We use the complexity ¼ action (CA) conjecture to study the full-time dependence of holographic complexity in anisotropic black branes. We find that the time behavior of holographic complexity of anisotropic systems shares a lot of similarities with the behavior observed in isotropic systems. In particular, the holographic complexity remains constant for some initial period, and then it starts to change so that the complexity growth rate violates the Lloyd's bound at initial times, and approaches this bound from above at later times. Compared with isotropic systems at the same temperature, the anisotropy reduces the initial period in which the complexity is constant and increases the rate of change of complexity. At late times the difference between the isotropic and anisotropic results is proportional to the pressure difference in the transverse and longitudinal directions. In the case of charged anisotropic black branes, we find that the inclusion of a Maxwell boundary term is necessary to have consistent results. Moreover, the resulting complexity growth rate does not saturate the Lloyd's bound at late times.
Abstract:We study linearized equations of motion of the newly proposed three dimensional gravity, known as minimal massive gravity, using its metric formulation. By making use of a redefinition of the parameters of the model, we observe that the resulting linearized equations are exactly the same as that of TMG . In particular the model admits logarithmic modes at critical points. We also study several vacuum solutions of the model, specially at a certain limit where the contribution of Chern-Simons term vanishes.
We study the complexity growth by using "complexity = action" (CA) proposal in Minimal Massive 3D Gravity(MMG) model which is proposed for resolving the bulkboundary clash problem of Topologically Massive Gravity(TMG). We observe that the rate of the complexity growth for BTZ black hole saturates the proposed bound by physical mass of the BTZ black hole in the MMG model, when the angular momentum parameter and the inner horizon of black hole goes to zero.
We study third order Lovelock Gravity in D = 7 at the critical point which three (A)dS vacua degenerate into one. We see there is not propagating graviton at the critical point. And also we compute the butterfly velocity for this theory at the critical point by considering the shock wave solutions near horizon, this is important to note that although there is no propagating graviton at the critical point, due to boundary gravitons the butterfly velocity is non-zero. Finally we observe that the butterfly velocity for third order Lovelock Gravity at the critical point in D = 7 is less than the butterfly velocity for Einstein-Gauss-Bonnet Gravity at the critical point in D = 7 which is less than the butterfly velocity in D = 7 for Einstein Gravity,. Maybe we can conclude that by adding higher order curvature corrections to Einstein Gravity the butterfly velocity decreases.
We study the butterfly effect by considering shock wave solutions near the horizon of the AdS black hole in some of 3-dimensional Gravity models including; 3D Einstein Gravity, Minimal Massive 3D Gravity, New Massive Gravity, Generalized Massive Gravity, Born-Infeld 3D Gravity and New Bi-Gravity. We calculate the butterfly velocities of these models and also we consider the critical points and different limits in some of these models. By studying the butterfly effect in the Generalized Massive Gravity, we observe a correspondence between the butterfly velocities and right-left moving degrees of freedom or the central charges of the dual 2D Conformal Field Theories.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.