Holographic complexity and two identities of action growth

Huang, Hyat; Feng, Xing-Hui; Lü, H.

doi:10.1016/j.physletb.2017.04.011

Cited by 50 publications

(46 citation statements)

References 36 publications

(58 reference statements)

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“…This is valid to generally static black holes in higher derivative gravities. The result covers previous results published in literatures [9,32,33,34,35,36].…”

Section: Discussionsupporting

confidence: 90%

“…On the other hand, according to Eq. (87), at late times the growth rate of the joint action equals to T S. However, in [34], it was also shown that…”

Section: Discussionmentioning

confidence: 98%

“…On the other hand, recent developments in AdS/CFT correspondence give rise to several distinct proposals for complexity for a holographic state [4,5,6,8,9]. However, though these proposals show interesting properties of complexity and have attracted a lot of attentions in literature [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,32,33,34,35,36,37,38,39,40], none of them obeys the Lloyd bound for general holographic theories.…”

Section: Introductionmentioning

confidence: 99%

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Holographic complexity and thermodynamics of AdS black holes

Fan

Guo

2019

Phys. Rev. D

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In this paper, we relate the complexity for a holographic state to a simple gravitational object of which the growth rate at late times is equal to temperature times black hole entropy. We show that if this is correct, the thermodynamics of AdS black holes implies that for generic holographic states dual to static AdS black holes, the complexity growth rate at late times will saturate the Lloyd bound at high temperature limit. In particular, for AdS planar black holes, the result holds at lower temperatures as well. We conjecture that the complexity growth is bounded above as dC/dt ≤ αT S/π or dC/dt ≤ α T + S + − T − S − /π for black holes with an inner horizon, where α is an overall coefficient for our new proposal.The conjecture passes a number of nontrivial tests for black holes in Einstein's gravity.However, we also find that the bound may be violated in the presence of stringy corrections.

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“…This is valid to generally static black holes in higher derivative gravities. The result covers previous results published in literatures [9,32,33,34,35,36].…”

Section: Discussionsupporting

confidence: 90%

“…On the other hand, according to Eq. (87), at late times the growth rate of the joint action equals to T S. However, in [34], it was also shown that…”

Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Holographic complexity and thermodynamics of AdS black holes

Fan

Guo

2019

Phys. Rev. D

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“…In the AdS/CFT correspondence, there are two popular proposals for complexity, usually dubbed by "Complexity=Volume" (CV) duality [7,8] and "Complex-ity=Action" (CA) duality [9,10]. The two conjectures have been extensively studied in literature [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46]. However, there are some drawbacks for the two proposals as well.…”

Section: Introductionmentioning

confidence: 99%

Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Phys. Rev. D

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We study the general time dependence of complexity for holographic states dual to Lovelock black holes using the "Complexity=Action" (CA) proposal. We observe that at early times, the critical time at which the complexity begins to increase is a decreasing function of the higher order coupling constants, which implies that the complexity evolves faster than that of Schwarzschild black holes. At late times, the rate of change of complexity is essentially determined by the generalised Gibbons-Hawking-York boundary term evaluated at the future singularity. In particular, its ratio to black hole mass is a characteristic constant, independent of the higher order couplings. Thus, in the vanishing coupling limit, the result in general does not reduce to that of Schwarzschild black holes, in spite of that the metric reduces to the latter as well as the gravitational action. In fact, the two differ by a constant during the whole time evolution. Including the next-to-leading order term around late times, we find that as the Einstein case, the late time limit is always approached from above, thus violating any conjectured upper bound given by the late time result. For charged Lovelock black holes, we find that with sufficient charge, the complexity roughly behaves the same as the Einstein case. However, for smaller charges, the two have some significant differences. In particular, unlike the Einstein case, in the uncharged limit the complexity growth rate does not match with the neutral case, differing by a constant in the whole time evolution.

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“…[20]. It was shown that the difference of the generalized enthalpy between the two corresponding horizons decides the action growth rate [20] and strong energy conditions of the matter outside the horizon of the black holes can ensure the validity of the complexity growth rate bound [18]. The action growth rates of the charged black holes with a single horizon were also studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Complexity growth rates for AdS black holes in massive gravity and f(R) gravity

Guo

Wei

et al. 2017

Eur. Phys. J. C

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The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black hole within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in f (R) gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.

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Holographic complexity and two identities of action growth

Cited by 50 publications

References 36 publications

Holographic complexity and thermodynamics of AdS black holes

Holographic complexity and thermodynamics of AdS black holes

Time dependence of complexity for Lovelock black holes

Complexity growth rates for AdS black holes in massive gravity and f(R) gravity

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