Eternal black holes in anti-de Sitter

By J. Maldacena. 2001

1,670 citations recorded by the source corpus.

We propose a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter spacetimes. The description involves two copies of the conformal field theory associated to the AdS spacetime and an initial entangled state. In this context we also discuss a version of the information loss paradox and its resolution.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e2fca9f882930e170b9c705955b8e3ec9f7609bb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. V. Hubeny
5. D. Stanford
6. J. Maldacena
7. S. Raju
8. M. Rangamani

In Nuclear and High Energy Physics

1. R. Myers
2. D. Harlow
3. T. Takayanagi
4. D. Stanford
5. V. Hubeny
6. J. Maldacena
7. S. Raju
8. M. Rangamani

In Statistical and Nonlinear Physics

1. D. Harlow
2. R. Myers
3. D. Stanford
4. S. Raju
5. V. Hubeny
6. T. Takayanagi
7. J. Maldacena
8. S. Shenker

Citations in the corpus

• Relative entropy equals bulk relative entropy (2015, background): “Let us now consider an eternal black hole and the thermofield double state [36].”
• Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence (2015, methodology): “As we have already noted, it also defines isometries from any set of 1, 2, or 3 indices to the complementary set of indices; these isometries may be regarded as the encoding maps for [[5, 1]], [[4, 2]], and [[3, 3]] stabilizer codes respectively.”
• Remarks on the Sachdev-Ye-Kitaev model (2016, background): “The fact that we have a complex shift in the two times by t1− t2 → t1− t2 + iβ/2 is related to the fact that we can easily create particles in the interior if we have access to both sides of the thermofield double, or if we perform small perturbations of the thermofield double state [43].”
• Switchbacks and the Bridge to Nowhere (2014, background): “The most studied case is the two-sided ADS black hole (really a pair of black holes), dual to a pair of entangled conformal field theories[2][3].”
• A Measure of de Sitter entropy and eternal inflation (2007, neutral): “Of course this asymptotic form of the scattering amplitude is a guess; it is hard to imagine that the amplitude is smaller than this but one might imagine that it can be larger (we thank J. Maldacena for pointing this out to us).”
• Wormholes, emergent gauge fields, and the weak gravity conjecture (2015, background): “Indeed these gravitational degrees of freedom seem to be precisely those which sew the two sides together, so understanding their description in the CFTs is maximally interesting from the point of view of understanding how the geometric connection emerges from the entanglement of the boundary CFTs [”
• Holographic Duality with a View Toward Many-Body Physics (2009, methodology): “• It has been derived from a holographic version of the Schwinger-Keldysh prescription [46, 45, 47].”
• Pure states in the SYK model and nearly-$AdS_2$ gravity (2017, neutral): “s on the full gravity theory in question. In some examples that arise from string theory we can certainly do it and the end of the world branes are the ones familiar in string constructions, see e.g. [26]. We will not discuss the full UV complete gravity theory here, we will simply consider a phenom”
• Black Hole Remnants and the Information Loss Paradox (2014, background): “on the other hand, [8]]. Nevertheless, correlation 34 functions between the outside and the inside of the event horizon seems to decay to zero as time goes on; this problem was discussed by Maldacena [200]. According to Maldacena, this demonstrates information loss of this eternal black hole. Perhap”
• Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT (2017, background): “In the thermofield double description [53], the wave functional is expressed by an Euclidean path-integral on a strip defined by − 4 (≡ z1) < z < β4 (≡ z2) in the Euclidean time direction, more explicitly”
• Entanglement entropy from a holographic viewpoint (2012, methodology): “The entanglement entropy has first been studied by using AdS/CFT setups with horizons in the pioneering works [19, 20].”
• On the architecture of spacetime geometry (2012, background): “Here one classic example is the eternal AdS black hole, in the AdS/CFT correspondence, where the horizon entropy is interpreted in terms of the entanglement entropy between the microscopic degrees of freedom of the boundary CFT and its thermofield double [23].”
• The Black Hole Information Problem (2016, background): “Maldacena noted a paradox in AdS which is presumably equivalent, but simpler to frame [28].”
• On the time dependence of holographic complexity (2017, positive): “This bulk geometry is dual to the thermofield double state in the boundary theory [20], ∣∣TFD(tL, tR)〉= Z−1/2∑ α e−Eα/(2T ) e−iEα(tL+tR) ∣∣Eα〉L∣∣Eα〉R , (1.”
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior (2006, background): “This shows quite explicitly that we can recover local physics outside the BTZ horizon using operators that act on a single copy of the CFT, while to describe the region inside the horizon we must use operators that act on both the CFT and its thermofield double [6, 16, 17, 18, 27].”