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Action Complexity for Semi-Classical Black Holes
High Energy Physics - Theory · Submitted 17 Jan 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The results are consistent with our previous numerical results for semi-classical black hole complexity using a volume prescription (CV) in the same model, but the CA calculation is fully analytic and provides a non-trivial positive test for the holographic representation of the black hole interior.
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The abstract, sentence by sentence
We adapt the complexity as action prescription (CA) to a semi-classical model of two-dimensional dilaton gravity and determine the rate of increase of holographic complexity for an evaporating black hole. The results are consistent with our previous numerical results for semi-classical black hole complexity using a volume prescription (CV) in the same model, but the CA calculation is fully analytic and provides a non-trivial positive test for the holographic representation of the black hole interior.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We adapt the complexity as action prescription (CA) to a semi-classical model of two-dimensional dilaton gravity and determine the rate of increase of holographic complexity for an evaporating black hole. | contribution 0.94 | 0.96 | 0.18 | asserted 0.99 |
| s1 | The results are consistent with our previous numerical results for semi-classical black hole complexity using a volume prescription (CV) in the same model, but the CA calculation is fully analytic and provides a non-trivial positive test for the holographic representation of the black hole interior. | interpretation 0.76 | 0.92 | 0.55 | hedged possibility 0.59 |
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The paper
Original abstract
We adapt the complexity as action prescription (CA) to a semi-classical model of two-dimensional dilaton gravity and determine the rate of increase of holographic complexity for an evaporating black hole. The results are consistent with our previous numerical results for semi-classical black hole complexity using a volume prescription (CV) in the same model, but the CA calculation is fully analytic and provides a non-trivial positive test for the holographic representation of the black hole interior.
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References
How the literature uses it
6 arXiv papers cite this in 8 sentences
Papers citing it · 4 sentences without a confident label
Uses its method or tool 1 paper
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One can also calculate complexity using the Complexity=Action (CA) prescription [ref] .
Krylov Complexity of Open Quantum Systems: From Hard Spheres to Black Holes · Discussion · 0.82
Compares with it 1 paper
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Other approaches [ref] introduce the backreaction of the quantum fields on the geometry, but not their own complexity, and this accounts for the differences in our findings about the consistency of AC.
Holographic Complexity of Quantum Black Holes · Conclusions and outlook · 0.96
Cites it as background 2 papers
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Beyond this leading order in the large-$c$ expansion, several aspects of holographic complexity have been investigated in two-dimensional dilaton gravity [ref] , but its more general defining properties still await further elucidation.
Holographic Complexity of Quantum Black Holes · Quantum bulk effects · 0.93
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The alternative formulation of holographic complexity in terms of the action on a Wheeler-DeWitt patch [ref] is also of interest for these dilaton gravity models, but it is more subtle to implement at the semi-classical level, and we postpone this to a forthcoming paper [ref] .
Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole · Introduction · 0.88
What it cites · 36 sentences without a confident label
Builds on 1 paper
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While this is more technically involved than the volume computations in [ref] , it has the distinct advantage that the entire semi-classical calculation can be carried out analytically and yields explicit results for the rate of complexity growth of an evaporating RST black hole throughout its evolution.
Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole · Introduction · 1.00
Uses the method or tool of 3 papers
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One way to remedy this problem is to introduce an auxiliary scalar field $Z$ and write the action in terms of integrals over local quantities only [ref] , [equation] with [equation] As one can easily check, integrating out the auxiliary field $Z$ will return the original non-local action, up to boundary terms.
Entropy in the RST Model · A well-posed variational principle · 0.98
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By working in so-called Kruskal gauge and arranging the boundary terms in the action to respect the same symmetry that simplifies the bulk field equations of the RST model [ref] , we are able to eliminate a certain ambiguity in the holographic action complexity and obtain a remarkably simple end result.
The Endpoint of Hawking Evaporation · Introduction · 0.84
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For technical simplicity, we follow [ref] and take the stretched horizon of an RST black hole formed by shockwave collapse to coincide with the apparent horizon during the period of evaporation.
The Stretched Horizon and Black Hole Complementarity · Evaporating Black Hole · 0.84
Compares with 2 papers
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First, it confirms linear falloff of $𝒞̇$ with time after the scrambling time $t_S$, already observed (numerically) in [ref] using a CV prescription.
Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole · Discussion and outlook · 0.90
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The next-to-leading order (logarithmic) term in the Bekenstein-Hawking entropy can also be read off from our analytic expression for the complexity growth and the result agrees with previous semi-classical entropy calculations in the RST model [ref] .
Two-dimensional Quantum-Corrected Eternal Black Hole · Introduction · 0.96
Cites as support 1 paper
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As was discussed in [ref] , it seems more physical to place the anchor curve at the stretched horizon and have the onset of complexity growth coincide, at least approximately, with the time of black hole formation (here defined as the tortoise time at which the shock wave meets the stretched horizon).
Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole · Gravitational Collapse · 0.97
Cites as background 10 papers
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A refined version of the conjecture instead relates the complexity to the gravitational action evaluated on a specific bounded region of the black hole spacetime, referred to as the Wheeler-DeWitt (WdW) patch, that intersects the black hole interior [ref] .
Complexity Equals Action · Introduction · 0.89
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A refined version of the conjecture instead relates the complexity to the gravitational action evaluated on a specific bounded region of the black hole spacetime, referred to as the Wheeler-DeWitt (WdW) patch, that intersects the black hole interior [ref] .
Complexity, action, and black holes · Introduction · 0.89
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The third term in the semi-classical action, [equation] was introduced by Russo et al. in [ref] .
The Endpoint of Hawking Evaporation · RST model · 0.80
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