Black-hole boundaries

Booth, Ivan

doi:10.1139/p05-063

Cited by 289 publications

(410 citation statements)

References 51 publications

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“…implying that the area of the apparent horizon monotonically increases with time, in agreement with the area theorems of [2] (see also [3]). 1 …”

Section: Jhep07(2015)137supporting

confidence: 87%

“…Note that the corrected boundary condition in equation (A.26) leads to a monotonic apparent horizon area, as opposed to the nonmonotonic behaviour in the published version of figures 1 and 2 (see the appendix for the new versions). In fact, it can be shown from constraint equation (3.18) evaluated at the horizon ρ = 1 α , that the change in the apparent horizon area is given byimplying that the area of the apparent horizon monotonically increases with time, in agreement with the area theorems of [2] (see also [3]). 1…”

supporting

confidence: 68%

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Erratum to: Nonlocal probes of thermalization in holographic quenches with spectral methods

Buchel

Myers

Niekerk

2015

J. High Energ. Phys.

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In the published version of this paper, the final equation in (A.26) on page 49 should appear as g c (τ, 0) = 6a 2,2 .(A.26)The incorrect version of this equation was implemented in the numerical solution of the system, and propagated to several places throughout the paper. The interested reader may find a revised version of the manuscript at [1]. Note that the corrected boundary condition in equation (A.26) leads to a monotonic apparent horizon area, as opposed to the nonmonotonic behaviour in the published version of figures 1 and 2 (see the appendix for the new versions). In fact, it can be shown from constraint equation (3.18) evaluated at the horizon ρ = 1 α , that the change in the apparent horizon area is given byimplying that the area of the apparent horizon monotonically increases with time, in agreement with the area theorems of [2] (see also [3]). 1 TextHere we list the required changes to the text of the paper.• Throughout the body of this paper (including the abstract) the claim is made that the thermalization times of the two-point function and entanglement entropy (EE) exceeds the thermalization time of the one-point function for wide enough separations of 2y m . However, as can be seen in the new version of figure 15 in the appendix, the new thermalization times of the two-point function and EE do not have longer thermalization times than the one-point function for the largest values of y m considered. This weakens these claims in the paper. However, as the behaviour for both observables' thermalization times is linear and monotonic, we expect that the thermalization times of the two-point function and EE will still exceed that of the one-point function for wide enough regions.• As discussed above, statements about the nonmonotonicity of the area density of the apparent horizon are no longer correct, and should be disregarded.• Because of the new table (see the next section), the discussion on page 16 should be changed from "In the table, we see that the equilibration times of the horizon become approximately constant for small α" to "In the table, we see that the equilibration times of the horizon become approximately constant for small α, (although we see some variation for the event horizon)."1 We would like to thank Mukund Rangamani and Moshe Rozali for valuable discussions regarding the area theorems.-1 - JHEP07(2015)137• Because of the changes in figure 17 (see the appendix to this erratum), the discussion in the parentheses on page 40 should be changed from "note that in figure 17, the equilibration curve for α = 1 is not significantly later deep in the bulk than near the boundary, while the effect becomes more pronounced for the smaller values of α," to "Note that in figure 17, the equilibration curve for α = 1 is an exception, equilibrating earlier at most points in the bulk than at the boundary (even the deepest part). The effect of the integrand equilibrating later in the bulk than near the boundary is visible for the smaller values of α, which correspond more to the universal behaviou...

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“…implying that the area of the apparent horizon monotonically increases with time, in agreement with the area theorems of [2] (see also [3]). 1 …”

Section: Jhep07(2015)137supporting

confidence: 87%

supporting

confidence: 68%

Erratum to: Nonlocal probes of thermalization in holographic quenches with spectral methods

Buchel

Myers

Niekerk

2015

J. High Energ. Phys.

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“…Here δ n refers to a deformation generated by n [5] and so the condition says that each MTS can be deformed into a surface with θ (ℓ) < 0 by an arbitrarily small evolution "inwards". For a sufficiently small deformation θ (n) must also remain negative, and so this condition says that there are fully trapped surfaces "just inside" the MTT and untrapped ones outside.…”

Section: A Slowly Evolving Horizonsmentioning

confidence: 99%

“…Thus, due to their teleological definition, event horizons will grow in anticipation of future interactions even when there is no proximate cause for such an expansion. In particular, lack of growth cannot be used to characterize (temporary) equilibrium states (see [5] for a further discussion of these points).…”

Section: Introductionmentioning

confidence: 99%

“…These "almost isolated" horizons include (most) truly isolated horizons as particular examples and in turn are special cases of Hayward's trapping horizons [7] and are closely related to standard apparent horizons as well as Ashtekar and Krishnan's dynamical horizons [2,8,9] (see [5] for a detailed discussion of how these objects are related).…”

Section: Introductionmentioning

confidence: 99%

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Spacetimes containing slowly evolving horizons

Kavanagh

Booth

2006

Phys. Rev. D

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Slowly evolving horizons are trapping horizons that are "almost" isolated horizons. This paper reviews their definition and discusses several spacetimes containing such structures. These include certain Vaidya and Tolman-Bondi solutions as well as (perturbatively) tidally distorted black holes. Taking into account the mass scales and orders of magnitude that arise in these calculations, we conjecture that slowly evolving horizons are the norm rather than the exception in astrophysical processes that involve stellar-scale black holes.

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Ergodic Concepts for a Self‐Organizing Trivalent Spin Network: A Path to (2+1)$(2+1)$‐D Black Hole Entropy

Cordula Dantas

2024

Annalen der Physik

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From a dynamical systems point of view, a trivalent spin network model in Loop Quantum Gravity is considered, which presents self‐organized criticality (SOC), arising from a spin propagation dynamics. A partition function is obtained for the domains of stability connecting gauge non‐invariant avalanches, leading to an entropy formula for the asymptotic SOC state. The microscopic origin of this SOC entropy is therefore given by the excitation‐relaxation spin dynamics in the avalanche cycle. The puncturing of trivalent spin networks (TSN) edges participating in the avalanche are counted in terms of an ensemble perimeter over the implicit avalanches. By identifying this perimeter with that of an isolated ‐D black hole horizon, it is conjectured that the SOC entropy reduces to the Bekenstein‐Hawking perimeter‐entropy law for the Bañados, Teitelboim, and Zanelli (BTZ) black hole, by an appropriate adjustment of a potential function based on the thermodynamical formalism of Sinai, Ruelle, and Bowen.

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Black-hole boundaries

Cited by 289 publications

References 51 publications

Erratum to: Nonlocal probes of thermalization in holographic quenches with spectral methods

Erratum to: Nonlocal probes of thermalization in holographic quenches with spectral methods

Spacetimes containing slowly evolving horizons

Ergodic Concepts for a Self‐Organizing Trivalent Spin Network: A Path to (2+1)$(2+1)$‐D Black Hole Entropy

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