Holographic complexity and thermodynamics of AdS black holes

Abstract

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 $d\mathcal{C}/dt\le \alpha TS/\pi \hslash$ or $d\mathcal{C}/dt\le \alpha (T_{+}{S}_{+}-T_{-}{S}_{-})/\pi \hslash$ for black holes with inner horizons, where $\alpha$ 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.

arXiv commentminor revisions, references added, to apperear in PRD; 31 pages, 8 figures

References in corpus (41)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Ultimate physical limits to computation
• The maximum speed of dynamical evolution
• Complexity Equals Action
• Complexity and Shock Wave Geometries
• Complexity, action, and black holes
• Viscosity Bound Violation in Higher Derivative Gravity
• Gravitational action with null boundaries
• Comments on Holographic Complexity
• On the Time Dependence of Holographic Complexity
• Noether charge, black hole volume, and complexity
• Complexity of Formation in Holography
• Complexity Growth for AdS Black Holes
• Causality constraints in AdS/CFT from conformal collider physics and Gauss-Bonnet gravity
• Holographic Lovelock Gravities and Black Holes
• Causality in AdS/CFT and Lovelock theory
• Hamiltonian formulation of f(Riemann) theories of gravity
• Holographic Complexity of Einstein-Maxwell-Dilaton Gravity
• Complexity Growth with Lifshitz Scaling and Hyperscaling Violation
• On Complexity for Higher Derivative Gravities
• The effect of Dilaton on the holographic complexity growth
• Complexity Growth Rate in Lovelock Gravity
• Evolution of Complexity Following a Global Quench
• Strong energy condition and complexity growth bound in holography
• Surface Counterterms and Regularized Holographic Complexity
• On the time dependence of holographic complexity in a dynamical Einstein-dilaton model
• Holographic Complexity and Two Identities of Action Growth
• Action growth rate for a higher curvature gravitational theory
• Divergences in the rate of complexification
• Complexity of Holographic Superconductors
• Fast quantum computation at arbitrarily low energy
• Surface term, corner term, and action growth in F(Riemann) gravity theory
• Generalised Smarr Formula and the Viscosity Bound for Einstein-Maxwell-Dilaton Black Holes
• On the Noether charge and the gravity duals of quantum complexity
• Holographic Complexity Growth Rate in Horndeski Theory
• Comparison of holographic and field theoretic complexities by time dependent thermofield double states
• Lovelock action with nonsmooth boundaries
• Modified "complexity equals action" conjecture
• Holographic entanglement entropy and complexity in St$\ddot{u}$ckelberg superconductor
• Note on Noether charge and holographic transports

Cited by in corpus (15)

• Modified "complexity equals action" conjecture
• Time dependence of complexity for Lovelock black holes
• Holographic complexity of charged Taub-NUT-AdS black holes
• Holographic complexity in general quadratic curvature theory of gravity
• Holographic Complexity in a Charged Supersymmetric Black Holes
• Action Growth of Dyonic Black Holes and Electromagnetic Duality
• Complexity growth for topological black holes by holographic method
• Effects of the acceleration on holographic complexity
• Complexity growth rate, grand potential and partition function
• Generalized volume-complexity for Lovelock black holes
• What kind of "complexity" is dual to holographic complexity?
• Complexity Growth of Dyonic Black holes with Quartic Field Strength Corrections
• Switchback effect of holographic complexity in multiple-horizon black holes
• Complexity vs. Vorticity
• D5-brane on topological black holes