On the Chaos Bound in Rotating Black Holes

Abstract

We study out-of-time-order correlators (OTOCs) of rotating BTZ black holes using two different approaches: the elastic eikonal gravity approximation, and the Chern-Simons formulations of 3-dimensional gravity. Within both methods the OTOC is given as a sum of two contributions, corresponding to left and right moving modes. The contributions have different Lyapunov exponents, ${\lambda }_L^{\pm }=\frac{2\pi }{\beta }\frac{1}{1\mp \ell \Omega }$, where $\Omega$ is the angular velocity and $\ell$ is the AdS radius. Since ${\lambda }_L^{-}\le \frac{2\pi }{\beta }\le {\lambda }_L^{+}$, there is an apparent contradiction with the chaos bound. We discuss how the result can be made consistent with the chaos bound if one views ${\beta }_{\pm }=\beta (1\mp \ell \Omega )$ as the effective inverse temperatures of the left and right moving modes.

arXiv comment35 pages, 2 figures. v2: references added, typos corrected, and clarifications added to the discussion section

References in corpus (56)

• Gauge Theory Correlators from Non-Critical String Theory
• The Black Hole in Three Dimensional Space Time
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Geometry of the 2+1 Black Hole
• Eternal Black Holes in AdS
• Black holes and the butterfly effect
• AdS3 Black Holes and a Stringy Exclusion Principle
• Chaos in AdS${}_2$ holography
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Localized shocks
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Multiple Shocks
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• The Black Hole Singularity in AdS/CFT
• A Generalization of Sachdev-Ye-Kitaev
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• Higher Spin Black Holes
• Eikonal Quantum Gravity and Planckian Scattering
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• Bi-Local Holography in the SYK Model
• Asymptotic W-symmetries in three-dimensional higher-spin gauge theories
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Bulk and Boundary Dynamics in BTZ Black Holes
• Strongly-coupled anisotropic gauge theories and holography
• Three Dimensional View of the SYK/AdS Duality
• Thermodynamics of Higher Spin Black Holes in AdS${}_3$
• 5D Rotating Black Holes and the nAdS${}_2$/nCFT${}_1$ Correspondence
• Dynamical entanglement entropy with angular momentum and U(1) charge
• Holographic entanglement entropy and gravitational anomalies
• Entanglement Entropy and Higher Spin Holography in AdS${}_3$
• Scalar fields and three-point functions in D=3 higher spin gravity
• Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models
• Higher Spin Entanglement and W_N Conformal Blocks
• Black Holes and Singularity Resolution in Higher Spin Gravity
• Menagerie of AdS${}_2$ boundary conditions
• Chaotic strings in AdS/CFT
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Three Dimensional View of Arbitrary $q$ SYK models
• A perturbative perspective on self-supporting wormholes
• AdS Maps and Diagrams of Bi-local Holography
• Beyond the veil: Inner horizon instability and holography
• Matching four-point functions in higher spin AdS_3/CFT_2
• On Holomorphic Factorization in Asymptotically AdS 3D Gravity
• Delocalizing Entanglement of Anisotropic Black Branes
• Chaos and entanglement spreading in a non-commutative gauge theory
• Supersymmetric SYK Model with Global Symmetry
• Entanglement Entropy of Extremal BTZ
• Butterflies with rotation and charge
• Wilson Lines and Ishibashi States in AdS${}_3$/CFT${}_2$
• On the Boundary Dynamics of Chern-Simons Gravity
• Scrambling time from local perturbations of the rotating BTZ black hole
• Chaos, Diffusivity, and Spreading of Entanglement in Magnetic Branes, and the Strengthening of the Internal Interaction
• Eternal Higher Spin Black Holes: a Thermofield Interpretation
• Chaos in Three-dimensional Higher Spin Gravity

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