On complexity for F (R) and critical gravity

Alishahiha, Mohsen; Astaneh, Amin Faraji; Naseh, Ali; Vahidinia, M. H.

doi:10.1007/jhep05(2017)009

Cited by 95 publications

(84 citation statements)

References 38 publications

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“…If we choose: f 0 = −R 2 f (z)e −χ(z) , f 1 = R 2 , f 2 = R 2 f (z) and d = 3, we arrive at our results (25)(26)(27)(28)(29).…”

Section: A the Subregion Complexity In (D+1)-dimensionsmentioning

confidence: 72%

On the complexity of a 2 + 1-dimensional holographic superconductor

Chakraborty

2020

Class. Quantum Grav.

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We present the results of our computation of the subregion complexity and also compare it with the entanglement entropy of a 2 + 1-dimensional holographic superconductor which has a fully backreacted gravity dual with a stable ground sate. We follow the "complexity equals volume" or the CV conjecture. We find that there is only a single divergence for a strip entangling surface and the complexity grows linearly with the large strip width. During the normal phase the complexity increases with decreasing temperature, but during the superconducting phase it behaves differently depending on the order of phase transition. We also show that the universal term is finite and the phase transition occurs at the same critical temperature as obtained previously from the free energy computation of the system. In one case, we observe multivaluedness in the complexity in the form of an "S" curve.

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“…If we choose: f 0 = −R 2 f (z)e −χ(z) , f 1 = R 2 , f 2 = R 2 f (z) and d = 3, we arrive at our results (25)(26)(27)(28)(29).…”

Section: A the Subregion Complexity In (D+1)-dimensionsmentioning

confidence: 72%

On the complexity of a 2 + 1-dimensional holographic superconductor

Chakraborty

2020

Class. Quantum Grav.

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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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“…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%

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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On complexity for F (R) and critical gravity

Cited by 95 publications

References 38 publications

On the complexity of a 2 + 1-dimensional holographic superconductor

On the complexity of a 2 + 1-dimensional holographic superconductor

Time dependence of complexity for Lovelock black holes

Holographic complexity and thermodynamics of AdS black holes

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