Universality in Chaos of Particle Motion near Black Hole Horizon

Abstract

Motion of a particle near a horizon of a spherically symmetric black hole is shown to possess a universal Lyapunov exponent of a chaos provided by its surface gravity. To probe the horizon, we introduce electromagnetic or scalar force to the particle so that it does not fall into the horizon. There appears an unstable maximum of the total potential where the evaluated maximal Lyapunov exponent is found to be independent of the external forces and the particle mass. The Lyapunov exponent is universally given by the surface gravity of the black hole. Unless there are other sources of a chaos, the Lyapunov exponent is subject to an inequality $\lambda \le 2\pi T_{\mathrm{BH}}/\hslash$, which is identical to the bound recently discovered by Maldacena, Shenker and Stanford.

12 pages, 4 figures; v2: references added, numerical plots in Fig. 4 corrected

References in corpus (73)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• The Large N Limit of Superconformal Field Theories and Supergravity
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Geodesic stability, Lyapunov exponents and quasinormal modes
• Complexity Equals Action
• Soft Hair on Black Holes
• Chaos in AdS${}_2$ holography
• Chaos in quantum channels
• The Spectrum in the Sachdev-Ye-Kitaev Model
• An Investigation of AdS${}_2$ Backreaction and Holography
• Bekenstein-Hawking Entropy and Strange Metals
• Multiple Shocks
• Two-dimensional conformal field theory and the butterfly effect
• Lieb-Robinson and the butterfly effect
• Universal Charge Diffusion and the Butterfly Effect
• Dirty blackholes: Thermodynamics and horizon structure
• Causality Constraints in Conformal Field Theory
• Numerical study of fermion and boson models with infinite-range random interactions
• Bi-Local Holography in the SYK Model
• Many-body chaos at weak coupling
• Chaos in Schwarzschild Spacetime : The Motion of a Spinning Particle
• Janis-Newman-Winicour and Wyman solutions are the same
• Bounding the Space of Holographic CFTs with Chaos
• Universal Diffusion in Incoherent Black Holes
• Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
• Conformal Bootstrap, Universality and Gravitational Scattering
• Chaos in the Gauge/Gravity Correspondence
• Disrupting Entanglement of Black Holes
• AdS${}_2$ Holographic Dictionary
• Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix
• Chaos in Static Axisymmetric Spacetimes I : Vacuum Case
• Analytic Non-integrability in String Theory
• The Information Paradox for Black Holes
• Evidence for fast thermalization in the plane-wave matrix model
• Chaos in the black hole S-matrix
• Dirty black holes: Symmetries at stationary non-static horizons
• Dirty black holes: Spacetime geometry and near-horizon symmetries
• Chaos around Holographic Regge Trajectories
• Chaos in Classical D0-Brane Mechanics
• (Non)-Integrability of Geodesics in D-brane Backgrounds
• Analytic solutions of the geodesic equation in axially symmetric space-times
• Integrability Lost
• On Marginal Deformations and Non-Integrability
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• Signature of chaos in gravitational waves from a spinning particle
• Homoclinic Orbits around Spinning Black Holes II: The Phase Space Portrait
• Chaotic strings in a near Penrose limit of AdS${}_5\times T^{1,1}$
• Large N classical dynamics of holographic matrix models
• Universal properties of the near-horizon optical geometry
• Killing(-Yano) Tensors in String Theory
• Chaos in chiral condensates in gauge theories
• Gravitational Waves from Chaotic Dynamical System
• Chaos from the ring string in Gauss-Bonnet black hole in $Ad{S}_5$ space
• Chaotic Fast Scrambling At Black Holes
• Dirty rotating black holes: regularity conditions on stationary horizons
• On Information Loss in AdS${}_3$/CFT${}_2$
• Fast Scramblers, Horizons and Expander Graphs
• Bi-Local Holography in the SYK Model: Perturbations
• Confining Backgrounds and Quantum Chaos in Holography
• Butterflies from Information Metric
• Chaos-Order Transition in Matrix Theory
• Gravitational Collapse, Chaos in CFT Correlators and the Information Paradox
• Strings in five-dimensional anti-de Sitter space with a symmetry
• Universal quantum constraints on the butterfly effect
• Gravitational Wave Signals from Chaotic System: A Point Mass with A Disk
• Fast Scramblers Of Small Size
• Four-point function in the IOP matrix model
• Quantum Black Hole Formation in the BFSS Matrix Model
• Turbulent strings in AdS/CFT

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