Black holes and the butterfly effect

2013/06/30 by Stephen H. Shenker, Douglas Stanford · 23 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Firewall (physics) #Gravitation #Particle physics theoretical and experimental studies #Physics #Quantum mechanics #Schwarzschild radius #Theoretical physics #hep-th

paper · pdf · doi:10.1007/jhep03(2014)067

29 pages, 4 figures. v2: references added/clarified, typos corrected. v3: reference added, referencing clarified

openalex publication_date 2014/03/01 · arxiv created 2014/04/21 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.

Citations

• Entangled black holes as ciphers of hidden information
• Extracting Data from Behind Horizons with the AdS/CFT Correspondence
• Excursions beyond the horizon: black hole singularities in Yang-Mills theories (I)
• Conformal collider physics: Energy and charge correlations
• Average entropy of a subsystem
• A continuity property of the entropy density for spin lattice systems
• Spacetime singularities in string theory
• Holographic Derivation of Entanglement Entropy from the anti–de Sitter Space/Conformal Field Theory Correspondence
• Black holes as mirrors: quantum information in random subsystems

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• Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems
• Out-of-time-ordered correlators and quantum walks
• Correlations vs connectivity in R-charge
• Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum
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