Holographic complexity and thermodynamics of AdS black holes

Self Cite

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.

Section: Growth Rate Of Bulk Actionmentioning

confidence: 99%

“…However, there are some drawbacks for the two proposals as well. This motivates people to search new proposals for complexity [47,48,49]. In addition, the active research in holography promotes studies of complexity for quantum field theories [50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66] as well as in condensed matter physics [67].…”

Section: Introductionmentioning

confidence: 99%

Time dependence of complexity for Lovelock black holes

Fan

Liang

2019

Self Cite

“…For example, the identities or the bound for action growth is obtained in [137,138]. It has a similar property to entropy as an increasing function of time [139,140,141]. Complexity in de Sitter space or negative curvature is studied in [43,94].…”

Section: Introductionmentioning

confidence: 99%

Complexity growth of rotating black holes with a probe string

Nagasaki

2018

We consider the growth of the action for black hole spacetime with a fundamental string. According to "complexity -action" conjecture it is expected to be equal to complexity which describes the quantum states of black holes. We consider black holes with three different horizon topologies. These have positive, negative and zero curvatures. We are interested in the complexity growth of these system with a fundamental string. We find that for the case where the black holes have the toroidal horizon structure the probe string behaves very differently from the other two cases.

“…with the blackening factor 15) and here we set r h,2 > r h,1 . This line element describes an infinitely thin shell collapse which generates a shape transition from a SAdS-type black hole with horizon r = r h,1 to another one with r = r h,2 .…”

Section: Switchback Effectmentioning

confidence: 99%

Adjusted complexity equals action conjecture

Jiang

2019

In this paper, we first use the "complexity equals action" conjecture to discuss the complexity growth rate in both perturbation Einsteinian cubic gravity and non-perturbation Einstein-Weyl gravity. We find that the CA complexity rate in these cases is divergent. To avoid this divergence, we modify the original conjecture, where we assume that the complexity of the boundary state equals the boundary actions contributed by the null segments as well as the joints of the Wheeler-DeWitt patch. Then, the late time growth rate of this modified holographic complexity is given by entropy S times temperature T , which is quite in agreement with the circuit analysis. Finally, to test its rationality, we also investigate the switchback effect by evaluating it in a Vaidya geometry and analyze the results in circuit models. arXiv:1903.05476v1 [hep-th]