^{\mu }{k}^{\nu }\langle :{T}_{\mu \nu }:\rangle -{S}^{{\prime}{\prime}}-\frac{6}{c}{\left({S}{\prime}\right)}^{2}$$ vanishes in any vacuum state, entailing a stronger version of Wall’s quantum null energy condition. We derive an entropy formula in the presence of a generic class of two reflecting boundaries, in order to apply our argument to the half reduction model of de Sitter JT gravity.
... The first one is a Z 2 -orbifold of dS 2 , and the second one is a two-dimensional reduction of Schwarzschild-de Sitter space. These models have been investigated in the literature [31][32][33][34][35][36][37][38][39][40] to study islands and information recovery in dS. We first review them in classical gravity, and then include in Section 2.2 semiclassical corrections by coupling gravity to a two-dimensional CFT with central charge c. ...
We prove the Strominger-Thompson quantum Bousso bound in the infinite class of conformal vacua in semiclassical JT gravity, with postive or negative cosmological constant. The Bousso-Fisher-Leichenauer-Wall quantum Bousso bound follows from an analogous derivation, requiring only initial quantum non-expansion. In this process, we show that the quantity 2π⟨:T_kk:⟩−S′′−6/c(S′)^2 vanishes in any vacuum state, entailing a stronger version of Wall’s quantum null energy condition. We derive an entropy formula in the presence of a generic class of two reflecting boundaries, in order to apply our argument to the half reduction model of de Sitter JT gravity.
... The island formula has found significant applications in various gravitational backgrounds, including the Reissner-Nordström black hole [24,25], the Schwarzschild black hole [26][27][28][29], dS spacetime [30][31][32][33][34][35][36][37][38][39][40][41][42], higher dimensional spacetime [43][44][45], among others [46][47][48][49][50][51][52][53][54][55][56][57][58][59]. Besides its applications to the black hole information paradox, the island formula has been utilized in various quantum information-related fields, such as reflected entropy [60][61][62], mutual information [63][64][65], entanglement negativity [66][67][68][69][70], partial entanglement entropy [67,69], quantum phase transformation [71], and more. ...
... This characteristic of the island configuration in dS spacetime has been proposed in refs. [12,31,107]. In the following subsection, we will validate our findings through conformal field theory calculations. ...
... As mentioned in the footnote 2.3, our model is different from the setup in refs.[30][31][32][33] and the standard dS/CFT correspondence[95,96,102]. Our model pairs the gravitational system with the flat bath at ρ = 0 instead of its conformal boundary. ...
A bstract
Double holography offers a profound understanding of the island formula by describing a gravitational system on AdS d coupled to a conformal field theory on ℝ 1, d− 1 , dual to an AdS d +1 spacetime with an end-of-the-world (EOW) brane. In this work, we extend the proposal in [12] by considering that the dual bulk spacetime has two EOW branes: one with a gravitational system and the other with a thermal bath. We demonstrate an equivalence between this proposal and the wedge holographic theory. We examine it in both Anti-de Sitter gravity and de Sitter gravity by calculating the entanglement entropy of the Hawking radiation. Finally, we employ the doubly holographic model to verify the formula for the entanglement entropy in a subregion within conformally flat spacetime.
... There have been also interesting attempts to apply it in the context of cosmology, see e.g. [29][30][31][32][33][34][35][36][37][38][39][40]. Recently, it has also been applied in the context of static patch holography for de Sitter space [41][42][43][44] in order to compute the fine grained entropy of subsystems of the dual holographic theory [45][46][47][48]. 1 Recall that the static patch holographic proposal for de Sitter space entails anchoring holographic screens on the two cosmological horizons associated with comoving observers at antipodal points of the spatial sphere. ...
We extend a recent de Sitter holographic proposal and entanglement entropy prescription to generic closed FRW cosmologies in arbitrary dimensions, and propose that for large classes of bouncing and Big Bang/Big Crunch cosmologies, the full spacetime can be encoded holo-graphically on two holographic screens, associated to two antipodal observers. In the expanding phase, the two screens lie at the apparent horizons. In the contracting phase, there is an infinite number of possible trajectories of the holographic screens, which can be grouped in equivalence classes. In each class the effective holographic theory can be derived from a pair of "parent" screens on the apparent horizons. A number of cases including moduli dominated cosmologies escape our discussion, and it is expected that two antipodal observers and their associated screens do not suffice to reconstruct these cosmologies. The leading contributions to the entanglement entropy between the screens arise from a minimal extremal trapped or anti-trapped surface lying in the region between them. This picture entails a time-dependent realization of the ER=EPR conjecture, where an effective geometrical bridge connecting the screens via the minimal extremal surface emerges from entanglement. For the Big Crunch contracting cases, the screens disentangle and the geometrical bridge closes off when the minimal extremal trapped sphere hits the Big Crunch singularity at a finite time before the collapse of the Universe. Semiclassical, thermal corrections are incorporated in the cases of radiation dominated cosmologies.
