No simple dual to the causal holographic information?

Engelhardt, Netta; Wall, Aron C.

doi:10.1007/jhep04(2017)134

Cited by 19 publications

(32 citation statements)

References 94 publications

(171 reference statements)

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“…In previous work, we showed that the outer entropy of a slice of the event horizon is not, in general, given by its area [21]; in fact in some situations the outer entropy vanishes, while the area of the event horizon does not. Although the area of the event horizon is generically greater than the HRT surface [22], it remains unclear what coarse graining procedure, if any, corresponds to its area [23,24].…”

Section: Ow[σ]mentioning

confidence: 92%

Coarse graining holographic black holes

Engelhardt

Wall

2019

J. High Energ. Phys.

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173

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We expand our recent work on the outer entropy, a holographic coarsegrained entropy defined by maximizing the boundary entropy while fixing the classical bulk data outside some surface. When the surface is marginally trapped and satisfies certain "minimar" conditions, we prove that the outer entropy is exactly equal to a quarter the area (while for other classes of surfaces, the area gives an upper or lower bound). We explicitly construct the entropy-maximizing interior of a minimar surface, and show that it satisfies the appropriate junction conditions. This provides a statistical explanation for the area-increase law for spacelike holographic screens foliated by minimar surfaces. Our construction also provides an interpretation of the area for a class of non-minimal extremal surfaces.On the boundary side, we define an increasing simple entropy by maximizing the entropy subject to a set of "simple experiments" performed after some time. We show (to all orders in perturbation theory around equilibrium) that the simple entropy is the boundary dual to our bulk construction.

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Section: Ow[σ]mentioning

confidence: 92%

Coarse graining holographic black holes

Engelhardt

Wall

2019

J. High Energ. Phys.

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173

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“…for Minkowski, AdS, and dS. This conclusion follows in general in the Minkowski case from the positive mass theorem[30,31] and in the (A)dS cases from its generalization to spacetimes that are not asymptotically flat; see Ref [32]. for an AdS/CFT perspective 13.…”

mentioning

confidence: 82%

Outer entropy and quasilocal energy

2019

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We define the coarse-grained entropy of a "normal" surface σ, i.e., a surface that is neither trapped nor antitrapped. Following Engelhardt and Wall, the entropy is defined in terms of the area of an auxiliary extremal surface. This area is maximized over all auxiliary geometries that can be constructed in the interior of σ, while holding fixed the spatial exterior (the outer wedge). We argue that the area is maximized when the stress tensor in the auxiliary geometry vanishes, and we develop a formalism for computing it under this assumption. The coarse-grained entropy can be interpreted as a quasilocal energy of σ. This energy possesses desirable properties such as positivity and monotonicity, which derive directly from its information-theoretic definition.

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“…We can also define an entropy associated with a more general subset of observables that does not necessarily form a subalgebra. 9 Entropies of this type have been discussed previously in the context of holography in [39][40][41]. Given a set of (not necessarily commuting) operators A = {O α } and a global state ρ, we can look for a state ρ A that maximizes the von Neumann entropy subject to the constraint that…”

Section: Entropy Associated With a Subset Of Observablesmentioning

confidence: 99%

Areas and entropies in BFSS/gravity duality

et al. 2020

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The BFSS matrix model provides an example of gauge-theory / gravity duality where the gauge theory is a model of ordinary quantum mechanics with no spatial subsystems. If there exists a general connection between areas and entropies in this model similar to the Ryu-Takayanagi formula, the entropies must be more general than the usual subsystem entanglement entropies. In this note, we first investigate the extremal surfaces in the geometries dual to the BFSS model at zero and finite temperature. We describe a method to associate regulated areas to these surfaces and calculate the areas explicitly for a family of surfaces preserving SO(8) symmetry, both at zero and finite temperature. We then discuss possible entropic quantities in the matrix model that could be dual to these regulated areas.

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No simple dual to the causal holographic information?

Cited by 19 publications

References 94 publications

Coarse graining holographic black holes

Coarse graining holographic black holes

Outer entropy and quasilocal energy

Areas and entropies in BFSS/gravity duality

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