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Black holes and the butterfly effect
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  • Open Access
  • Published: 13 March 2014

Black holes and the butterfly effect

  • Stephen H. Shenker1,2 &
  • Douglas Stanford1,2 

Journal of High Energy Physics volume 2014, Article number: 67 (2014) Cite this article

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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.

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This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Authors and Affiliations

  1. Stanford Institute for Theoretical Physics and Department of Physics, Stanford University, Stanford, CA, 94305, U.S.A

    Stephen H. Shenker & Douglas Stanford

  2. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, U.S.A

    Stephen H. Shenker & Douglas Stanford

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  1. Stephen H. Shenker
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  2. Douglas Stanford
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Correspondence to Douglas Stanford.

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ArXiv ePrint: 1306.0622

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Shenker, S.H., Stanford, D. Black holes and the butterfly effect. J. High Energ. Phys. 2014, 67 (2014). https://doi.org/10.1007/JHEP03(2014)067

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  • Received: 03 January 2014

  • Accepted: 20 February 2014

  • Published: 13 March 2014

  • DOI: https://doi.org/10.1007/JHEP03(2014)067

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Keywords

  • AdS-CFT Correspondence
  • Black Holes
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