Late-Time Saturation of Black Hole Complexity
arXiv:2502.17179 · doi:10.1007/JHEP08(2025)056
Abstract
The holographic complexity of a static spherically symmetric black hole, defined as the volume of an extremal surface, grows linearly with time at late times in general relativity. The growth comes from a region at a constant transverse area inside the black hole and continues forever in the classical theory. In this region the volume complexity of any spherically symmetric black hole in spacetime dimensions reduces to a geodesic length in an effective two-dimensional JT-gravity theory. The length in JT-gravity has been argued to saturate at very late times via non-perturbative corrections obtained from a random matrix description of the gravity theory. The same argument, applied to our effective JT-gravity description of the volume complexity, leads to complexity saturation at times of exponential order in the Bekenstein-Hawking entropy of a -dimensional black hole. Along the way, we explore a simple toy model for complexity growth, based on a discretisation of Nielsen complexity geometry, that can be analytically shown to exhibit the expected late-time complexity saturation.
35 pages and 9 figures. v2: typos fixed and references added
References in corpus (23)
- The Stretched Horizon and Black Hole Complementarity
- Complexity Equals Action
- Complexity and Shock Wave Geometries
- Complexity, action, and black holes
- Quantum Computation as Geometry
- Mass, Entropy and Holography in Asymptotically de Sitter Spaces
- On the Time Dependence of Holographic Complexity
- On the Dynamics of Near-Extremal Black Holes
- On The Evolution Of Operator Complexity Beyond Scrambling
- Quantum Complexity and Negative Curvature
- Linear growth of quantum circuit complexity
- Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
- Quantum Complexity of Time Evolution with Chaotic Hamiltonians
- Thermodynamics of Black Holes in Two (and Higher) Dimensions
- The Typical-State Paradox: Diagnosing Horizons with Complexity
- The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity
- AdS/CFT correspondence and near-extremal black hole entropy
- Eigenbranes in Jackiw-Teitelboim gravity
- Complexity Growth in Integrable and Chaotic Models
- Complex Entangling Surfaces for AdS and Lifshitz Black Holes?
- Equivalence of JT Gravity and Near-extremal Black Hole Dynamics in Higher Derivative Theory
- Cayley graphs and complexity geometry
- Non-Perturbative Corrections to Charged Black Hole Evaporation